CN108919316B - A single-station multi-system hardware delay estimation method based on the assumption of local spherical symmetry - Google Patents

Abstract

The invention discloses a single-station multi-system hardware delay estimation method based on the assumption of local spherical symmetry in the field of space technology. The technical solution is to use a single-station GNSS multi-system receiver to receive observation signals including Beidou, GPS, GLONASS and other satellite constellations, and obtain the ionospheric oblique TEC on each observation path by using a phase smoothing pseudorange method. ; At the same time, the geometric information on each path is calculated, including the geographic latitude, geographic longitude and elevation angle of the penetration point; at each epoch, all satellite combinations that meet the geometric conditions of local spherical symmetry are screened out, and the observation equation is constructed ; Using the least squares method, solve the combined hardware delay of the receiver and each satellite; According to the combined hardware delay, solve the oblique TEC on the path of the satellite and the receiver, and the vertical TEC at the penetration point position. The beneficial effect of the invention is that, based on the assumption of local spherical symmetry and the multi-system observation technology, the combined hardware delay of the satellite and the receiver can be efficiently and accurately calculated, which can further obtain the real-time high-precision ionospheric TEC and improve the ionospheric space environment. Monitoring and short-term forecasting are of great value.

Description

A single-station multi-system hardware delay estimation method based on the assumption of local spherical symmetry

technical field

The invention belongs to the field of GNSS hardware delay calculation method design, in particular to a single-station multi-system hardware delay estimation method based on the assumption of local spherical symmetry.

Background technique

The Total Electron Content (TEC) of the ionosphere is not only an important parameter to describe the shape and structure of the ionosphere, but also an ionospheric correction parameter that is often used in precise positioning and navigation services. Nowadays, GNSS receivers are mainly used to measure TEC, and its biggest error source comes from the hardware delays of GNSS receivers and satellites. Therefore, how to accurately calculate these hardware delays is the basis for ionospheric research using GNSS.

The existing literature shows that the hardware delay of satellite and receiver is relatively stable, and it is generally regarded as a constant within one day. Common estimation methods include: (1) Factory calibration: use the calibrated GNSS receiver to calibrate the hardware delay of the GNSS receiver before leaving the factory; (2) TEC model-dependent calibration: map the vertical TEC published in the TEC model It is the oblique TEC on the GNSS observation path, and interpolates according to time and location. According to the difference between the two, the combined hardware delay of the receiver and the GNSS satellite is solved. In particular, it sometimes depends on the satellites provided by other agencies. For the hardware delay data, the hardware delay part of the satellite is directly deducted from the observed oblique TEC, and then the difference between the observed TEC and the model TEC is used to obtain the hardware delay of the receiver; (3) Calibration relying on GNSS network observation: using intensive The GNSS ground observation network, divides the plane where the height of the satellite penetration point around the network is located into a two-dimensional grid. Assuming that the vertical TECs in the grid are equal within the limited space-time range, the observation equations are used to solve the problem in each grid. The hardware latency of the vertical TEC and GNSS receivers and satellites. The above three methods all have certain limitations. The first method is affected by the aging and environment of GNSS satellites and receivers, and its hardware delay will no longer be the value at the time of factory calibration; the second method relies on ionization The accuracy of the layer TEC model, where the description of the ionosphere model is not accurate enough, the calculated combined hardware delay is not accurate; the third method is suitable for the accurate solution of the local TEC, but it relies on the observation network composed of many stations. , the amount of calculation is large, and it is not flexible and simple enough.

In view of the limitations of the above three methods, we propose a single-station multi-system hardware delay estimation method based on the assumption of local spherical symmetry. The spherical surface is locally symmetrical, making full use of the observation data of constellations such as BDS, GPS and GLONASS, establishing equations for all observation data that meet this assumption, and using the least squares method to solve the combined hardware delay of the station and each satellite. This method only needs the observation data of one station, and does not need to rely on the TEC model or the observation data of other stations. The calculation amount is small, and it has the characteristics of being independent, fast and flexible. By using the combined hardware delay, the vertical distance over the station can be obtained. TEC provides stable and reliable data support for the study of ionospheric morphology and ionospheric correction.

SUMMARY OF THE INVENTION

Aiming at the limitation of the existing conventional methods in solving the GNSS hardware delay, the present invention proposes a single-station multi-system hardware delay estimation method based on the assumption of local spherical symmetry.

A single-station multi-system hardware delay estimation method based on the assumption of local spherical symmetry, characterized in that it specifically includes the following steps:

Step 1: Use a single-station GNSS multi-system receiver to receive observation signals including Beidou, GPS, GLONASS and other satellite constellations, and obtain the ionospheric oblique TEC on each observation path by using a phase-smoothed pseudorange method;

Step 2: Calculate the geometric information on each path, including the geographic latitude, geographic longitude and elevation of the penetration point;

Step 3: At each epoch, screen out all satellite combinations that meet the geometric conditions of local spherical symmetry, and construct an observation equation;

Step 4: Use the least squares method to solve the combined hardware delay of the receiver and each satellite; and according to this combined hardware delay, obtain the oblique TEC on the path of the satellite and the receiver, and convert it into the position of the penetration point according to the mapping function. Vertical TEC.

In step 1, the calculation formula of the ionospheric oblique TEC is:

为第i颗卫星在第t时刻至地面的GNSS接收机观测路径上的电离层斜向TEC观测值(单位为TECU，1TECU＝1.0×10¹⁶个电子/m²)，c为光速，f₁与f₂分别表示GNSS卫星的两个载波频率，

与

分别表示第i颗卫星的1号和2号载波频率在第t时刻的相位观测，

与

则分别表示相应的伪距观值，N为第i颗卫星在一个连续观测弧段内的观测样本数。Among them, the superscript i represents the GNSS satellite number, the subscript t represents the time, the subscripts 1 and 2 represent the two GNSS carriers, the subscript obs represents the observation value,

is the oblique TEC observation value of the ionosphere on the observation path of the GNSS receiver from the ith satellite to the ground at time t (unit: TECU, 1TECU=1.0×10 ¹⁶ electrons/m ² ), c is the speed of light, f ₁ and f ₂ represent the two carrier frequencies of the GNSS satellite, respectively,

and

are the phase observations of the carrier frequencies 1 and 2 of the ith satellite at time t, respectively,

and

Then respectively represent the corresponding pseudorange values, and N is the number of observation samples of the i-th satellite in a continuous observation arc.

Here, the oblique TEC contains hardware delay, and the relationship between it and the "real" TEC can be expressed as:

就表示第i颗卫星在第t时刻至地面的GNSS接收机观测路径上的电离层斜向TEC真值，

就是接收机硬件延迟(B_R)与卫星硬件延迟(Bⁱ)之和，即

它们的单位也是TECU。Among them, the subscript real represents the "real" value,

It represents the true value of the ionospheric oblique TEC on the observation path of the GNSS receiver from the ith satellite to the ground at time t,

is the sum of the receiver hardware delay (B _R ) and the satellite hardware delay (B ⁱ ), namely

Their units are also TECUs.

In step 2, the formulas for calculating the geographic latitude, geographic longitude and elevation angle of the penetrating point position over the station are as follows:

和

分别是在第t时刻的第i颗卫星在穿透点高度上的地理纬度和地理经度，

是在穿透点位置相对于GNSS卫星的仰角，

则是在地面相对于GNSS卫星的仰角，ζ是GNSS卫星相对于台站的方位角，R_E是地球的平均半径，z是电离层穿透点所在的高度，

是地球角，

θ₀和λ₀分别是地面台站的地理纬度和经度。in,

and

are the geographic latitude and geographic longitude of the i-th satellite at the height of the penetration point at the t-th time, respectively,

is the elevation angle relative to the GNSS satellite at the penetration point position,

is the elevation angle relative to the GNSS satellite on the ground, ζ is the azimuth angle of the GNSS satellite relative to the station, R _E is the average radius of the earth, z is the height of the ionospheric penetration point,

is the angle of the earth,

θ ₀ and λ ₀ are the geographic latitude and longitude of the ground station, respectively.

According to the elevation angle at the penetration point, the vertical TEC can be easily converted. The formula is as follows:

表示第i颗卫星在t时刻的映射函数，它是关于穿透点仰角的函数，

in,

represents the mapping function of the i-th satellite at time t, which is a function of the elevation angle of the penetration point,

In step 3, the local spherical symmetry condition is jointly determined by the elevation and azimuth angles between the two satellites. When the difference between their elevation angles is not greater than 10° and the difference in azimuth angles is not greater than 15°, it is considered that the vertical TEC between them is Equally, this vertical TEC is the "real" TEC after removing hardware delays. For any two satellites i and j that meet the conditions of local spherical symmetry, the observation equation between them is as follows:

和

分别表示第i和第j颗卫星在t时刻的映射函数。Among them, i and j represent the satellite number, respectively,

and

are the mapping functions of the i-th and j-th satellites at time t, respectively.

和

这两个未知数的方程，存在大量的冗余数据。为了减少计算冗余，对所有时刻取平均，得到一个简化方程如下：Obviously, for a fixed combination of satellites i and j, their observation equations within one day are all about

and

There is a lot of redundant data in the equations of these two unknowns. In order to reduce computational redundancy, take the average of all times to obtain a simplified equation as follows:

和

分别表示第i和第j颗卫星组合中各自的映射函数平均值。Among them, T represents the number of observation samples of this satellite combination,

and

are the mean values of the respective mapping functions in the i-th and j-th satellite combinations, respectively.

In step 4, based on step 3, the combination of satellites numbered i and j is recorded as the combination numbered k, and the simplified equations of each satellite combination can be combined into the following sparse matrix form:

由元素f_ki构成的K×M矩阵F是一个稀疏矩阵，它的每一行有且只有两个非零元素，行下标k表示卫星组合的序号，列下标i表示编号为i的卫星，f_ki表示卫星i在组合k中的映射函数平均值。Among them, M represents the number of combined hardware delays to be solved, K represents the number of satellite combinations, b _m represents the combined hardware delay of the mth satellite and the receiver, and y _k represents the number of i and j in combination k. Combined observations from satellites:

The K×M matrix F composed of elements f _ki is a sparse matrix, each row of which has one and only two non-zero elements, the row subscript k represents the sequence number of the satellite combination, and the column subscript i represents the satellite number i, f _ki represents the mean value of the mapping function of satellite i in combination k.

In this observation matrix FB=Y, only the vector B is an unknown quantity, which can be solved by the least square method.

The beneficial effect of the present invention is that, based on the multi-system observation conditions and the assumption of local spherical symmetry, the resources of GNSS constellations such as Beidou, GPS and GLONASS are effectively utilized, and only one station can quickly and accurately calculate the station and GNSS satellites The combined hardware delay of , has the ability to solve the ionospheric vertical TEC in real time, and has important application value in the future monitoring of the ionospheric space environment.

Description of drawings

FIG. 1 is a graph showing the time-dependent change of the oblique TEC observation value of the Beidou No. 1 satellite calculated by the method provided in the present invention.

FIG. 2 is a distribution diagram of geographic longitude and latitude of ionospheric penetration points calculated by the method provided by the present invention.

FIG. 3 is a time-dependent diagram of the elevation and azimuth angles of two satellites calculated by the method provided by the present invention.

FIG. 4 is a histogram of the combined hardware delay of a single-station receiver and a GNSS satellite within one day calculated by the method provided by the present invention.

FIG. 5 is a graph showing the variation of the vertical TEC of the Beidou No. 1 satellite with time calculated by the method provided in the present invention.

FIG. 6 is a graph showing the variation of the vertical TEC of the ionosphere of a single station with time calculated by the method provided by the present invention.

Detailed ways

The preferred embodiments will be described in detail below with reference to the accompanying drawings. It should be emphasized that the following description is exemplary only, and is not intended to limit the scope of the invention and its application.

Taking the data of a station that supports three-system GNSS observations as an example, it can simultaneously receive the epoch, pseudorange and phase data of the Beidou, GPS and GLONASS satellite constellations, and perform the following steps:

Step 1: Use the differential phase observations of each GNSS satellite to smooth the differential pseudorange to obtain the ionospheric oblique TEC:

它是一颗地球同步卫星，全天都可以观测到，它在一天以内共有N＝2733个观测值。Here, taking Beidou's No. 1 satellite (i=1) as an example, its two carrier frequencies are f ₁ =1575.42MHz, f ₂ =1227.6MHz, the speed of light c=2.99792458×10 ⁸ m/s, at t= The two phase observations at time 1 are

It is a geostationary satellite and can be observed throughout the day, and it has a total of N=2733 observations in one day.

与

分别表示1号卫星的两个频率在第t时刻的伪距观测，

与

分别表示第1号卫星的两个频率在第t时刻的相位观测。按照相位差分来平滑伪距差分的方法，获得第1号卫星在第1时刻的电离层斜向TEC观测值，它的数值约为-34.35TECU。Among them, i=1,2,...,2733, N=2733,

and

respectively represent the pseudorange observations of the two frequencies of the No. 1 satellite at time t,

and

respectively represent the phase observations of the two frequencies of the No. 1 satellite at time t. According to the method of smoothing the pseudorange difference by the phase difference, the oblique TEC observation value of the ionosphere of the No. 1 satellite at the first moment is obtained, and its value is about -34.35TECU.

FIG. 1 shows a curve diagram of the oblique TEC observation value of the Beidou No. 1 satellite over time obtained by a single-station multi-system hardware delay estimation method based on the assumption of local spherical symmetry provided by the present invention.

和

穿透点距离地面的高度为450km，经计算得到的各个几何参数如下：Step 2: Here we still take the observation information of Beidou-1 satellite at the first moment as an example. Based on the station coordinates (geographical latitude θ ₀ =18.35°, geographic longitude λ ₀ =109.62°), the ground elevation angle and azimuth angle are respectively

and

The height of the penetration point from the ground is 450km, and the calculated geometric parameters are as follows:

(1) Earth angle

(2) Geographical latitude of penetration point

(3) Geographical longitude of penetration point

(4) Elevation angle of penetration point

FIG. 2 shows a distribution diagram of geographic longitude and latitude of ionospheric penetration points calculated by the method provided by the present invention.

In step 3, according to the judgment condition of local spherical symmetry, the qualified satellites are combined in pairs, still taking Beidou No. 1 satellite (i=1) as an example, which is at 06 UTC with GPS No. 25 satellite (j=36). At :43:50, the first combination (k=1) satisfies the local spherical symmetry condition, and the parameters are:

y ₁ =-19.26.

The observation equation at this moment is as follows:

C01—G25:

In the whole sky, the two satellites have a total of 86 moments that satisfy the local spherical symmetry condition. The observation equations at each moment are averaged to obtain the following simplified equation:

C01—G25:

FIG. 3 is a time-dependent diagram of the elevation and azimuth angles of two satellites calculated by the method provided by the present invention. "C01" and "G25" in the figure represent Beidou No. 1 satellite and GPS No. 25 satellite respectively, they are satellite numbers represented by three-digit "SNN", the first letter "S" represents the satellite constellation, " C", "G" and "R" represent the BeiDou, GPS and GLONASS satellite constellations respectively, and the 2-3 characters represent the serial number of the satellite in the constellation. The part sandwiched by the two vertical dashed lines indicates the observations that satisfy the local spherical symmetry condition.

Step 4: For the Beidou No. 1 satellite in Step 3, a total of 8 satellites can form an observation equation with it, which are G02, G14, G17, G19, G25, R06, R11 and R21, their respective simplified equations They are as follows:

C01—G02:

C01—G14:

C01—G17:

C01—G19:

C01—G25:

C01—R06:

C01—R11:

C01—R21:

A total of 66 satellites were observed throughout the day, including 13 Beidou satellites, 30 GPS satellites and 23 GLONASS satellites. There are a total of 256 satellite combinations available. By combining all the observation equations, a system of equations with 66 unknowns can be obtained. This is an overdetermined system of equations that can be solved directly using the method of least squares. The result of the solution is the optimal estimate of the combined hardware delay of the ground receiver and each GNSS satellite.

The combined hardware delay of a single-station receiver and a GNSS satellite within one day calculated according to the method provided by the present invention is shown in the bar graph in FIG. 4 .

The oblique TEC on the path from the ground to the GNSS satellite can be obtained by directly subtracting this combined hardware delay from the observed oblique TEC. Still taking Beidou-1 satellite as an example, its oblique TEC can be expressed as the following formula:

Correspondingly, according to the transformation of the mapping function, the vertical TEC of the penetration point height can be obtained:

As shown in FIG. 5 , the curve diagram of the ionospheric vertical TEC of the Beidou-1 satellite calculated according to the method provided in the present invention changes with time.

FIG. 6 is a graph showing the variation of the vertical TEC of the ionosphere of a single station with time calculated by the method provided by the present invention.

The above description is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited to this. Substitutions should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (5)

1. a single-station multi-system hardware delay estimation method based on local spherical symmetry assumption, is characterized in that, specifically comprises the following steps: Step 1: Use a single-station GNSS multi-system receiver to receive observation signals including Beidou, GPS, and GLONASS satellite constellations, and obtain the ionospheric oblique TEC on each observation path by using a phase-smoothed pseudorange method; Step 2: Calculate the geometric information on each path, including the geographic latitude, geographic longitude and elevation of the penetrating point over the station; Step 3: At each epoch, when the difference in elevation angle between the two satellites is not greater than 10° and the difference in azimuth angle is not greater than 15°, they are considered to meet the geometric conditions of local spherical symmetry, and all satellites that meet the local spherical symmetry are screened out. Satellite combination of spherically symmetric geometric conditions to construct observation equations; Step 4: Use the least squares method to solve the combined hardware delay of the receiver and each satellite in the observation equation; and based on this combined hardware delay, obtain the oblique TEC on the path of the satellite and the receiver, and convert it into a wear-through TEC according to the mapping function. Vertical TEC at the penetration point location. 2. a kind of single-station multi-system hardware delay estimation method based on local spherical symmetry assumption according to claim 1, is characterized in that, in described step 1, the calculation formula of ionospheric oblique TEC is:

Among them, the superscript i represents the GNSS satellite number, the subscript t represents the time, the subscripts 1 and 2 represent the two GNSS carriers, the subscript obs represents the observation value,

is the oblique TEC observation value of the ionosphere on the observation path of the GNSS receiver from the ith satellite to the ground at time t, the unit is TECU, 1TECU=1.0×10 ¹⁶ electrons/m ² , c is the speed of light, f ₁ and f ₂ respectively represent the two carrier frequencies of the GNSS satellites,

and

represent the phase observations of the ith satellite's carrier frequency No. 1 and No. 2 at time t, respectively,

and

Then respectively represent the corresponding pseudorange observations, and N is the number of observation samples of the i-th satellite in a continuous observation arc. 3. a kind of single-station multi-system hardware delay estimation method based on local spherical symmetry assumption according to claim 1, is characterized in that, in step 2, the geographical latitude, geographical longitude and elevation angle of the penetration point position over the station The calculation formula is as follows:

in,

and

are the geographic latitude and geographic longitude of the i-th satellite at the height of the penetration point at the t-th time, respectively,

is the elevation angle relative to the GNSS satellite at the penetration point position,

is the elevation angle on the ground relative to the GNSS satellite,

is the azimuth of the GNSS satellite relative to the station, R _E is the mean radius of the Earth, z is the height at which the ionospheric penetration point is located,

is the angle of the earth,

θ ₀ and λ ₀ are the geographic latitude and longitude of the ground station, respectively. 4. a kind of single-station multi-system hardware delay estimation method based on local spherical symmetry assumption according to claim 2, it is characterized in that, in step 3, for any two observed at time t that meet the local spherical symmetry condition For satellites i and j, the observation equation between them is as follows:

Among them, i and j represent the satellite number, respectively,

and f _t ^j represent the mapping functions of the i-th and j-th satellites at time t, respectively,

is the combined hardware delay of the receiver and the satellite, which is the sum of the receiver hardware delay _BR and the i-th satellite hardware delay B ⁱ , namely

To reduce computational redundancy, the simplified equation after averaging over all times is as follows:

Among them, T represents the number of observation samples of this satellite combination,

and

are the mean values of the respective mapping functions in the i-th and j-th satellite combinations, respectively. 5. a kind of single-station multi-system hardware delay estimation method based on partial spherical symmetry assumption according to claim 4, is characterized in that, in step 4, the combination that the satellites that are numbered i and j are formed is marked as numbered k The combination of , the simplified equations of each satellite combination can be combined into the following sparse matrix form:

Among them, M represents the number of combined hardware delays to be solved, K represents the number of satellite combinations, b _m represents the combined hardware delay of the mth satellite and the receiver, and y _k represents the number of i and j in combination k. Combined observations from satellites:

The K×M-dimensional matrix composed of elements f _ki is a sparse matrix, each row of which has one and only two non-zero elements, the row subscript k represents the serial number of the satellite combination, and the column subscript i represents the satellite number i, f _ki represents the average value of the mapping function of satellite i in the combination k, and the M×1-dimensional vector composed of elements b _m is an unknown quantity, which can be solved by the least square method.

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