CN116502477B - A Method of Realizing Nonlinear Frequency Sweeping SAR Based on Nonlinear Frequency Modulation Signal - Google Patents

Abstract

The invention discloses a method for realizing a nonlinear frequency scanning SAR based on a nonlinear frequency modulation signal, comprising: step 1, obtaining a nonlinear frequency scanning response model, and obtaining a scanning coefficient vector by solving the nonlinear frequency scanning response model; step 2, obtaining a nonlinear frequency scanning response model; Polynomial fitting method to obtain the group delay function model; step 3, solve the group delay function of the nonlinear frequency modulation signal by scanning the coefficient vector; step 4, solve the time-frequency function of the nonlinear frequency modulation signal through the piecewise linear function method; step 5, The nonlinear frequency modulation signal template is obtained by solving the time-frequency function. The invention can effectively realize specific nonlinear frequency sweep response, and has strong engineering realizability.

Description

A Method of Realizing Nonlinear Frequency Sweeping SAR Based on Nonlinear Frequency Modulation Signal

technical field

The invention relates to the technical field of High Resolution Wide Swath (HRWS) spaceborne synthetic aperture radar (Synthetic Aperture Radar, SAR), in particular to a method for realizing nonlinear frequency scanning SAR based on a nonlinear frequency modulation signal.

Background technique

High Resolution Wide Swath (HRWS) spaceborne Synthetic Aperture Radar (SAR) plays an important role in the field of remote sensing observation. High resolution helps to accurately extract information and features of targets, and wide swaths can increase the revisit frequency of specific areas. Therefore, "high resolution and wide width" has become an important direction for the future development of spaceborne SAR.

However, for the traditional spaceborne SAR system, due to the principle of minimum antenna area, the azimuth resolution and range imaging width are mutually restricted. In order to alleviate or even break through the contradiction between high resolution and wide swath, some effective methods and technologies have been proposed, such as azimuth multi-channel technology, quaternary array technology, variable repetition frequency technology, etc. Although these technologies can perform wide-area imaging without loss of resolution, they cannot solve the problem of low receiving gain in wide-area surveying and mapping. Specifically, wide-format imaging requires wide beams to illuminate the surveying zone, but this will inevitably lead to a decrease in transceiver gain and limited system sensitivity. The gain of the narrow beam is high, but a static narrow beam cannot directly cover a wide swath, so the insufficient signal reception gain in wide imaging becomes a problem that must be faced. The digital beamforming (DBF) elevation multi-channel SAR system (DBF-SAR) with digital beamforming capability can effectively alleviate the contradiction between wide imaging and insufficient gain by forming high-gain pencil beams in real time to improve receiving gain. It is worth mentioning that the use of DBF technology doubles the cost and complexity of the system, and the huge amount of calculation puts a heavy burden on the digital hardware. In addition, the consistency of the amplitude and phase between the channels is also difficult to guarantee. In view of the above reasons, DBF technology has not been practically applied to on-orbit SAR observation missions at present.

Recently, scholars of DLR proposed a SAR system (Frequency Scan SAR, F-SAR) using Frequency Scan (FS) technology. The system uses the dispersion principle of the antenna to generate a dynamic beam through frequency scanning to realize the illumination and imaging of the surveying zone. Realizable, which makes FS technology more competitive than DBF technology. However, there is a problem with this model. The range resolution and imaging width are mutually restricted. Under a large survey swath, the range resolution is very limited, and the ground distance resolution is also limited. In order to alleviate the above problems, scholars from AIR and Ocean University of China proposed a nonlinear frequency scan response (Nonlinear Frequency Scan Response, NFSR). distance resolution. However, little is known about how to specifically realize the nonlinear frequency sweep response.

Contents of the invention

In order to solve the above technical problems, the main purpose of the present invention is to provide a method for realizing nonlinear frequency scanning SAR based on nonlinear frequency modulation signal, which can effectively realize specific nonlinear frequency scanning response, which is based on nonlinear frequency modulation signal ( Nonlinear Frequency Modulated (NLFM) is a method of realizing nonlinear frequency sweep response, which has high precision and engineering realizability.

In order to achieve the above object, technical solution of the present invention is achieved in that way:

A method for realizing nonlinear frequency scanning SAR based on nonlinear frequency modulation signal, comprising the steps of:

Step 1. Obtain a nonlinear frequency sweep response model, and obtain a sweep coefficient vector by solving the nonlinear frequency sweep response model;

Step 2, obtain the group delay function model by the method of polynomial fitting;

Step 3, solving the time-frequency function of the nonlinear frequency modulation signal by the series inverse solution method;

Step 4. Obtain an approximate time-frequency function that meets the accuracy requirements through the piecewise linear function method;

Step 5. Obtain the nonlinear frequency modulation signal template through the solved approximate time-frequency function.

Further, said step 1 includes:

The nonlinear frequency sweep response model is obtained according to the sweep constraints, scene constraints and expected nonlinear frequency sweep constraints, and then the sweep coefficient vector is solved by an optimization method.

Further, the step 2 includes:

The linear equation of scan angle and scan time is solved according to the initial conditions, and then the group delay function model of the nonlinear frequency modulation signal is obtained by polynomial fitting method, and finally the polynomial coefficient of the group delay function model is solved by combining the scan coefficient vector.

Further, said step 3 includes:

The group delay matrix is obtained based on the solved group delay function model, the discrete frequency vector is obtained according to the prior information, and then the polynomial coefficients of the time-frequency function are solved by generalized matrix inversion, and finally the nonlinear frequency modulation signal is obtained by polynomial fitting time-frequency function.

Further, said step 4 includes:

According to the number of sampling points of the nonlinear frequency modulation signal, initially determine the number of segments of the piecewise linear function, then calculate the slope and intercept of each segment of the linear function, determine the approximate time-frequency function, and finally calculate the nonlinear frequency sweep response error based on the approximate time-frequency function , if the nonlinear frequency sweep response error does not meet the requirements, modify the number of segments of the piecewise linear function until the nonlinear frequency sweep response error meets the requirements.

Beneficial effect:

The invention provides a method for realizing the nonlinear frequency scanning SAR based on the nonlinear frequency modulation signal, so as to make up for the gap in the research in this aspect. In addition, this method can not only realize the desired nonlinear frequency sweep response, but also adopts a piecewise linear approximation nonlinear frequency modulation signal generation method, which greatly reduces the complexity of the algorithm and is beneficial to the engineering of the entire technology.

Description of drawings

Fig. 1 is a kind of flow chart of the method for realizing nonlinear frequency scanning SAR based on nonlinear frequency modulation signal of the present invention;

Fig. 2 obtains the schematic diagram of the principle of the approximate time-frequency function based on the piecewise linear function method;

Figure 3 The relationship between beam pointing and instantaneous frequency;

Fig. 4a is the group delay function diagram of nonlinear frequency modulation signal;

Fig. 4b is the time-frequency function of the non-linear frequency modulation signal;

Figure 5a is a real part diagram of a chirp signal;

Fig. 5b is the real part diagram of the non-linear frequency modulation signal;

Fig. 5c is the spectrogram of chirp signal;

Figure 5d is a spectrum diagram of a non-linear frequency modulation signal;

Fig. 6a, Fig. 6b, and Fig. 6c are the simulation result diagrams of various parameters based on the nonlinear frequency sweep response; wherein Fig. 6a is the distribution diagram of the dwell pulse width at each lower angle of view, and Fig. 6b is the distribution diagram of the dwell bandwidth at each The distribution diagram at the lower viewing angle, Figure 6c is the distribution diagram of the ground distance resolution at each lower viewing angle;

Fig. 7a, Fig. 7b, Fig. 7c, Fig. 7d, Fig. 7e, and Fig. 7f are the performance simulation results diagrams of the approximate description of the nonlinear frequency sweep response by the piecewise linear function, wherein Fig. 7a-7e respectively shows that the number of segments is 1, The results of 10, 100, 1000, and 15000, Figure 7f shows the variation of the average error of ground distance resolution with the number of segments.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

According to an embodiment of the present invention, as shown in FIG. 1, a method for realizing nonlinear frequency scanning SAR based on a nonlinear frequency modulation signal of the present invention includes the following steps:

Step 101: Obtain a nonlinear frequency sweep response model, and obtain a sweep coefficient vector by solving the nonlinear frequency sweep response model.

When the SAR system based on the frequency scanning antenna is working, it uses the dispersion effect of the antenna to form a beam pointing direction through the frequency scanning antenna. and signal frequency /> The linearly corresponding narrow beam can scan and illuminate the surveying zone within one pulse transmission time. At the receiving end, the echo signals from different viewing angles are also received by means of frequency scanning. Different from the spaceborne SAR system using phased array, the beam pointing and the instantaneous frequency of the transmitted signal satisfy the following polynomial form:

/> ,

where, denotes the order of the polynomial, is the scanning coefficient, and for the convenience of subsequent derivation, formula (1) may be rewritten as:

/> ,

in, represents the transpose of a matrix, /> is the scan coefficient vector, is a frequency series vector. It can be seen from formula (1) that when the scanning coefficient changes, the beam pointing /> and signal frequency /> The relationship between will also change accordingly, that is, different sweep coefficients can produce different frequency sweep responses. When the high-order term coefficients in formula (1) exist, it is called nonlinear frequency sweep response. Considering the constraints of scenarios and system performance, the nonlinear frequency sweep response model can be expressed as:

/> ,

in, Indicates the error between the actual nonlinear sweep response and the expected nonlinear sweep response, the specific form is related to the expected nonlinear frequency sweep response, /> represents an inequality constraint, /> On behalf of No. /> constraints, represents an equality constraint, /> Represents the number of inequality constraints, /> is the total number of constraints. The above optimization model can be solved by optimization methods such as genetic algorithm, and then the scanning coefficient vector is obtained , /> Represents a given scan coefficient vector down, /> reach the minimum.

Step 102: Obtain a group delay function model by polynomial fitting.

The invention aims at realizing the nonlinear frequency sweep response by transmitting the nonlinear frequency modulation signal. Assumed beam pointing angle and scan time /> Still satisfying the linear relationship, as follows:

/> ,

in, is a constant term, related to the width and beam width, /> is a one-time item. In order to ensure that the received echo has the possibility of compression, it should be satisfied that when the signal is started to be transmitted, the beam points to the far end of the survey zone, and when the signal is transmitted, the beam points to the near end of the survey zone, so /> and /> satisfy:

/> ,

in, is the scanning angle range, /> is the duration of the transmitted signal, /> is the starting scan angle, where /> is the down view of the far end of the scene, /> beam width.

Different from the linear sweep method, the nonlinear frequency sweep response requires a non-linear frequency modulation signal to be generated at the transmitter, and its group delay function can be expressed in the form of a polynomial:

/> ,

in, is the coefficient of the polynomial. Substituting formula (2) into formula (1) can get:

/> ,

Obviously, at this time, there is a nonlinear relationship between the beam pointing and the frequency, that is, the nonlinear frequency is scanned. So the key is to solve the group delay function of the transmitted signal . For the convenience of derivation, formula (7) is rewritten as:

/> ,

in, is the coefficient vector of the group delay function, and is the frequency series vector, then formula (8) can be expressed as:

/> ,

May as well, let the beam pointing satisfy the following form:

/> ,

Simultaneous formula (2) and formula (10) can get:

/> ,

If the above formula is established, the following two points must be satisfied: first, the vector with /> The lengths are the same; second, the left side of the equal sign is a constant, so there should be no non-constant terms on the right side of the equal sign. order /> , then satisfy:

/> ,

in, As an intermediate variable, there is no special meaning, and it can be further deduced:

/> ,

So far, the group delay function of the nonlinear frequency modulation signal can be obtained.

Step 103: Solve the time-frequency function of the nonlinear frequency modulation signal through the series inverse solution method.

It is not possible to solve the NLFM signal directly through the group delay function. It is necessary to find its inverse function through the group delay function, that is, the frequency function, and then solve the NLFM signal based on the time-frequency function. For an NLFM signal with N sampling points, its time-frequency function can be written as:

/> ,

in, represents the coefficient vector of the time-frequency function, /> Represents a discrete frequency vector, each discrete frequency point satisfies:

/> ,

in, is the range sampling rate, /> is the number of sampling points, /> is the group delay function matrix:

/> ,

in, is a vector composed of discrete values of the group delay function, which can be solved by formula (8) and formula (13). In general, /> , so the coefficient vector of the time-frequency function can be solved by the generalized inverse method:

/> ,

Step 104: Obtain an approximate time-frequency function that satisfies the accuracy requirement by the piecewise linear function method:

Generally speaking, the process of inversion is very resource-intensive. It requires more computing and storage resources for operations such as matrix decomposition and matrix transposition, which is not conducive to the real-time generation of nonlinear frequency modulation signals. Therefore, the present invention adopts a piecewise linear function to describe the time-frequency function to approximate and replace the precise time-frequency function. For an NLFM signal with N sampling points, it can be described by M piecewise linear functions, as shown in Figure 2, the slope and intercept of each linear function are:

/> ,

/> ,

in, for No. /> The start and end frequency values on the segment linear function can be obtained according to the serial number of the segment number and the discrete frequency vector, /> for No. /> The start and end time values on the segment linear function can also be obtained according to the serial number of the segment number and the discrete frequency vector. The subscript "1" indicates the start value of the piecewise function, and the subscript "2" indicates the end value of the piecewise function. Then each piece of linear function can be expressed as:

/> ,

So far, the time-frequency function that can be approximated with the piecewise linear function can be obtained. However, it should be noted that the fewer the number of segments, the less resource consumption, but the accuracy will also decrease, so it needs to be based on the error tolerance of the nonlinear scanning response To determine a suitable M.

Example 1

The embodiment selects some system parameters of a spaceborne mission for simulation. The system uses a frequency scanning antenna, and achieves a more balanced ground distance resolution through the set quadratic nonlinear frequency scanning response. The system parameters are shown in Table 1. Show.

Table 1

,

Based on the scan coefficient vector given in the table , the polynomial coefficients of the group delay function of the corresponding nonlinear frequency modulation signal can be solved, as shown in Table 2.

Table 2

,

Figure 3 shows the results of the nonlinear response based on the parameters described in Table 1. It can be seen that the beam pointing and frequency no longer satisfy a linear relationship at this time, but present a characteristic of a quadratic function. Figure 4a shows the group delay function of the NLFM signal calculated according to the scanning coefficient; Figure 4b shows the time-frequency function of the NLFM signal based on the series reverse connection method. It is not difficult to find that the group delay function and the time-frequency function interact is the inverse function. Figure 5a shows the real part of the chirp signal with the same parameters as those in Table 1, and Figure 5b shows the real part of the NLFM signal based on the precise time-frequency function design, and Figure 5c and Figure 5d show the spectrum of the two respectively, it can be seen that The spectrum of the NLFM signal can be regarded as the result of windowing the spectrum of the chirp signal. Figure 6a shows the dwell pulse width under the nonlinear frequency sweep response. It can be seen that the dwell bandwidth is basically a constant in the entire scan angle range. This is because the beam pointing has a linear relationship with time, that is, the scan speed is constant Yes, since the angular displacement generated by the beam is equal to the beam width when the target is irradiated at any viewing angle, the time for each target to be irradiated is also constant; Figure 6b shows the dwell bandwidth of the target at each viewing angle, which can be It can be seen that the transmission bandwidth of the entire signal is characterized by a large near-end and a small far-end, that is to say, the transmission bandwidth is "allocated on demand". is the balanced ground distance resolution, as shown in Fig. 6c. Figure 7a, Figure 7b, Figure 7c, Figure 7d, Figure 7e, and Figure 7f show the performance of the piecewise linear function to describe the nonlinear frequency sweep response. Figure 7a-7e shows that the number of segments is 1, 10, 100, 1000 , the result of 15000, it can be seen that when the number of segments is 1000, the error of the nonlinear frequency sweep response at this time is basically negligible, that is to say, using 1000 segments of linear function is enough to describe the nonlinear frequency sweep response signal and realize the desired Non-linear frequency sweep response; Figure 7f shows the variation of the average error of ground distance resolution with the number of segments. When the number of segments reaches 1e3 level, it can be seen that the average error of ground distance resolution basically reaches the order of 1e-2. This is much lower than the level of resolution; in short, using the method of piecewise linear function approximation to generate NLFM signals can greatly reduce the complexity while ensuring the accuracy of the nonlinear frequency sweep response, which is beneficial to the NLFM signal Generated in real time.

The above descriptions are only some embodiments of the present invention, and the present invention is still applicable in other cases, and are not intended to limit the protection scope of the present invention.

Claims (1)

1. A method based on nonlinear frequency modulation signal to realize nonlinear frequency scanning SAR, is characterized in that, comprises the steps: Step 1. Obtain a nonlinear frequency sweep response model according to the sweep constraints, scene constraints, and expected nonlinear frequency sweep constraints, and then solve the sweep coefficient vector by an optimization method; Step 2, solve the linear equation of scanning angle and scanning time according to the initial conditions, then adopt the method of polynomial fitting to obtain the group delay function model of the nonlinear frequency modulation signal, finally solve the polynomial coefficient of the group delay function model in conjunction with the scanning coefficient vector; Step 3. Obtain the group delay matrix based on the solved group delay function model, obtain the discrete frequency vector according to the prior information, and then use the generalized matrix inversion method to solve the polynomial coefficients of the time-frequency function, and finally use the polynomial fitting method to obtain the non- Time-frequency function of chirp signal; Step 4. Preliminarily determine the number of segments of the piecewise linear function according to the number of sampling points of the nonlinear frequency modulation signal, then calculate the slope and intercept of each segment of the linear function, determine the approximate time-frequency function, and finally calculate the nonlinear frequency based on the approximate time-frequency function Sweeping response error, if the nonlinear frequency sweeping response error does not meet the requirements, modify the number of segments of the piecewise linear function until the nonlinear frequency sweeping response error meets the requirements; Step 5. Obtain the nonlinear frequency modulation signal template through the solved approximate time-frequency function.