CN112835040B - Spherical aperture zoned progressive phase iterative imaging method and device - Google Patents

Abstract

The disclosure relates to a method and device for progressive phase iterative imaging of spherical aperture sub-regions. The method includes: forming a synthetic aperture or real aperture radar whose aperture is located on the same spherical surface through azimuth-pitch rotation; calculating the distance based on the step-by-step distance compensation factor Error analysis; based on the area division of the sampling point of the spherical aperture radar, the distance history from any point in the observation area to the sampling point is obtained through iterative calculation of the step-by-step distance compensation factor to complete the three-dimensional reconstruction of the observation area. The device includes: an error analysis module and an imaging module. Through various embodiments of the present disclosure, the three-dimensional imaging efficiency can be greatly improved by constructing sub-regional non-linear progressive Doppler compensation factors to replace the global point-by-point stacking imaging method.

Description

Method and device for spherical aperture-divided-area progressive phase iteration imaging

Technical Field

The present invention relates to the field of radar three-dimensional imaging, and in particular to a method and device for spherical aperture-divided-area progressive phase iterative imaging.

Background Art

Compared with other traditional micro-change monitoring methods such as GPS, micro-change monitoring radar has the advantages of all-weather, large range, and high precision, and is widely used in the detection of small deformations of steep slopes, bridges, and buildings. Micro-change monitoring radar 3D imaging can achieve 3D resolution imaging and 3D deformation information extraction of the observation area, and can also effectively suppress the overlap and top and bottom inversion caused by the observation geometry, and has broad application prospects in the monitoring of slope landslides and artificial buildings.

Due to the large observation area, existing imaging algorithms are difficult to perform 3D reconstruction of large scene areas; the 3D back-projection algorithm can perform 3D reconstruction of the area of interest by virtue of its point-by-point reconstruction, which has certain advantages, but due to the point-by-point calculation of the distance history, its calculation amount is high, which affects the imaging efficiency and is difficult to meet the needs of real-time monitoring. In short, it is impossible to achieve fast and accurate reconstruction of a large field of view area.

Summary of the invention

The present disclosure intends to provide a method and device for spherical aperture-divided regional progressive phase iteration imaging, which greatly improves the three-dimensional imaging efficiency by constructing a regional nonlinear progressive Doppler compensation factor to replace the global point-by-point stacking imaging method.

According to one of the solutions of the present disclosure, a method for spherical aperture-divided-area progressive phase iterative imaging is provided, comprising:

By rotating in azimuth and elevation, a synthetic aperture or real aperture radar with apertures located on the same sphere is formed;

Based on the step-by-step distance compensation factor calculation, distance error analysis is performed;

Based on the regional division of the sampling points of the spherical aperture radar, the distance history from any point in the observation area to the sampling point is calculated iteratively through a step-by-step distance compensation factor to complete the three-dimensional reconstruction of the observation area.

In some embodiments, the step-by-step distance compensation factor calculation and distance error analysis include:

Get the azimuth distance compensation factor;

Get the pitch distance compensation factor;

According to the azimuth distance compensation factor and the elevation distance compensation factor, smaller azimuth step angle and elevation step angle are obtained to reduce the distance error.

In some embodiments, wherein

The obtaining of the azimuth distance compensation factor includes:

Set the number of steps of the radar sampling point in azimuth and in elevation relative to the radar starting sampling point to obtain its Maclaurin expression;

Based on the processing of Maclaurin's expression, the Maclaurin approximate distance is obtained;

Based on the McLaughlin approximate distance, the azimuth distance compensation factor is obtained;

The obtaining of the pitch distance compensation factor comprises:

Set the number of steps of the radar sampling point in azimuth and in elevation relative to the radar starting sampling point to obtain its Maclaurin expression;

Based on the processing of Maclaurin's expression, the Maclaurin approximate distance is obtained;

Based on the McLaughlin approximate distance, the pitch distance compensation factor is obtained.

In some embodiments, performing distance error analysis includes:

Combining the azimuth distance compensation factor and the elevation distance compensation factor, based on the distance from any point in the observation area to the radar initial sampling point, the distance history from any point in the observation area to the radar sampling point is solved step by step;

The distance error caused by the distance history from any point in the observation area to the radar sampling point is solved step by step.

In some embodiments, the spherical aperture-divided-region nonlinear progressive phase iteration imaging method comprises:

Compress the echo signal at each radar sampling point along the distance direction;

Dividing the imaging area into a plurality of pixel areas, each pixel area having a plurality of pixels;

The phase of each pixel in the imaging area is calculated using a regional step-by-step phase iteration method.

The size of the sampling point area is calculated according to the step-by-step distance solution error, and the spherical synthetic aperture is divided into several sampling point areas;

Calculate the value of each pixel in the observation area point by point.

In some embodiments, the step of dividing the imaging area into a plurality of pixel areas, each pixel area having a plurality of pixels, comprises:

According to the obtained radar resolution, the observation area is divided into a number of pixels, so that the size of each pixel in the range, azimuth and elevation directions is smaller than the radar range, azimuth and elevation resolutions, respectively.

In some embodiments, the step of calculating the phase of each pixel in the imaging area using a region-by-region step-by-step phase iteration method includes:

Based on the observation area's proximity, pixel size along the range direction, radar center frequency, step initial value, and number of pixels along the range direction, the starting pixel phase and phase compensation factor are calculated;

Iteratively calculate the phase of the pixel points along the range direction until the initial step value is greater than the number of pixels in the range direction;

Output the pixel point phase matrix along the range direction;

Based on the expansion of the pixel phase matrix along the range direction, the phases of the pixels at the same radial distance are iteratively calculated.

In some embodiments, the step of calculating the sampling point area size based on the step-by-step distance solution error and dividing the spherical synthetic aperture into a plurality of sampling point areas includes:

Select the pixel points in the observation area and the radar starting sampling point;

Calculate the distance history from the pixel point in the observation area to the radar starting sampling point;

Calculate the azimuth distance compensation factor coefficient and the elevation distance compensation factor coefficient;

Solve the Maclaurin approximation for distance history;

Solve the actual distance history;

Calculate the size of the sampling point area and the number of divided areas, and calculate the sampling point area based on the phase error constraint.

In some embodiments, calculating the value of each pixel point in the observation area point by point includes:

Based on the algorithm, each pixel in the observation area is reconstructed point by point to achieve three-dimensional resolution imaging of the observation area.

According to one of the solutions disclosed in the present invention, a device for spherical aperture-divided-area progressive phase iterative imaging is provided, which is used to form a synthetic aperture or real aperture radar with apertures located on the same spherical surface through azimuth-elevation rotation; the device comprises:

an error analysis module configured to perform distance error analysis based on step-by-step distance compensation factor calculation;

The imaging module is configured to be used for regional division of sampling points based on the spherical aperture radar, so that the distance history from any point in the observation area to the sampling point is calculated iteratively by a step-by-step distance compensation factor to complete the three-dimensional reconstruction of the observation area.

According to one of the solutions of the present disclosure, a computer-readable storage medium is provided, on which computer-executable instructions are stored, and when the computer-executable instructions are executed by a processor, the following are implemented:

According to the above-mentioned spherical aperture-divided-region progressive phase iterative imaging method.

The method and device for spherical aperture area progressive phase iteration imaging of various embodiments of the present disclosure form a synthetic aperture or real aperture radar with an aperture located on the same sphere at least through azimuth-pitch rotation; perform distance error analysis based on step-by-step distance compensation factor calculation; based on the regional division of the sampling points of the spherical aperture radar, the distance history from any point in the observation area to the sampling point is obtained by iterative calculation of the step-by-step distance compensation factor to complete the three-dimensional reconstruction of the observation area, thereby realizing regional division of the sampling points of the spherical synthetic aperture radar, and in each area, the distance from the pixel point of the observation area to the sampling point is calculated by adopting a step-by-step iteration method, which reduces the root exponential operation in the distance solution and improves the efficiency of the algorithm; this paper derives the specific method steps for calculating the distance compensation factor, and at the same time analyzes the distance error caused by the step-by-step distance iteration solution of the distance history, and calculates the maximum range of the sampling point regional division according to the phase error condition; this paper provides a method for iteratively solving the pixel point phase of the observation area according to the particularity of the imaging area, which reduces the root exponential operation in the pixel point phase solution and further improves the efficiency of the algorithm.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, which are not necessarily drawn to scale, like reference numerals in different views may represent similar components. Like reference numerals with letter suffixes or like reference numerals with different letter suffixes may represent different instances of similar components. The drawings generally illustrate various embodiments by way of example and not limitation, and together with the description and claims, serve to explain the disclosed embodiments.

FIG1 is a schematic diagram of a spherical aperture micro-variation monitoring radar according to an embodiment of the present disclosure;

FIG2 is a schematic diagram of a step-by-step distance solution according to an embodiment of the present disclosure;

FIG3 is a schematic diagram of solving an azimuth distance compensation factor according to an embodiment of the present disclosure;

FIG4 is a schematic diagram of solving a pitch distance compensation factor according to an embodiment of the present disclosure;

FIG5 is a schematic diagram of an error analysis according to an embodiment of the present disclosure;

FIG6 is a schematic diagram of pixel point division of an observation area according to an embodiment of the present disclosure;

FIG. 7 is a phase matrix PHI _3D of pixels in an observation area according to an embodiment of the present disclosure;

FIG8 is a schematic diagram of three-dimensional reconstruction of pixels in an observation area according to an embodiment of the present disclosure;

FIG9 is a flowchart of a step-by-step distance calculation according to an embodiment of the present disclosure;

FIG10 is a pixel division of an observation area according to an embodiment of the present disclosure;

FIG11 is a flow chart of sampling point area division according to an embodiment of the present disclosure;

FIG12 is a flowchart of a three-dimensional reconstruction of an observation area according to an embodiment of the present disclosure;

FIG. 13 is a schematic flow chart of an imaging method according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the embodiments of the present disclosure clearer, the technical solution of the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings of the embodiments of the present disclosure. Obviously, the described embodiments are part of the embodiments of the present disclosure, not all of the embodiments. Based on the described embodiments of the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present disclosure.

Unless otherwise defined, the technical terms or scientific terms used in the present disclosure shall have the common meanings understood by persons with ordinary skills in the field to which the present disclosure belongs. "Include" or "comprising" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

In order to keep the following description of the embodiments of the present disclosure clear and concise, the present disclosure omits detailed descriptions of well-known functions and well-known components.

分布于面XOZ右侧的半球内，ρ表示采样点P_Radar到原点O的径向距离,θ表示采样点P_Radar与原点O连线在面XOY的投影线与X轴正方向的夹角，

表示采样点P_Radar与原点O连线与Z轴正方向的夹角，Θ_SynA为方位向合成孔径角度，Φ_SynE为俯仰向合成孔径角度，Δθ表示雷达方位向采样间隔，

表示雷达俯仰向采样间隔,N_θ表示方位向采样点数，

表示俯仰向采样点数。应当说明的是：图中只画出了θ＝π/2和

的采样点位置示意图，其它采样点位置未在图中展示。As shown in Figure 1, the spherical aperture three-dimensional imaging micro-variable monitoring radar is a synthetic aperture or real aperture radar with an aperture located on the same spherical surface through, but not limited to, the azimuth-pitch rotation of the turntable. The above radar can achieve three-dimensional resolution imaging of the observation area. In Figure 1, the radar sampling point

Distributed in the hemisphere on the right side of the surface XOZ, ρ represents the radial distance from the sampling point P _Radar to the origin O, θ represents the angle between the projection line of the sampling point P _Radar and the origin O on the surface XOY and the positive direction of the X-axis,

represents the angle between the line connecting the sampling point P _Radar and the origin O and the positive direction of the Z axis, Θ _SynA is the synthetic aperture angle in azimuth, Φ _SynE is the synthetic aperture angle in elevation, Δθ represents the radar azimuth sampling interval,

represents the radar pitch sampling interval, N _θ represents the number of sampling points in azimuth,

It should be noted that only θ＝π/2 and

Schematic diagram of the sampling point locations. The locations of other sampling points are not shown in the figure.

As one of the solutions, an embodiment of the present disclosure provides a method for spherical aperture-divided-area progressive phase iterative imaging, comprising:

By rotating in azimuth and elevation, a synthetic aperture or real aperture radar with apertures located on the same sphere is formed;

Based on the step-by-step distance compensation factor calculation, distance error analysis is performed;

Based on the regional division of the sampling points of the spherical aperture radar, the distance history from any point in the observation area to the sampling point is calculated iteratively through a step-by-step distance compensation factor to complete the three-dimensional reconstruction of the observation area.

One of the inventive concepts disclosed herein is to realize regional division of the sampling points of the spherical synthetic aperture radar. In each region, the distance from the pixel point in the observation area to the sampling point is calculated by adopting a step-by-step iteration method, thereby reducing the root exponential operation during distance calculation and improving the efficiency of the algorithm.

The present disclosure mainly focuses on two aspects: step-by-step distance compensation factor calculation and distance error analysis, and a spherical aperture area nonlinear progressive phase iteration imaging method based on this. The present disclosure can be performed by any device, equipment or specific imaging system that can obtain spherical aperture area progressive phase iteration imaging.

In some embodiments, the step-by-step distance compensation factor calculation of the present disclosure is used to perform distance error analysis, including:

Get the azimuth distance compensation factor;

Get the pitch distance compensation factor;

According to the azimuth distance compensation factor and the elevation distance compensation factor, smaller azimuth step angle and elevation step angle are obtained to reduce the distance error.

Specifically, the distance compensation factors ΔTh and ΔPh in azimuth and elevation are calculated first; then the error _Er of step-by-step distance calculation is analyzed, and a method for calculating the maximum error of the sampling point area is given.

为观测区域任意一点，

为雷达的采样点；R_n为点P_n到坐标原点O的径向距离；θ_n为点P_n与原点O连线在面XOY的投影线与X轴正方向的夹角，

为点P_n与原点O连线与Z轴正方向的夹角；ρ为雷达采样点P_Radar到原点O的径向距离,θ为采样点P_Radar与原点O连线在面XOY的投影线与X轴正方向的夹角，

为采样点P_Radar与原点O连线与Z轴正方向的夹角。As shown in Figure 2,

is any point in the observation area,

is the sampling point of the radar; _Rn is the radial distance from point _Pn to the origin O; _θn is the angle between the projection line of the line connecting point _Pn and the origin O on the plane XOY and the positive direction of the X-axis,

is the angle between the line connecting point _Pn and the origin O and the positive direction of the Z axis; ρ is the radial distance from the radar sampling point P _Radar to the origin O, θ is the angle between the projection line of the line connecting the sampling point P _Radar and the origin O on the surface XOY and the positive direction of the X axis,

It is the angle between the line connecting the sampling point P _Radar and the origin O and the positive direction of the Z axis.

即起始采样点

位置开始，分别沿方位向、俯仰向间隔采样，方位向、俯仰向采样间隔分别为Δθ、

则雷达采样点坐标

中θ、

可表示为：The radar starts from θ = θ ₀ ,

The starting sampling point

Starting from the position, sampling is performed in the azimuth and elevation directions. The sampling intervals in the azimuth and elevation directions are Δθ,

The radar sampling point coordinates are

Medium θ,

It can be expressed as:

θ＝θ ₀ +n _θ ·Δθ (1)

表示采样点P_Radar相对雷达起始采样点P_Radar-Start沿俯仰向的步进次数，

N_θ表示雷达方位向采样点数，

表示雷达俯仰向采样点数；任一雷达采样点P_Radar表示为

Wherein, n _θ represents the number of steps along the azimuth direction of the sampling point P _Radar relative to the radar starting sampling point P _Radar-Start , n _θ = 0, 1, …, (N _θ -1);

Indicates the number of steps along the pitch direction of the sampling point P _Radar relative to the radar starting sampling point P _Radar-Start .

N _θ represents the number of radar azimuth sampling points,

Represents the number of radar pitch sampling points; any radar sampling point P _Radar is expressed as

The distance history from any point in the observation area to the radar sampling point is solved in a step-by-step manner. The distance compensation factors ΔTh and ΔPh in the azimuth and elevation directions need to be calculated respectively; then the distance history is solved step-by-step using the distance compensation factors.

In some embodiments, the obtaining of the azimuth distance compensation factor of the present disclosure includes:

Set the number of steps of the radar sampling point in azimuth and in elevation relative to the radar starting sampling point to obtain its Maclaurin expression;

Based on the processing of Maclaurin's expression, the Maclaurin approximate distance is obtained;

Based on the McLaughlin approximate distance, the azimuth distance compensation factor is obtained;

The obtaining of the pitch distance compensation factor comprises:

Set the number of steps of the radar sampling point in azimuth and in elevation relative to the radar starting sampling point to obtain its Maclaurin expression;

Based on the processing of Maclaurin's expression, the Maclaurin approximate distance is obtained;

Based on the McLaughlin approximate distance, the pitch distance compensation factor is obtained.

About the azimuth distance compensation factor ΔTh:

到雷达起始采样点

的距离为：As shown in Figure 3, any point in the observation area

To the radar starting sampling point

The distance is:

相对雷达起始采样点P_Radar-Start沿方位向步进次数为n_θ，沿俯仰向步进次数为0；采样点坐标表示为

其中n_θ＝0,1,…,(N_θ-1)。观测区域任意一点

到点

的距离为：When calculating the azimuth distance compensation factor, the radar sampling point

The number of steps relative to the radar starting sampling point P _Radar-Start along the azimuth direction is n _θ , and the number of steps along the elevation direction is 0; the sampling point coordinates are expressed as

Where n _θ = 0, 1, …, (N _θ -1). Any point in the observation area

To point

The distance is:

为点P_n与原点O连线与Z轴正方向的夹角；ρ为雷达起始采样点P_Radar-Start到原点O的径向距离,θ₀为雷达起始采样点P_Radar-Start与原点O连线在面XOY的投影线与X轴正方向的夹角，

为雷达起始采样点P_Radar-Start与原点O连线与Z轴正方向的夹角；n_θ为雷达采样点

相对起始采样点P_Radar-Start沿方位向的步进次数；Δθ为雷达沿方位向采样间隔。Where _Rn is the radial distance from point _Pn to the origin O; _θn is the angle between the projection line of the line connecting point _Pn and the origin O on the plane XOY and the positive direction of the X-axis,

is the angle between the line connecting point _Pn and the origin O and the positive direction of the Z axis; ρ is the radial distance from the radar starting sampling point P _Radar-Start to the origin O, _θ0 is the angle between the projection line of the line connecting the radar starting sampling point P _Radar-Start and the origin O on the surface XOY and the positive direction of the X axis,

is the angle between the line connecting the radar starting sampling point P _Radar-Start and the origin O and the positive direction of the Z axis; n _θ is the radar sampling point

The number of steps along the azimuth direction relative to the starting sampling point P _Radar-Start ; Δθ is the radar sampling interval along the azimuth direction.

The Maclaurin formula of cosn _θ Δθ and sinn _θ Δθ in formula (4) is expressed as:

Among them, o(*) is called the Peano remainder term, and n _θ Δθ∈[0,1].

Ignore the Peano remainder o(*) in equations (5) and (6), and analyze the distance calculation error caused by ignoring the Peano remainder.

到雷达采样点

的麦克劳林近似距离为：Ignoring the Peano remainder o(*) in equations (5) and (6), and substituting equations (3), (5), and (6) into equation (4), we can obtain

To the radar sampling point

The Maclaurin approximate distance is:

in,

By taking the derivative of formula (7) with respect to _nθ , we can obtain the azimuth distance compensation factor:

ΔTh(n _θ )＝2A _θ ·Δθ ² ·n _θ +B _θ ·Δθ (10)

为点P_n与原点O连线与Z轴正方向的夹角；ρ为雷达起始采样点P_Radar-Start到原点O的径向距离,θ₀为雷达起始采样点P_Radar-Start与原点O连线在面XOY的投影线与X轴正方向的夹角，

为雷达起始采样点P_Radar-Start与原点O连线与Z轴正方向的夹角；n_θ为雷达采样点

相对起始采样点P_Radar-Start沿方位向的步进次数；Δθ为雷达沿方位向采样间隔；

为观测区域任意点

到雷达采样点

的麦克劳林近似距离；

为观测区域任意点

到雷达起始采样点

的距离；A_θ、B_θ为方位向距离补偿因子系数。Where _Rn is the radial distance from point _Pn to the origin O; _θn is the angle between the projection line of the line connecting point _Pn and the origin O on the plane XOY and the positive direction of the X-axis,

is the angle between the line connecting point _Pn and the origin O and the positive direction of the Z axis; ρ is the radial distance from the radar starting sampling point P _Radar-Start to the origin O, _θ0 is the angle between the projection line of the line connecting the radar starting sampling point P _Radar-Start and the origin O on the surface XOY and the positive direction of the X axis,

is the angle between the line connecting the radar starting sampling point P _Radar-Start and the origin O and the positive direction of the Z axis; n _θ is the radar sampling point

The number of steps along the azimuth direction relative to the starting sampling point P _Radar-Start ; Δθ is the radar sampling interval along the azimuth direction;

Any point in the observation area

To the radar sampling point

The Maclaurin approximate distance of

Any point in the observation area

To the radar starting sampling point

A _θ and B _θ are the azimuth distance compensation factor coefficients.

Regarding the pitch distance compensation factor ΔPh:

到雷达起始采样点

的距离为：As shown in Figure 4, any point in the observation area

To the radar starting sampling point

The distance is:

相对雷达起始采样点P_Radar-Start沿方位向步进次数为0，沿俯仰向步进次数为

采样点坐标表示为

其中

观测区域任意点

到点

的距离为：When calculating the pitch distance compensation factor, the radar sampling point

Relative to the radar starting sampling point P _Radar-Start, the number of steps along the azimuth direction is 0, and the number of steps along the elevation direction is

The sampling point coordinates are expressed as

in

Any point in the observation area

To point

The distance is:

为点P_n与原点O连线与Z轴正方向的夹角；ρ为雷达起始采样点P_Radar-Start到原点O的径向距离,θ₀为雷达起始采样点P_Radar-Start与原点O连线在面XOY的投影线与X轴正方向的夹角，

为雷达起始采样点P_Radar-Start与原点O连线与Z轴正方向的夹角；

为雷达采样点

相对起始采样点P_Radar-Start沿俯仰向的步进次数；

为雷达沿俯仰向采样间隔。Where _Rn is the radial distance from point _Pn to the origin O; _θn is the angle between the projection line of the line connecting point _Pn and the origin O on the plane XOY and the positive direction of the X-axis,

is the angle between the line connecting point _Pn and the origin O and the positive direction of the Z axis; ρ is the radial distance from the radar starting sampling point P _Radar-Start to the origin O, _θ0 is the angle between the projection line of the line connecting the radar starting sampling point P _Radar-Start and the origin O on the surface XOY and the positive direction of the X axis,

The angle between the line connecting the radar starting sampling point P _Radar-Start and the origin O and the positive direction of the Z axis;

Radar sampling point

The number of steps along the pitch direction relative to the starting sampling point P _Radar-Start ;

is the radar sampling interval along the pitch direction.

的麦克劳林(Maclaurin)公式表示为：In formula (12),

The Maclaurin formula is expressed as:

Among them, o(*) is called the Peano remainder,

Ignore the Peano remainder o(*) in equations (13) and (14), and analyze the distance calculation error caused by ignoring the Peano remainder.

到点

的麦克劳林近似距离为：Ignoring the Peano remainder o(*) in equations (13) and (14), and substituting equations (11), (13), and (14) into equation (12), we can obtain

To point

The Maclaurin approximate distance is:

in,

求导，得到俯仰向距离补偿因子为：Reverse equation (15)

Taking the derivative, we get the pitch distance compensation factor:

为点P_n与原点O连线与Z轴正方向的夹角；ρ为雷达起始采样点P_Radar-Start到原点O的径向距离,θ₀为雷达起始采样点P_Radar-Start与原点O连线在面XOY的投影线与X轴正方向的夹角，

为雷达起始采样点P_Radar-Start与原点O连线与Z轴正方向的夹角；

为雷达采样点

相对起始采样点P_Radar-Start沿俯仰向的步进次数；

为雷达沿俯仰向采样间隔；

为观测区域任意点

到点

的麦克劳林近似距离；

为观测区域任意点

到雷达起始采样点

的距离；

为俯仰向距离补偿因子系数。Where _Rn is the radial distance from point _Pn to the origin O; _θn is the angle between the projection line of the line connecting point _Pn and the origin O on the plane XOY and the positive direction of the X-axis,

is the angle between the line connecting point _Pn and the origin O and the positive direction of the Z axis; ρ is the radial distance from the radar starting sampling point P _Radar-Start to the origin O, _θ0 is the angle between the projection line of the line connecting the radar starting sampling point P _Radar-Start and the origin O on the surface XOY and the positive direction of the X axis,

The angle between the line connecting the radar starting sampling point P _Radar-Start and the origin O and the positive direction of the Z axis;

Radar sampling point

The number of steps along the pitch direction relative to the starting sampling point P _Radar-Start ;

is the radar sampling interval along the pitch direction;

Any point in the observation area

To point

The Maclaurin approximate distance of

Any point in the observation area

To the radar starting sampling point

distance;

is the pitch distance compensation factor coefficient.

雷达起始采样点

雷达方位向、俯仰向采样间隔Δθ、

区域采样点方位向、俯仰向个数N_SubAzi、N_SubEle。The flow chart of the algorithm for calculating the distance history by stepping the distance compensation factors in azimuth and elevation is shown in Figure 9.

Radar start sampling point

Radar azimuth and elevation sampling intervals Δθ,

The number of regional sampling points in azimuth and elevation is N _SubAzi and N _SubEle .

In some implementations, the present disclosure performs distance error analysis, including:

Combining the azimuth distance compensation factor and the elevation distance compensation factor, based on the distance from any point in the observation area to the radar initial sampling point, the distance history from any point in the observation area to the radar sampling point is solved step by step;

The distance error caused by the distance history from any point in the observation area to the radar sampling point is solved step by step.

ΔTh(n_θ)分别由式(7)、(15)在忽略皮亚诺余项o(*)即保留有限项后求导得到，故方位向步进角度(n_θΔθ)和俯仰向步进角度

越小，求得的距离误差越小。Specifically, the distance compensation factor

ΔTh(n _θ ) is derived from equations (7) and (15) respectively after ignoring the Peano remainder o(*) and retaining the finite term. Therefore, the azimuth step angle (n _θ Δθ) and the elevation step angle

The smaller it is, the smaller the distance error is.

The following analysis shows that the distance error of the step-by-step distance calculation is obtained after ignoring the Peano remainder o(*), as shown in equations (5), (6), (13), and (14).

为观测区域任意一点，

为雷达起始采样点，

为雷达分别沿方位向、俯仰向步进n_θ、

次的采样点。As shown in Figure 5,

is any point in the observation area,

is the radar starting sampling point,

is the radar stepping in azimuth and elevation directions n _θ ,

The sampling points of times.

到雷达起始采样点

的距离表示为

观测区域任意点

到雷达采样点

的实际距离历程表示为

而步进式求解观测区域任意点

到雷达采样点

的距离历程为：Any point in the observation area

To the radar starting sampling point

The distance is expressed as

Any point in the observation area

To the radar sampling point

The actual distance history is expressed as

The step-by-step method solves any point in the observation area

To the radar sampling point

The distance history is:

分别为雷达采样点

相对起始采样点P_Radar-Start沿方位向、俯仰向的步进次数；Δθ、

分别为雷达方位向、俯仰向的采样间隔。Among them, n _θ ,

The radar sampling points are

The number of steps along the azimuth and elevation directions relative to the starting sampling point P _Radar-Start ; Δθ,

are the sampling intervals of radar azimuth and elevation respectively.

到雷达采样点

的距离历程产生的距离误差Er表示为：Use step-by-step method to solve any point in the observation area

To the radar sampling point

The distance error Er generated by the distance history is expressed as:

为观测区域任意点P_n到雷达起始采样点P_Radar-Start的距离历程；

为观测区域任意点P_n到采样点

的实际距离历程；n_θ、

分别为雷达采样点

相对起始采样点P_Radar-Start沿方位向、俯仰向的步进次数；Δθ、

分别为雷达方位向、俯仰向的采样间隔。in,

is the distance history from any point _Pn in the observation area to the radar starting sampling point P _Radar-Start ;

From any point P _n in the observation area to the sampling point

The actual distance history of n _θ ,

The radar sampling points are

The number of steps along the azimuth and elevation directions relative to the starting sampling point P _Radar-Start ; Δθ,

are the sampling intervals of radar azimuth and elevation respectively.

From the geometric relationship:

为观测区域任意点P_n到雷达起始采样点P_Radar-Start与采样点

的距离历程差；

为雷达起始采样点P_Radar-Start到采样点

的弧长。in,

From any point _Pn in the observation area to the radar starting sampling point P _Radar-Start and the sampling point

The distance history is poor;

From the radar starting sampling point P _Radar-Start to the sampling point

The arc length.

的延长线时，步进式求解距离历程的误差Er最大。In summary, when the observation area point _Pn is located between the radar starting sampling point P _Radar-Start and the sampling point

When the extension line is used, the error Er of the step-by-step solution of the distance history is the largest.

In some embodiments, referring to FIG. 13 , the spherical aperture-divided-region nonlinear progressive phase iteration imaging method disclosed in the present invention includes:

Compress the echo signal at each radar sampling point along the distance direction;

Dividing the imaging area into a plurality of pixel areas, each pixel area having a plurality of pixels;

The phase of each pixel in the imaging area is calculated using a regional step-by-step phase iteration method.

The size of the sampling point area is calculated according to the step-by-step distance solution error, and the spherical synthetic aperture is divided into several sampling point areas;

Calculate the value of each pixel in the observation area point by point.

In each embodiment of the present disclosure, the sampling points of the spherical aperture radar are clearly divided into regions, so that the distance history from any point in the observation area to the sampling point can be iteratively solved by the step compensation factor, thereby reducing the root exponential operation.

即点

位置开始，分别沿方位向、俯仰向间隔采样，方位向、俯仰向采样间隔分别为Δθ、

采样点

为雷达沿方位向、俯仰向分别步进n_θ、

次的采样点。雷达在采样点

处回波方程表示为：As shown in Figure 2, the radar

Point

Starting from the position, sampling is performed in the azimuth and elevation directions. The sampling intervals in the azimuth and elevation directions are Δθ,

Sampling point

The radar steps n _θ in azimuth and elevation respectively.

The radar is at the sampling point.

The echo equation is expressed as:

f＝{f _min ,…,f _max } (23)

为雷达采样点

到成像区域像素点的距离。Where f is the step frequency of the radar echo, f _min is the minimum frequency of the radar step, f _max is the maximum frequency of the radar step, C is the speed of light,

Radar sampling point

The distance to the pixel point in the imaging area.

Specifically, the imaging method of this embodiment includes:

Step S1: Range compression: compress the echo signal at each radar sampling point along the range direction. The inverse Fourier transform (IFFT) method can be used. The range compression signal is:

Where, f _c is the center frequency of the radar echo, which can be taken as (f _min +f _max )/2;

其中M_R、M_Θ、M_Φ分别表示成像区域距离向、方位向、俯仰向像素个数，m_Rn为像素点m_n到坐标原点O的径向距离，m_θn为像素点m_n与原点O连线在面XOY的投影线与X轴正方向的夹角，

为像素点m_n与原点O连线与Z轴正方向的夹角；Step S2: Observation area pixel division: divide the imaging area into _MR ×M _Θ ×M _Φ pixels, and the pixel coordinates are expressed as

Where M _R , M _Θ , M _Φ represent the number of pixels in the range, azimuth, and elevation directions of the imaging area, respectively; m _Rn is the radial distance from the pixel point m _n to the origin O; m _θn is the angle between the projection line of the line connecting the pixel point m _n and the origin O on the plane XOY and the positive direction of the X-axis;

is the angle between the line connecting the pixel point m _n and the origin O and the positive direction of the Z axis;

Step S3: Calculate the phase of each pixel point, and use a step-by-step phase iteration method to calculate the phase PHI _3D of each pixel point in the imaging area;

Step S4: spherical sampling point area division, the sampling point area size is calculated according to the step-by-step distance solution error Er, and the spherical synthetic aperture is divided into I sampling point areas;

Step S5: Three-dimensional reconstruction of the observation area, calculating the value of each pixel point in the observation area point by point, and completing the three-dimensional reconstruction of the observation area.

均为0.4°，方位向、俯仰向采样点数N_θ、

均为151，雷达方位向、俯仰向合成孔径角度Θ_SynA、Φ_SynE均为60°；观测区域像素点的近距m_R-near为800m，距离向观测范围m_R-ob为500m；观测区域的起始方位角m_θ-Start为60°，终止方位角m_θ-Stop为120°，起始俯仰角

为60°，终止俯仰角

为120°。In the embodiments of the present disclosure, the parameter settings are as follows: the minimum frequency _fmin of the radar step is 77GHz, the maximum frequency _fmax is 77.25GHz, the radar bandwidth B is 250M, the frequency point number Γ is 5001; the radar starting sampling point coordinates are P _Radar-Start (0.6, 60°, 60°), and the radar sampling intervals Δθ, Δθ, Δθ along the azimuth and elevation directions are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,

The angle of sampling points in azimuth and elevation is N _θ ,

The radar synthetic aperture angles Θ _SynA and Φ _SynE in azimuth and elevation are both 151°; the near distance m _R-near of the observation area pixel point is 800m, and the range observation range m _R-ob is 500m; the starting azimuth angle m _θ-Start of the observation area is 60°, the ending azimuth angle m _θ-Stop is 120°, and the starting elevation angle is 120°.

The end pitch angle is 60°

is 120°.

Regarding the pixel division of the observation area: the imaging area is divided into a number of pixel areas in the present disclosure, each pixel area has a number of pixels, including:

According to the obtained radar resolution, the observation area is divided into a number of pixels, so that the size of each pixel in the range, azimuth and elevation directions is smaller than the radar range, azimuth and elevation resolutions, respectively.

雷达俯仰向角度分辨率为

Specifically, in step S2, the imaging area is divided into _MR ×M _Θ ×M _Φ pixels. According to the parameter setting, the radar range resolution is C/(2·B); the radar azimuth angle resolution is

The radar elevation angle resolution is

分别小于雷达距离向、方位向、俯仰向分辨率。应当说明的是，像素大小越小，重建区域图像的细节越清晰，但重建像素个数越多。成像区域像素点划分。成像区域像素点划分如图6所示。According to the radar resolution calculated above, the observation area is divided into M _R ×M _Θ ×M _Φ pixels, so that the size of each pixel in the range, azimuth, and elevation directions is Δm _R , Δm _θ ,

They are smaller than the radar resolution in range, azimuth, and elevation directions, respectively. It should be noted that the smaller the pixel size, the clearer the details of the reconstructed area image, but the more pixels are required for reconstruction. Pixel point division of the imaging area. The pixel point division of the imaging area is shown in Figure 6.

Regarding the calculation of the phase of each pixel point: the phase of each pixel point in the imaging area is calculated by using the regional step-by-step phase iteration method disclosed in the present invention, including:

Based on the observation area's proximity, pixel size along the range direction, radar center frequency, step initial value, and number of pixels along the range direction, the starting pixel phase and phase compensation factor are calculated;

Iteratively calculate the phase of the pixel points along the range direction until the initial step value is greater than the number of pixels in the range direction;

Output the pixel point phase matrix along the range direction;

Based on the expansion of the pixel phase matrix along the range direction, the phases of the pixels at the same radial distance are iteratively calculated.

Specifically, in step S3, a step-by-step phase iteration method is used to calculate the phase of each pixel, and the flow chart is shown in FIG10 . The specific steps are as follows:

Step S31: parameter setting, observation area near distance is m _R-near , pixel size along the range direction is Δm _R , radar center frequency f _c , step initial value i _mR =1, number of pixels in the range direction is M _R ;

Step S32: Calculate the phase of the starting pixel and the phase compensation factor. The radial distance between the starting pixel of the observation area and the coordinate origin O is m _R-near , and the phase is expressed as:

The range phase compensation factor ΔPHI is expressed as:

Where _fc is the center frequency of the radar echo, C is the speed of light, _mR-near is the near distance of the observation area, and _ΔmR is the size of the pixel in the observation area along the distance direction;

为：Step S33: Iteratively calculate the phase of the distance pixel, i _mR = i _mR + 1, if i _Rm ≤ _R M, iteratively calculate the phase of the distance pixel

for:

Otherwise, execute step S34;

Step S34: Output the pixel point phase matrix PHI along the distance direction as:

Step S35: PHI is expanded into PHI _3D , and the phases of pixels at the same radial distance are iteratively calculated. According to the geometric relationship, the phases of pixels at the same radial distance are the same. The phase matrix PHI is expanded into a three-dimensional matrix PHI _3D of _MR ×M _Θ ×M _Φ to obtain the phases of all pixels in the observation area, as shown in FIG7 .

Regarding the division of spherical sampling point areas: the present disclosure calculates the size of the sampling point area based on the step-by-step distance solution error, and divides the spherical synthetic aperture into several sampling point areas, including:

Select the pixel points in the observation area and the radar starting sampling point;

Calculate the distance history from the pixel point in the observation area to the radar starting sampling point;

Calculate the azimuth distance compensation factor coefficient and the elevation distance compensation factor coefficient;

Solve the Maclaurin approximation for distance history;

Solve the actual distance history;

Calculate the size of the sampling point area and the number of divided areas, and calculate the sampling point area based on the phase error constraint.

的延长线时，步进式求解距离历程的误差Er最大，所以，根据误差最大时的相位限制条件计算球面合成孔径可划分的最大采样点区域。From the step-by-step distance error analysis in the first part, we can see that when the observation area point _Pn is located between the radar starting sampling point P _Radar-Start and the sampling point

When the extended line is , the error Er of the step-by-step solution of the distance history is the largest, so the maximum sampling point area that can be divided by the spherical synthetic aperture is calculated according to the phase constraint condition when the error is the largest.

开始，选取方位向采样点数N_SubAzi与俯仰向采样点数N_SubEle相同的采样点区域；并选择观测区域像素点

计算可划分的最大采样点区域，流程图如图11所示。具体的步骤如下：In order to facilitate calculation, when dividing the sampling point area, the radar starts sampling point

First, select the sampling point area with the same number of sampling points N _SubAzi in azimuth and N _SubEle in elevation; and select the pixel points in the observation area

Calculate the maximum sampling point area that can be divided, and the flow chart is shown in Figure 11. The specific steps are as follows:

与雷达起始采样点

雷达采样点坐标

Step S41: Selecting pixels in the observation area

The radar starting sampling point

Coordinates of radar sampling points

到雷达起始采样点

的距离历程，即将公式(3)中

替换为

表示为：Step S42: Calculate the pixels in the observation area

To the radar starting sampling point

The distance history is that in formula (3)

Replace with

It is expressed as:

为雷达起始采样点P_Radar-Start与原点O连线与Z轴正方向的夹角；m_R-near为观测区域近距，m_θ-Stop为观测区域终止方位角，

为观测区域终止俯仰角。Where, ρ is the radial distance from the radar starting sampling point P _Radar-Start to the origin O, _θ0 is the angle between the projection line of the line connecting the radar starting sampling point P _Radar-Start and the origin O on the surface XOY and the positive direction of the X-axis,

is the angle between the line connecting the radar starting sampling point P _Radar-Start and the origin O and the positive direction of the Z axis; m _R-near is the near distance of the observation area, m _θ-Stop is the end azimuth of the observation area,

Ending elevation angle for the observation area.

替换为

可分别写为：Step S43: Calculate the azimuth distance compensation factor coefficients A _θ and B _θ , and replace equations (8) and (9) with

Replace with

They can be written as:

将式(16)式(17)中

替换为

可分别写为：Step S44: Calculate the pitch distance compensation factor coefficient

In formula (16) and formula (17),

Replace with

They can be written as:

为距离补偿因子系数，ρ为雷达起始采样点P_Radar-Start到原点O的径向距离,θ₀为雷达起始采样点P_Radar-Start与原点O连线在面XOY的投影线与X轴正方向的夹角，

为雷达起始采样点P_Radar-Start与原点O连线与Z轴正方向的夹角；m_R-near为观测区域近距，m_θ-Stop为观测区域终止方位角，

为观测区域终止俯仰角。Among them, A _θ , B _θ ,

is the distance compensation factor coefficient, ρ is the radial distance from the radar starting sampling point P _Radar-Start to the origin O, _θ0 is the angle between the projection line of the line connecting the radar starting sampling point P _Radar-Start and the origin O on the surface XOY and the positive direction of the X-axis,

is the angle between the line connecting the radar starting sampling point P _Radar-Start and the origin O and the positive direction of the Z axis; m _R-near is the near distance of the observation area, m _θ-Stop is the end azimuth of the observation area,

Ending elevation angle for the observation area.

替换为

可解得区域像素点

到雷达采样点

的距离历程为：Step S45: Solve the Maclaurin approximation of the distance history, and replace the equation (19) with

Replace with

Solvable regional pixel points

To the radar sampling point

The distance history is:

分别为雷达采样点

相对起始采样点P_Radar-Start沿方位向、俯仰向的步进次数，Δθ、

分别为雷达沿方位向、俯仰向的采样间隔；A_θ、B_θ为方位向距离补偿因子系数，

为俯仰向距离补偿因子系数。Among them, n _θ ,

The radar sampling points are

The number of steps along the azimuth and elevation directions relative to the starting sampling point P _Radar-Start , Δθ,

are the radar sampling intervals in azimuth and elevation directions respectively; A _θ and B _θ are the azimuth distance compensation factor coefficients,

is the pitch distance compensation factor coefficient.

到雷达采样点

的实际距离为：Step S46: Solve the actual distance history, pixel point

To the radar sampling point

The actual distance is:

Step S47: Calculate the size of the sampling point area and the number of divided areas, and calculate the sampling point area according to the phase error constraint condition, that is,

为步进式求解像素点

到雷达采样点

的距离历程，

为像素点

到雷达采样点

的实际距离；将式(34)式(35)带入式(36)，当

时，求得n_θ、

的最大值未N_Sub；因此，将雷达采样点划分为沿方位向I_Azi＝N_θ/N_Sub个区域，沿俯仰向

个区域，区域个数为：Where _fc is the center frequency of the radar echo,

Solve the pixel points step by step

To the radar sampling point

The distance journey,

Pixel

To the radar sampling point

The actual distance; Substitute equation (34) and equation (35) into equation (36), when

When n _θ ,

The maximum value is N _Sub ; therefore, the radar sampling points are divided into regions along the azimuth direction I _Azi = N _θ / N _Sub and along the elevation direction

Regions, the number of regions is:

I＝I _Azi ·I _Ele (37)

i＝1,2,…,I。The coordinates of the starting point of the i-th sampling point area are

i＝1,2,…,I.

Regarding the three-dimensional reconstruction of the observation area: the point-by-point calculation of the value of each pixel point in the observation area disclosed in the present invention includes:

Based on the algorithm, each pixel in the observation area is reconstructed point by point to achieve three-dimensional resolution imaging of the observation area.

Specifically, in step S5, as shown in FIG8 , the algorithm reconstructs each pixel point in the observation area point by point to achieve three-dimensional resolution imaging of the observation area, as shown in FIG12 . The steps are as follows:

雷达方位向采样间隔Δθ，雷达俯仰向采样间隔

像素点相位PHI_3D，观测区域像素点编号k，初始值为1，采样点区域编号i，初始值为1；Step S501: parameter setting, radar echo range compression signal Sr, number of pixels in the observation area _MR × _MΘ × _MΦ , number of radar sampling point areas I and size of each sampling point area _NSub × _NSub , radar starting sampling point in the i-th sampling point area

Radar azimuth sampling interval Δθ, radar elevation sampling interval

Pixel phase PHI _3D , observation area pixel number k, initial value 1, sampling point area number i, initial value 1;

第i个采样点区域的起始点坐标为

根据式(3)计算像素点m_k到采样点P_{Radar-Start-i}的初始距离

再依据式(8)、(9)、(16)、(17)分别计算补偿因子系数A_θ-i、B_θ-i、

进而由式(10)、(18)计算距离补偿因子ΔTh_i(n_θ)、

Step S502: Calculate the initial distance and distance compensation factor of the i-th region, the coordinates of the k-th pixel point

The coordinates of the starting point of the i-th sampling point area are

According to formula (3), the initial distance from pixel _mk to sampling point P _{Radar-Start-i} is calculated

Then, according to equations (8), (9), (16), and (17), the compensation factor coefficients A _θ-i , B _θ-i ,

Then, the distance compensation factors ΔTh _i (n _θ ) and

Step S503: iteratively calculate the distance history from the k-th pixel point m _k to the i-th sampling point area in the pitch direction of the sampling point;

第i个采样点区域中的雷达采样点

为起始采样点

则第k个像素点m_k到雷达采样点P_Radar-00-i的距离历程为：Step S5031: Calculate the starting distance, set the azimuth step number n _θ = 0, the elevation step number n θ =

Radar sampling point in the i-th sampling point area

The starting sampling point

Then the distance history from the kth pixel m _k to the radar sampling point P _Radar-00-i is:

若

计算第k个像素点m_k到采样点

的距离历程为：Step S5032: Iteratively calculate the distance history of the pitch sampling point.

like

Calculate the kth pixel m _k to the sampling point

The distance history is:

为第i个区域沿俯仰向第

次步进的距离补偿因子；Otherwise, proceed to step S54;

is the i-th region along the pitch to the

Distance compensation factor for sub-steps;

Step S504: iteratively calculate the distance history from the k-th pixel point m _k to the i-th sampling point area sampling point;

n_θ＝0；Step S5041: Set the step start value.

_nθ ＝0;

的距离历程为：Step S5042: Iteratively calculate the distance history of the sampling point in the azimuth direction, n _θ = n _θ + 1, if n _θ < N _Sub , calculate the distance from the k-th pixel point m _k to the sampling point

The distance history is:

Otherwise, proceed to step S5043;

若

重复步骤S5042；否则，执行步骤S505；Step S5043: Iterate along the pitch direction,

like

Repeat step S5042; otherwise, execute step S505;

Step S505: Iterate the sampling point area, the sampling point area number i=i+1, if i≤I, repeat steps S502 to S504, otherwise go to step S506, at this time, obtain the distance history from the k-th pixel point m _k to all radar sampling points;

分别表示雷达方位向、俯仰向采样点数；Among them, N _θ ,

Respectively represent the number of radar sampling points in azimuth and elevation directions;

在各采样点距离压缩信号中的峰值位置为，Step S506: Calculate pixel points

The peak position of the distance compression signal at each sampling point is,

的矩阵；Where B is the radar signal bandwidth, in this case (f _max -f _min ), f _min is the minimum step frequency, f _max is the maximum step frequency, and τ _k is

Matrix of

处的相位为，Step S507: Calculate the pixel

The phase at is,

的矩阵；Where f _c is the radar center frequency, expressed as (f _max -f _min )/2 in this example, and φ _k is

Matrix of

Step S508: According to the peak frequency position of the distance compression signal of each sampling point calculated in formula (42), the corresponding peak value of the distance compression signal of each sampling point is taken out and expressed as:

的矩阵；Among them, r _k represents the distance history from the kth pixel point m _k to all radar sampling points, S r _k is

Matrix of

的值为：Step S509: Calculate pixel points

The values are:

m _k ＝∑Sr _k .*exp{jφ _k } (45)

Among them, “.*” means multiplication of corresponding positions of matrix elements, and “∑” means addition of matrix elements;

Step S510: Iterate the pixels in the observation area. The pixel number of the area is k=k+1. If _k≤MR × _MΘ × _MΦ , repeat steps S502 to S509. Otherwise, execute step S511. At this time, the values of all the pixels in the area are obtained as follows:

m＝{m _k } (46)

Where m _k represents the value of the kth pixel in the observation area, and m is a three-dimensional matrix of M _R ×M _Θ ×M _Φ ;

Step S511: Reconstruct the region, multiply the pixel value m of the observation region by the pixel phase PHI _3D of the observation region, and complete the pixel reconstruction of the observation region.

m _complex =m.*exp{-j·PHI _3D } (47)

Where m is the value of the pixel in the observation area, PHI _3D is the phase of the pixel in the observation area, and “.*” indicates the multiplication of the corresponding elements of the matrix.

As one of the solutions of the present disclosure, the present disclosure also provides a synthetic aperture or real aperture radar for forming an aperture located on the same spherical surface through azimuth-pitch rotation; the device comprises:

an error analysis module configured to perform distance error analysis based on step-by-step distance compensation factor calculation;

The imaging module is configured to be used for regional division of sampling points based on the spherical aperture radar, so that the distance history from any point in the observation area to the sampling point is calculated iteratively by a step-by-step distance compensation factor to complete the three-dimensional reconstruction of the observation area.

In conjunction with the foregoing examples, in some implementations, the error analysis module of the present disclosure may be further configured to:

Get the azimuth distance compensation factor;

Get the pitch distance compensation factor;

According to the azimuth distance compensation factor and the elevation distance compensation factor, smaller azimuth step angle and elevation step angle are obtained to reduce the distance error.

In conjunction with the foregoing examples, in some implementations, the error analysis module of the present disclosure may be further configured to:

Set the number of steps of the radar sampling point in azimuth and in elevation relative to the radar starting sampling point to obtain its Maclaurin expression;

Based on the processing of Maclaurin's expression, the Maclaurin approximate distance is obtained;

Based on the McLaughlin approximate distance, the azimuth distance compensation factor is obtained;

Set the number of steps of the radar sampling point in azimuth and in elevation relative to the radar starting sampling point to obtain its Maclaurin expression;

Based on the processing of Maclaurin's expression, the Maclaurin approximate distance is obtained;

Based on the McLaughlin approximate distance, the pitch distance compensation factor is obtained.

In conjunction with the foregoing examples, in some implementations, the error analysis module of the present disclosure may be further configured to:

Combining the azimuth distance compensation factor and the elevation distance compensation factor, based on the distance from any point in the observation area to the radar initial sampling point, the distance history from any point in the observation area to the radar sampling point is solved step by step;

The distance error caused by the distance history from any point in the observation area to the radar sampling point is solved step by step.

In combination with the foregoing examples, in some implementations, the imaging module of the present disclosure may be further configured to:

Compress the echo signal at each radar sampling point along the distance direction;

Dividing the imaging area into a plurality of pixel areas, each pixel area having a plurality of pixels, including: dividing the observation area into a plurality of pixels according to the obtained radar resolution, so that the size of each pixel in the range direction, the azimuth direction, and the elevation direction is respectively smaller than the radar range direction, the azimuth direction, and the elevation direction resolution;

The phase of each pixel in the imaging area is calculated by using a regional step-by-step phase iteration method, including: calculating the phase of the starting pixel and the phase compensation factor based on the observation area proximity, the pixel size along the range direction, the radar center frequency, the step initial value, and the number of pixels in the range direction; iteratively calculating the phase of the pixel along the range direction until the step initial value is greater than the number of pixels in the range direction; outputting the pixel phase matrix along the range direction; iteratively calculating the phase of the pixel at the same radial distance based on the expansion of the pixel phase matrix along the range direction;

The size of the sampling point area is calculated based on the step-by-step distance solution error, and the spherical synthetic aperture is divided into several sampling point areas, including: selecting the pixel points in the observation area and the radar starting sampling point; calculating the distance history from the pixel points in the observation area to the radar starting sampling point; calculating the azimuth distance compensation factor coefficient and the elevation distance compensation factor coefficient; solving the McLaughlin approximation of the distance history; solving the actual distance history; calculating the size of the sampling point area and the number of divided areas, and calculating the sampling point area based on the phase error constraint condition;

The value of each pixel point in the observation area is calculated point by point, including: based on an algorithm, each pixel point in the observation area is reconstructed point by point to achieve three-dimensional resolution imaging of the observation area.

Specifically, one of the inventive concepts of the present disclosure is to form a synthetic aperture or real aperture radar with an aperture located on the same sphere at least through azimuth-pitch rotation; perform distance error analysis based on step-by-step distance compensation factor calculation; based on the regional division of the sampling points of the spherical aperture radar, the distance history from any point in the observation area to the sampling point is obtained by iterative calculation of the step-by-step distance compensation factor compensation factor to complete the three-dimensional reconstruction of the observation area, thereby realizing regional division of the sampling points of the spherical synthetic aperture radar, and in each area, the distance from the pixel point of the observation area to the sampling point is calculated by adopting a step-by-step iteration method, which reduces the root exponential operation during distance solution and improves the efficiency of the algorithm; this paper derives the specific method steps for calculating the distance compensation factor, and at the same time analyzes the distance error caused by the step-by-step distance iteration to solve the distance history, and calculates the maximum range of the sampling point regional division according to the phase error condition; this paper provides a method for iteratively solving the pixel point phase of the observation area according to the particularity of the imaging area, which reduces the root exponential operation during the pixel point phase solution and further improves the efficiency of the algorithm.

As one of the solutions of the present disclosure, the present disclosure further provides a computer-readable storage medium on which computer executable instructions are stored. When the computer executable instructions are executed by a processor, the method of progressive phase iteration imaging based on the spherical aperture region is mainly implemented, which at least includes:

By rotating in azimuth and elevation, a synthetic aperture or real aperture radar with apertures located on the same sphere is formed;

Based on the step-by-step distance compensation factor calculation, distance error analysis is performed;

Based on the regional division of the sampling points of the spherical aperture radar, the distance history from any point in the observation area to the sampling point is iteratively calculated through a step-by-step distance compensation factor to complete the three-dimensional reconstruction of the observation area.

In some embodiments, the processor that executes computer executable instructions may be a processing device including one or more general processing devices, such as a microprocessor, a central processing unit (CPU), a graphics processing unit (GPU), etc. More specifically, the processor may be a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a processor that runs other instruction sets, or a processor that runs a combination of instruction sets. The processor may also be one or more special-purpose processing devices, such as an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), a system on a chip (SoC), etc.

In some embodiments, the computer-readable storage medium may be a memory such as a read-only memory (ROM), a random access memory (RAM), a phase-change random access memory (PRAM), a static random access memory (SRAM), a dynamic random access memory (DRAM), an electrically erasable programmable read-only memory (EEPROM), other types of random access memory (RAM), a flash disk or other form of flash memory, a cache, a register, a static memory, a compact disk read-only memory (CD-ROM), a digital versatile disk (DVD) or other optical storage, a cassette or other magnetic storage device, or any other possible non-temporary medium used to store information or instructions that can be accessed by a computer device.

In some embodiments, the computer executable instructions may be implemented as a plurality of program modules, and the plurality of program modules together implement the spherical aperture-divided-region progressive phase iteration imaging method according to any one of the present disclosures.

The present disclosure describes various operations or functions, which can be implemented as software codes or instructions or defined as software codes or instructions. The display unit can be implemented as a software code or instruction module stored on a memory, which can implement corresponding steps and methods when executed by a processor.

Such content may be source code or differential code ("delta" or "patch" code) that can be directly executed ("object" or "executable" form). The software implementation of the embodiments described herein may be provided by an article having code or instructions stored thereon, or by a method of operating a communication interface to send data through a communication interface. A machine or computer readable storage medium may enable a machine to perform the functions or operations described, and includes any mechanism for storing information in a form accessible by a machine (e.g., a computing display device, an electronic system, etc.), such as a recordable/unrecordable medium (e.g., a read-only memory (ROM), a random access memory (RAM), a disk storage medium, an optical storage medium, a flash memory display device, etc.). The communication interface includes any mechanism for communicating with other display devices by interfacing with any of hardwired, wireless, optical, etc. media, such as a memory bus interface, a processor bus interface, an Internet connection, a disk controller, etc. The communication interface may be configured by providing configuration parameters and/or sending signals to prepare the communication interface to provide a data signal describing the software content. The communication interface may be accessed by sending one or more commands or signals to the communication interface.

The computer executable instructions of the embodiments of the present disclosure can be organized into one or more computer executable components or modules. Any number and combination of such components or modules can be used to implement various aspects of the present disclosure. For example, various aspects of the present disclosure are not limited to the specific computer executable instructions or specific components or modules shown in the drawings and described herein. Other embodiments may include different computer executable instructions or components with more or less functions than those shown and described herein.

The above description is intended to be illustrative rather than restrictive. For example, the above examples (or one or more of them) can be used in combination with each other. For example, a person of ordinary skill in the art can use other embodiments when reading the above description. In addition, in the above-mentioned specific embodiments, various features can be grouped together to simplify the present disclosure. This should not be interpreted as an intention that a disclosed feature that is not required to be protected is necessary for any claim. On the contrary, the subject matter of the present disclosure may be less than all the features of a specific disclosed embodiment. Thus, the following claims are incorporated into the specific embodiments as examples or embodiments, wherein each claim is independently used as a separate embodiment, and it is considered that these embodiments can be combined with each other in various combinations or arrangements. The scope of the present disclosure should be determined with reference to the attached claims and the full scope of equivalent forms granted by these claims.

The above embodiments are only exemplary embodiments of the present disclosure and are not intended to limit the present disclosure. The protection scope of the present disclosure is defined by the claims. Those skilled in the art may make various modifications or equivalent substitutions to the present disclosure within the essence and protection scope of the present disclosure, and such modifications or equivalent substitutions shall also be deemed to fall within the protection scope of the present disclosure.

Claims (7)

1. The method for spherical aperture zonal progressive phase iterative imaging comprises the following steps:

forming a synthetic aperture or a real aperture radar with apertures positioned on the same spherical surface through azimuth-pitching rotation;

calculating based on a stepping distance compensation factor, and analyzing a distance error;

based on the regional division of sampling points of the spherical aperture radar, the distance process from any point of an observation region to the sampling points is obtained through iterative calculation of a stepping distance compensation factor so as to finish the three-dimensional reconstruction of the observation region;

the step-based distance compensation factor calculation, performing distance error analysis, includes:

obtaining an azimuth distance compensation factor;

obtaining a pitching distance compensation factor;

acquiring smaller azimuth stepping angles and pitch stepping angles according to the azimuth distance compensation factors and the pitch distance compensation factors so as to reduce distance errors;

Wherein,,

the obtaining the azimuth distance compensation factor comprises the following steps:

setting the number of steps of a radar sampling point along the azimuth direction and the number of steps of a radar initial sampling point along the pitching direction, and obtaining a Maclalin expression of the radar sampling point;

obtaining an approximate distance of Maclalin based on the processing of the Maclalin expression;

obtaining an azimuth distance compensation factor based on the Maclalin approximate distance;

the obtaining the pitching distance compensation factor comprises the following steps:

setting the number of steps of a radar sampling point along the azimuth direction and the number of steps of a radar initial sampling point along the pitching direction, and obtaining a Maclalin expression of the radar sampling point;

obtaining an approximate distance of Maclalin based on the processing of the Maclalin expression;

obtaining a pitching direction distance compensation factor based on the Maclalin approximate distance;

wherein, carry out the distance error analysis, include:

combining the azimuth distance compensation factor and the pitching distance compensation factor, and solving the distance course from any point of the observation area to the radar sampling point in a stepping way based on the distance from any point of the observation area to the radar initial sampling point;

step-by-step solving a distance error generated by the distance process from any point of the observation area to the radar sampling point;

when the observation area point is positioned at the radar initial sampling point and the extension line of the sampling point, the error of the step-by-step solving distance course is maximum.

2. The method of claim 1, wherein the spherical aperture zoned nonlinear progressive phase iterative imaging method comprises:

compressing echo signals at all sampling points of the radar along the distance direction;

dividing an imaging area into a plurality of pixel areas, wherein each pixel area is provided with a plurality of pixels;

calculating the phase of each pixel point in an imaging area by adopting a zonal stepping phase iteration method;

calculating the size of a sampling point region according to the step-by-step distance solving error, and dividing the spherical synthetic aperture into a plurality of sampling point regions;

the value of each pixel point of the observation area is calculated point by point.

3. The method of claim 2, wherein the dividing the imaging region into a number of pixel regions, each pixel region having a number of pixels, comprises:

according to the obtained radar resolution, the observation area is divided into a plurality of pixels, so that the size of each pixel along the distance direction, the azimuth direction and the pitching direction is respectively smaller than the radar distance direction, the azimuth direction and the pitching direction resolution.

4. A method according to claim 3, wherein the calculating the phase of each pixel point in the imaging region by using a split-region step-and-step phase iterative method comprises:

Calculating initial pixel point phase and phase compensation factors based on the near distance of an observation area, the distance direction size of a pixel, the radar center frequency, the stepping initial value and the number of distance direction pixels;

iteratively calculating the phase of the pixel points along the distance direction until the stepping initial value is larger than the number of the pixels along the distance direction;

outputting a pixel point phase matrix along the distance direction;

based on the expansion of the pixel point phase matrix along the distance direction, the phase of the pixel points located at the same radial distance is calculated iteratively.

5. The method of claim 4, wherein calculating the sample point region size from the step-wise range solution error and dividing the spherical synthetic aperture into a number of sample point regions comprises:

selecting an observation area pixel point and a radar initial sampling point;

calculating the distance course from the pixel point of the observation area to the radar initial sampling point;

calculating an azimuth distance compensation factor coefficient and a pitching distance compensation factor coefficient;

solving maxwell Lin Jinshi of the distance history;

solving an actual distance course;

and calculating the size of the sampling point region and the number of the dividing regions, and calculating the sampling point region according to the phase error limiting condition.

6. The method of claim 5, wherein calculating the value of each pixel of the observation region point by point comprises:

And reconstructing each pixel point of the observation area point by point based on an algorithm so as to realize three-dimensional resolution imaging of the observation area.

7. The device is used for forming a synthetic aperture or a real aperture radar with apertures positioned on the same sphere through azimuth-pitching rotation; the device comprises:

an error analysis module configured to perform a distance error analysis based on a step-wise distance compensation factor calculation as described in the method of claim 1;

the imaging module is configured to be used for carrying out area division on sampling points of the spherical aperture radar, so that the distance process from any point of an observation area to the sampling points is obtained through iterative calculation of a stepping distance compensation factor, and three-dimensional reconstruction of the observation area is completed.

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