Independent positioning and navigation system based on synthetic aperture radar

Abstract

The present invention discloses an independent positioning and navigation system based on synthetic aperture radar, which relates to the field of radar signal processing technology, including using synthetic aperture radar to collect echo signals, and sparsely reconstructing the echo signals through a double-layer sparse reconstruction unit to obtain a reconstructed and restored signal; inputting the reconstructed and restored signal into a Kalman filter to estimate platform motion parameters and construct a motion compensation parameter matrix; dynamically compensating the reconstructed and restored signal according to the motion compensation parameter matrix, and outputting target positioning parameters. The present invention accurately compensates for the distance migration, Doppler frequency modulation effect and signal envelope broadening caused by target motion, and ultimately achieves the technical effect of improving the positioning accuracy, anti-interference ability and navigation performance of the system in a complex electromagnetic environment.

Description

Technical Field

[0001] The present invention relates to the field of radar signal processing technology, in particular to a non-supported positioning and navigation system based on synthetic aperture radar. Background Art

[0002] Synthetic aperture radar (SAR) technology plays an important role in the field of independent positioning and navigation. Traditional SAR systems transmit electromagnetic waves and receive echo signals reflected by targets, combining signal processing technology to achieve target positioning and navigation. With the development of information technology, SAR systems have made significant progress in signal acquisition, processing and positioning accuracy. At present, commonly used SAR signal processing methods include range-Doppler algorithm, range-azimuth algorithm and wave number domain algorithm. These algorithms show good performance in imaging and positioning of static or slow-moving targets. However, in complex electromagnetic environments, traditional algorithms often use a single-dimensional analysis method to process echo signals, which makes it difficult to effectively deal with signal distortion problems under multi-source interference; at the same time, due to the lack of accurate modeling and compensation mechanism for target motion characteristics, the positioning accuracy is limited.

[0003] Existing SAR signal processing technology faces many challenges when dealing with high-speed moving targets. First, the rapid movement of the target will cause complex effects such as range unit migration, Doppler frequency modulation, and signal envelope broadening, which will cause signal characteristics to be distorted. Second, traditional signal reconstruction methods often use a fixed measurement matrix and a single reconstruction algorithm, which is difficult to adapt to the dynamic changes of signal characteristics. Third, when estimating motion parameters, existing methods mostly use simplified motion models, which fail to fully consider the coupling relationship between target motion and signal distortion, affecting positioning accuracy.

[0004] In view of the above problems, the present invention proposes an independent positioning and navigation system based on synthetic aperture radar, which belongs to the field of radar signal processing technology. The method realizes accurate reconstruction of echo signals by constructing a double-layer sparse reconstruction unit, and uses multidimensional tensor analysis and dynamic compensation technology to process signal distortion, effectively improving the positioning and navigation accuracy in complex environments. Summary of the invention

[0005] The purpose of this section is to summarize some aspects of embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0006] In view of the above existing problems, the present invention is proposed.

[0007] Therefore, the present invention provides a support-free positioning and navigation system based on synthetic aperture radar, which can solve the problems mentioned in the background technology.

[0008] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0009] In a first aspect, the present invention provides an independent positioning and navigation system based on synthetic aperture radar, which comprises: using synthetic aperture radar to collect echo signals, and performing sparse reconstruction processing on the echo signals through a double-layer sparse reconstruction unit to obtain a reconstructed and restored signal;

[0010] Inputting the reconstructed restoration signal into a Kalman filter to estimate platform motion parameters and construct a motion compensation parameter matrix;

[0011] The reconstructed restoration signal is subjected to dynamic compensation processing according to the motion compensation parameter matrix, and a target positioning parameter is output.

[0012] As a preferred solution of the independent positioning and navigation system based on synthetic aperture radar described in the present invention, wherein: the acquisition of echo signals includes:

[0013] Synthetic aperture radar is used to transmit detection signals to the target area and receive echo signals reflected by the target;

[0014] Convert the echo signal into a digital baseband signal through a high-speed analog-to-digital converter, and perform noise reduction preprocessing on the digital baseband signal;

[0015] The echo signal includes: an interference echo signal, a target echo signal and a noise signal; wherein the interference echo signal includes ground clutter echo, meteorological clutter echo and electromagnetic interference signal, the target echo signal includes the main lobe echo signal and the side lobe echo signal of the target, and the noise signal includes thermal noise inside the radar system and external environmental noise;

[0016] The characteristics of the target echo signal include: signal amplitude characteristics, frequency characteristics, phase characteristics, polarization characteristics and Doppler characteristics; the signal amplitude characteristics are used to characterize the size of the target reflection cross-sectional area; the frequency characteristics are used to characterize the radial motion speed of the target; the phase characteristics are used to characterize the spatial position information of the target; the polarization characteristics are used to characterize the geometric shape and material properties of the target; the Doppler characteristics are used to characterize the motion state of the target;

[0017] The characteristics of the interference echo signal include: random fluctuation characteristics, spatial distribution characteristics, spectrum characteristics and time-varying characteristics; the random fluctuation characteristics are used to express the random changes in signal amplitude and phase; the spatial distribution characteristics are used to express the distribution law of the interference source in space; the spectrum characteristics are used to express the energy distribution of the interference signal in the frequency domain; the time-varying characteristics are used to express the change law of the interference signal intensity over time.

[0018] As a preferred solution of the independent positioning and navigation system based on synthetic aperture radar described in the present invention, the sparse reconstruction process includes:

[0019] Based on the signal energy to noise variance ratio and the signal amplitude to noise standard deviation criteria, marking the signal segment that meets the criteria as a valid signal segment;

[0020] Constructing a measurement matrix based on orthogonal basis functions, applying the measurement matrix to a valid signal segment for compression sampling, and obtaining a sampled signal after dimensionality reduction;

[0021] Constructing a three-dimensional tensor structure to perform multi-dimensional reorganization on the sampled signal, wherein the three-dimensional tensor structure consists of a distance dimension, an azimuth dimension, and a Doppler dimension;

[0022] Calculating a proportional relationship between a tensor rank of the three-dimensional tensor and a minimum dimension value, and when the tensor rank is less than one third of the minimum dimension value, performing a core tensor decomposition operation on the three-dimensional tensor to obtain a core tensor and three factor matrices;

[0023] The core tensor and factor matrix obtained by the tensor decomposition operation are used to restore the signal through a signal reconstruction model to obtain a reconstructed and restored signal.

[0024] As a preferred solution of the independent positioning and navigation system based on synthetic aperture radar of the present invention, wherein: the obtained core tensor and three factor matrices include:

[0025] Constructing a three-dimensional tensor structure to perform multi-dimensional reorganization on the sampled signal, wherein the three-dimensional tensor structure consists of a distance dimension, an azimuth dimension, and a Doppler dimension;

[0026] The multi-dimensional reorganization includes distance dimension reorganization, azimuth dimension reorganization and Doppler dimension reorganization; the distance dimension reorganization divides the sampling interval based on the distance resolution of the radar system, and arranges the sampling data of each range gate into a distance vector; the azimuth dimension reorganization divides the sampling interval based on the angle increment of the antenna rotation, and arranges the sampling data of different azimuth angles into an azimuth vector; the Doppler dimension reorganization divides the sampling interval based on the inverse of the pulse repetition period, and arranges the sampling data at different times into a Doppler vector;

[0027] The proportional relationship between the tensor rank and the minimum dimension value of the three-dimensional tensor is calculated. When the tensor rank is less than one third of the minimum dimension value, the low rank property is satisfied. The core tensor decomposition operation is performed on the three-dimensional tensor that satisfies the low rank condition to obtain a core tensor and three factor matrices.

[0028] As a preferred solution of the independent positioning and navigation system based on synthetic aperture radar described in the present invention, wherein: satisfying the low-rank characteristic includes: extracting the distance dimension value, the azimuth dimension value and the Doppler dimension value in the structure of the three-dimensional tensor, and selecting the minimum dimension value therefrom;

[0029] Expand the three-dimensional tensor into matrices along three dimensions to obtain three expanded matrices;

[0030] Compute the singular values ​​of the three unfolded matrices;

[0031] Count the number of singular values ​​in each unfolded matrix that are greater than a given threshold;

[0032] The maximum number of valid singular values ​​of the three unfolded matrices is defined as the tensor rank;

[0033] Calculate the ratio of the tensor rank to the minimum dimension value. When the ratio is less than one-third, the three-dimensional tensor satisfies the low-rank property.

[0034] The expansion matrix includes a distance dimension expansion matrix, an azimuth dimension expansion matrix and a Doppler dimension expansion matrix;

[0035] The execution of core tensor decomposition includes: establishing a Tucker decomposition model and initializing three factor matrices;

[0036] The core tensor is calculated by iterative optimization using the alternating least squares method;

[0037] Extract the main elements from the core tensor as signal features;

[0038] The Tucker decomposition model is established to represent a three-dimensional tensor as the product of a core tensor and three factor matrices;

[0039] Initialize the three factor matrices by performing singular value decomposition on the three unfolded matrices respectively, and take the first R left singular vectors as the initial factor matrix;

[0040] By using the alternating least squares method to iterate and fix two factor matrices, the third factor matrix is ​​updated; the three factor matrices are updated cyclically until convergence;

[0041] The calculation of the core tensor is to project the original tensor into the space formed by three factor matrices. The calculation formula is as follows: ;

[0042] in, is the position in the core tensor The elements at is the index of the distance dimension, is the index of the orientation dimension, is the index of the Doppler dimension, is the position in the original three-dimensional tensor The elements at is the index of the original distance dimension, is the index of the original orientation dimension, is the index of the original Doppler dimension, is the element in the dth row and ith column of the distance dimension factor matrix, is the element in the ath row and jth column of the orientation dimension factor matrix, is the element in the mth row and kth column of the Doppler dimension factor matrix, is the distance dimension size of the original tensor, is the azimuth dimension of the original tensor, is the Doppler dimension size of the original tensor.

[0043] As a preferred solution of the independent positioning and navigation system based on synthetic aperture radar described in the present invention, wherein: the construction of the motion compensation parameter matrix includes:

[0044] A relative motion relationship model between the radar platform and the target is established based on the target motion state vector;

[0045] A motion compensation parameter matrix is ​​constructed through a line of sight angle change rate matrix, wherein the motion compensation parameter matrix includes a distance dimension compensation coefficient, an azimuth dimension compensation coefficient, and a Doppler dimension compensation coefficient.

[0046] As a preferred solution of the independent positioning and navigation system based on synthetic aperture radar described in the present invention, the dynamic compensation processing includes:

[0047] Compensate for the range unit migration effect caused by target motion, the Doppler frequency modulation effect in azimuth, and the signal envelope broadening effect caused by complex motion;

[0048] Establish a mapping relationship between target motion and signal distortion;

[0049] The original signal is corrected using the compensation parameter matrix.

[0050] As a preferred solution of the independent positioning and navigation system based on synthetic aperture radar described in the present invention, the signal reconstruction module is used to collect echo signals using synthetic aperture radar, and perform sparse reconstruction processing on the echo signals through a double-layer sparse reconstruction unit to obtain a reconstructed and restored signal;

[0051] The compensation evaluation module is used to input the reconstructed restoration signal into the Kalman filter to estimate the platform motion parameters and construct a motion compensation parameter matrix;

[0052] The signal compensation module is used to perform dynamic compensation processing on the reconstructed restoration signal according to the motion compensation parameter matrix and output target positioning parameters.

[0053] In a second aspect, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, wherein: when the processor executes the computer program, the steps of an independent positioning and navigation system based on synthetic aperture radar are implemented.

[0054] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, the steps of an independent positioning and navigation system based on synthetic aperture radar are implemented.

[0055] Compared with the prior art, the beneficial effect of the present invention is that the present invention realizes efficient compression and accurate reconstruction of echo signals in complex environments by using synthetic aperture radar to collect echo signals and introducing a double-layer sparse reconstruction unit for processing, greatly reducing the computational complexity of signal processing, and improving the signal reconstruction quality under low signal-to-noise ratio conditions; further, by inputting the reconstructed and restored signal into the Kalman filter to estimate the platform motion parameters and constructing a motion compensation parameter matrix, the real-time accurate tracking of the platform motion state and the adaptive filter gain adjustment are realized, and an accurate motion compensation model is established; finally, the motion compensation parameter matrix is ​​used to dynamically compensate the reconstructed and restored signal, accurately compensating for the distance migration, Doppler frequency modulation effect and signal envelope broadening caused by the target motion, and finally achieving the technical effect of improving the positioning accuracy, anti-interference ability and navigation performance of the system in a complex electromagnetic environment. This solution is particularly suitable for unsupported navigation application scenarios with high requirements for positioning accuracy, complex electromagnetic environment and frequent platform maneuvers. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0057] Figure 1 A flowchart of a non-supported positioning and navigation system based on synthetic aperture radar provided by one embodiment of the present invention;

[0058] Figure 2 A module diagram of a non-supported positioning and navigation system based on synthetic aperture radar provided by one embodiment of the present invention;

[0059] Figure 3 An internal structural diagram of a computer device of an independent positioning and navigation system based on synthetic aperture radar provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0060] In order to make the above-mentioned purposes, features and advantages of the present invention more understandable, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0061] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0062] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0063] Example 1, reference Figure 1 , which is the first embodiment of the present invention, and which provides an independent positioning and navigation system based on synthetic aperture radar, comprising:

[0064] Before describing the embodiments of the present application in detail, some related concepts are first explained for the sake of clarity.

[0065] Restricted isometry (RIP condition): This is an important concept in compressed sensing theory, which indicates the basic conditions that the measurement matrix needs to meet when compressing and sampling a signal. Specifically, when the measurement matrix samples any two signals with the same sparsity, the ratio of the Euclidean distance between the two signals before and after compression should be kept within a fixed range, which ensures that the compressed sampling process does not destroy the key information in the signal, so that the original signal can be accurately reconstructed later.

[0066] Tucker decomposition model: This is a mathematical model for decomposing high-dimensional data tensors, which can decompose a high-dimensional tensor into the product of a core tensor and multiple factor matrices. In the present invention, it is used to decompose a three-dimensional signal tensor (including distance dimension, azimuth dimension and Doppler dimension) into a more compact representation, which is convenient for extracting signal features and subsequent processing. This decomposition method retains the main features of the signal in each dimension, while greatly reducing the complexity of data storage and calculation.

[0067] Line of sight angle change rate matrix: This concept describes an important parameter in the relative motion relationship between the radar platform and the target, indicating the change characteristics of the line of sight direction of the target relative to the radar platform over time. This matrix contains the change rates of the three angle components of radial angle, azimuth angle and pitch angle, which is used to characterize the motion characteristics of the target and is an important basis for constructing motion compensation parameters. By analyzing the change characteristics of the line of sight angle, various signal distortion effects caused by target motion can be accurately compensated.

[0068] Signal distortion effect: This is a general term for various distortion phenomena caused by target motion on radar signals, which mainly include three categories: distance unit migration effect in the distance direction (i.e., distance measurement deviation caused by target motion), Doppler frequency modulation effect in the azimuth direction (i.e., frequency modulation caused by target tangential motion), and signal envelope broadening effect caused by complex motion (i.e., complex target motion causes signal energy to diffuse in the time-frequency domain). These effects will reduce the positioning accuracy of the radar system, and need to be eliminated or weakened by specific compensation algorithms.

[0069] Figure 1 The system flow chart of a non-supported positioning and navigation system based on synthetic aperture radar is shown, including:

[0070] S1: Use synthetic aperture radar to collect echo signals, and perform sparse reconstruction processing on the echo signals through a double-layer sparse reconstruction unit to obtain a reconstructed and restored signal;

[0071] Further, collecting the echo signal includes transmitting a detection signal to the target area using a synthetic aperture radar and receiving an echo signal reflected by the target;

[0072] The echo signal is converted into a digital baseband signal through a high-speed analog-to-digital converter, and the digital baseband signal is pre-processed for noise reduction to improve the signal quality.

[0073] Specifically, the echo signal includes: interference echo signal, target echo signal and noise signal; wherein the interference echo signal includes ground clutter echo, meteorological clutter echo and electromagnetic interference signal, the target echo signal includes the main lobe echo signal and side lobe echo signal of the target, and the noise signal includes thermal noise inside the radar system and external environmental noise;

[0074] The characteristics of the target echo signal include: signal amplitude characteristics, frequency characteristics, phase characteristics, polarization characteristics and Doppler characteristics; the signal amplitude characteristics are used to characterize the size of the target reflection cross-sectional area; the frequency characteristics are used to characterize the radial motion speed of the target; the phase characteristics are used to characterize the spatial position information of the target; the polarization characteristics are used to characterize the geometric shape and material properties of the target; the Doppler characteristics are used to characterize the motion state of the target;

[0075] The characteristics of the interference echo signal include: random fluctuation characteristics, spatial distribution characteristics, spectrum characteristics and time-varying characteristics; random fluctuation characteristics are used to express the random changes in signal amplitude and phase; spatial distribution characteristics are used to express the distribution law of interference sources in space; spectrum characteristics are used to express the energy distribution of interference signals in the frequency domain; time-varying characteristics are used to express the change law of interference signal intensity over time;

[0076] The sampling parameter settings of the high-speed analog-to-digital converter include: the sampling frequency is set to more than 2.5 times the highest frequency of the signal to meet the Nyquist sampling theorem; the quantization bit number is not less than 14 bits to ensure the dynamic range of the signal; the sampling clock jitter is less than one thousandth of the signal period to ensure sampling accuracy;

[0077] Preferably, by analyzing and processing the above characteristics of the echo signal, the target echo signal and the interference echo signal can be distinguished more effectively, and the accuracy of subsequent signal processing can be improved. At the same time, the reasonable sampling parameter setting ensures the complete retention of signal characteristics during the digitization process, providing a reliable data basis for subsequent signal processing.

[0078] Furthermore, based on the dual criteria of the ratio of signal energy to noise variance and the signal amplitude to noise standard deviation, the signal segments that meet the dual criteria are marked as valid signal segments, and the time domain start and end positions of the valid signal segments are recorded.

[0079] The acquisition of signal energy value includes: segmenting the digital baseband signal by using the signal window interception method, and obtaining the signal energy value by calculating the square sum of the sampling points in the window; the acquisition of signal amplitude includes: segmenting the digital baseband signal by using the signal window interception method, and obtaining the signal amplitude by obtaining the absolute maximum value of the sampling points in the window; the acquisition of background noise variance value includes: selecting a noise estimation window at the start or end of the radar scanning cycle, and obtaining the background noise variance value by calculating the square sum of the deviations between the sampling points in the window and the mean; the acquisition of background noise standard deviation includes: obtaining the background noise standard deviation value by taking the square root of the obtained background noise variance value.

[0080] Specifically, a time domain analysis is performed on the digital baseband signal, and a signal quality parameter is obtained by calculating the ratio of signal energy to background noise variance; when the signal quality parameter is greater than a first preset threshold and the signal amplitude exceeds three times the background noise standard deviation, the signal segment that meets the dual criteria is marked as a valid signal segment, and the time domain start and end positions of the valid signal segment are recorded.

[0081] It should be noted that, in the present embodiment, the length of the signal window is dynamically adjusted according to the duration of the target echo, and is generally 2-4 times the duration of the target echo; the length of the noise window needs to ensure the reliability of the statistical characteristics, and usually no less than 1000 sampling points are selected; to improve the accuracy of noise estimation, the present invention adopts the mean of multiple noise windows as the final result; in practical applications, considering the working characteristics of the radar system, the noise window is usually selected in the time period before the target echo signal appears, when the received signal is mainly composed of system noise; the calculation of the signal quality parameter is expressed by the ratio of the signal energy to the background noise variance; the present invention forms a dual criterion mechanism by setting a reasonable first preset threshold (typical value is 13dB) and combining the criterion that the signal amplitude exceeds three times the background noise standard deviation, thereby effectively improving the recognition reliability of the effective signal segment.

[0082] Preferably, the present invention integrates the signal-to-noise ratio and amplitude criteria in multiple dimensions, and adopts differentiated criteria threshold strategies according to different radar working modes, so as to overcome the defect of separating signal detection and feature extraction in the prior art; in the criterion design process of signal recognition, the present invention not only considers the relative relationship between signal energy and noise, but also introduces signal amplitude analysis, and designs specific criterion combinations for different signal features. Specifically, by selecting a noise estimation window at the start or end of the radar scanning cycle, combined with the signal window interception method, accurate estimation of signal energy and background noise is achieved. For example, when detecting a target signal, the system first calculates the background noise variance in a noise window (no less than 1000 sampling points), and then calculates the signal energy in a signal window (2-4 times the duration of the target echo); when the system detects that the signal quality parameter exceeds the first preset threshold (13dB) and the signal amplitude exceeds 3 times the background noise standard deviation, it can be determined as a valid signal; this dual criterion design is particularly suitable for signal detection in a complex electromagnetic environment; under a strong interference background, the traditional single threshold detection method is easily affected by interference signals and produces false alarms; the present invention effectively improves the reliability of signal recognition by simultaneously considering the ratio of signal energy to background noise variance and the multiple of the signal amplitude exceeding the background noise standard deviation. When the signal received by the radar system contains target echo signals, interference echo signals and noise signals at the same time, by calculating the ratio of the energy value in the signal window to the variance in the noise window, combined with the signal amplitude criterion, it can effectively distinguish between valid signals and interference signals.

[0083] Furthermore, a measurement matrix is ​​constructed based on the orthogonal basis function, and the measurement matrix is ​​applied to the effective signal segment for compression sampling to obtain a sampled signal after dimensionality reduction.

[0084] Specifically, compressed sampling includes three steps: constructing a measurement matrix, determining the number of sampling points, and performing compressed sampling.

[0085] First, select appropriate orthogonal basis functions when constructing the measurement matrix; when the signal exhibits sparse characteristics, select Fourier basis functions to construct the measurement matrix; when the signal has piecewise smooth characteristics, select wavelet basis functions to construct the measurement matrix; when the signal exhibits time-frequency localization characteristics, select Gabor basis functions to construct the measurement matrix; measurement matrices constructed based on different orthogonal basis functions have different characteristics, among which Fourier basis is suitable for processing periodic signals, wavelet basis is suitable for processing transient signals, and Gabor basis is suitable for processing signals with complex time-frequency characteristics.

[0086] Secondly, according to the signal compression theory, when the restricted isometry (RIP) condition is met, the number of compressed sampling points of the measurement matrix needs to be positively correlated with the signal sparsity; therefore, the present invention sets the ratio of the number of compressed sampling points to the original signal length in the range of 0.3 to 0.5. For example, for signals with a high signal-to-noise ratio (>20dB), the ratio can be set to 0.3; for signals with a medium signal-to-noise ratio (10-20dB), it is recommended to set the ratio to 0.4; for signals with a low signal-to-noise ratio (<10dB), the ratio needs to be increased to 0.5 to ensure the quality of the reconstructed signal.

[0087] Finally, the measurement matrix is ​​applied to the effective signal segment to perform compressed sampling. The present invention uses matrix multiplication operation to implement the compressed sampling process, and obtains the reduced-dimensional sampling signal through the inner product operation of the measurement matrix and the original signal. In this process, the number of rows of the measurement matrix determines the length of the signal after compressed sampling, while the number of columns is the same as the length of the original signal.

[0088] Preferably, the present invention adopts an adaptive measurement matrix selection strategy when performing compression sampling, and selects the most suitable orthogonal basis function according to the signal characteristics. This strategy overcomes the problem that the fixed measurement matrix is ​​often used in the prior art, resulting in unsatisfactory compression effect. In particular, in determining the number of sampling points, different compression ratios are used according to the signal-to-noise ratio of the signal. This differentiated compression mechanism can better balance the data compression rate and reconstruction quality. For example, when processing a signal with periodic characteristics, the Fourier basis function can be selected to construct the measurement matrix, and the appropriate compression ratio can be set according to the signal quality; for a signal with transient characteristics, the wavelet basis function can be selected to construct the measurement matrix, and the compression ratio can be appropriately adjusted to ensure the signal reconstruction effect; this adaptive compression sampling method based on signal characteristics provides a theoretical basis for subsequent signal processing by reasonably selecting basis functions and compression parameters.

[0089] Furthermore, a three-dimensional tensor structure is constructed to perform multi-dimensional reorganization of the sampled signal, and the three-dimensional tensor structure consists of a distance dimension, an azimuth dimension, and a Doppler dimension;

[0090] The proportional relationship between the tensor rank and the minimum dimension value of the three-dimensional tensor is calculated. When the tensor rank is less than one-third of the minimum dimension value, the low rank property is satisfied. The core tensor decomposition operation is performed on the three-dimensional tensor that satisfies the low rank condition to obtain the core tensor and three factor matrices.

[0091] Among them, the three-dimensional tensor reorganization of the sampling signal includes distance dimension reorganization, azimuth dimension reorganization and Doppler dimension reorganization. Specifically, the distance dimension reorganization divides the sampling interval based on the distance resolution of the radar system, and arranges the sampling data of each range gate into a distance vector; the azimuth dimension reorganization divides the sampling interval based on the angle increment of the antenna rotation, and arranges the sampling data of different azimuth angles into an azimuth vector; the Doppler dimension reorganization divides the sampling interval based on the inverse of the pulse repetition period, and arranges the sampling data at different times into a Doppler vector. It should be noted that when the sampling signal is reorganized into a three-dimensional tensor structure, the data of each sampling point is arranged according to the sampling intervals of the above three dimensions to form a complete three-dimensional data structure.

[0092] The low-rank characteristic determination of a three-dimensional tensor includes: extracting the distance dimension value, azimuth dimension value and Doppler dimension value from the structure of the three-dimensional tensor, and selecting the minimum dimension value therefrom; expanding the three-dimensional tensor into a matrix along three dimensions to obtain three expanded matrices; calculating the singular values ​​of the three expanded matrices; counting the number of singular values ​​in each expanded matrix that are greater than a given threshold; defining the maximum value of the number of valid singular values ​​of the three expanded matrices as the tensor rank; calculating the ratio of the tensor rank to the minimum dimension value, and when the ratio is less than one-third, the three-dimensional tensor satisfies the low-rank characteristic; the expanded matrices include the distance dimension expanded matrix, the azimuth dimension expanded matrix and the Doppler dimension expanded matrix.

[0093] Performing core tensor decomposition on a three-dimensional tensor that satisfies the low-rank property includes: establishing a Tucker decomposition model and initializing three factor matrices; iteratively optimizing through alternating least squares method; calculating the core tensor; and extracting the main elements from the core tensor as signal features.

[0094] Specifically, the Tucker decomposition model is established by expressing the three-dimensional tensor as the product of the core tensor and three factor matrices; the three factor matrices are initialized by performing singular value decomposition on the three unfolded matrices respectively, and the first R left singular vectors are taken as the initial factor matrix; the alternating least squares method is used to iterate to fix two factor matrices and update the third factor matrix; the three factor matrices are updated cyclically until convergence; the core tensor is calculated by projecting the original tensor into the space spanned by the three factor matrices, and the calculation formula is as follows: ;

[0095] in, is the position in the core tensor The elements at is the index of the distance dimension, is the index of the orientation dimension, is the index of the Doppler dimension, is the position in the original three-dimensional tensor The elements at is the index of the original distance dimension, is the index of the original orientation dimension, is the index of the original Doppler dimension, is the element in the dth row and ith column of the distance dimension factor matrix, is the element in the ath row and jth column of the orientation dimension factor matrix, is the element in the mth row and kth column of the Doppler dimension factor matrix, is the distance dimension size of the original tensor, is the azimuth dimension of the original tensor, is the Doppler dimension size of the original tensor.

[0096] The generation of feature descriptors includes: constructing the main elements of the core tensor into a feature matrix; normalizing the feature matrix; converting the normalized feature matrix into a feature vector; establishing a mapping relationship between the feature vector and the original signal feature to obtain a feature descriptor.

[0097] Preferably, the present invention adopts a three-dimensional tensor structure to reorganize the sampled signals, and expresses the signal characteristics through the combination of distance dimension, azimuth dimension and Doppler dimension; in the tensor decomposition process, the low-rank characteristics are determined based on the singular value distribution of the unfolded matrix, and Tucker decomposition is used to extract features for the tensor that meets the low-rank condition; this three-dimensional joint analysis method overcomes the problem of insufficient information utilization in traditional single-dimensional or two-dimensional analysis methods; the present invention defines the tensor rank as the maximum value of the number of valid singular values ​​of the three unfolded matrices, judges the low-rank characteristics by the ratio with the minimum dimensional value, and uses the alternating least squares method to solve the Tucker decomposition model, thereby realizing the mapping from high-dimensional tensor to feature descriptor; this feature extraction method based on tensor decomposition establishes a mathematical expression of signal characteristics, and provides a reliable data basis for subsequent processing.

[0098] Furthermore, the core tensor and factor matrix obtained by the tensor decomposition operation are used to restore the signal through the signal reconstruction model to obtain the reconstructed and restored signal.

[0099] The construction of the signal reconstruction model includes: using the core tensor and factor matrix to restore the signal through the tensor reconstruction algorithm, and establishing an error measurement relationship between the reconstructed signal and the original signal; calculating the root mean square error based on the time domain characteristics as the main evaluation parameter, and introducing the frequency domain characteristics to calculate the signal power spectrum density correlation coefficient as an auxiliary evaluation parameter; combining the main evaluation parameters and the auxiliary evaluation parameters to construct a reconstruction quality evaluation matrix. Specifically, the signal reconstruction model includes: using the core tensor and factor matrix to restore the signal through the tensor reconstruction algorithm, and calculating the root mean square error between the reconstructed signal and the original signal as the main evaluation parameter; calculating the mutual correlation coefficient based on the power spectrum density of the two signals as an auxiliary evaluation parameter; judging that the reconstruction is valid when the following conditions are met at the same time: the root mean square error value between the reconstructed signal and the original signal is less than 10% of the root mean square of the original signal, and the mutual correlation coefficient is greater than 0.9; the reconstruction result that meets the dual criteria is output as a reconstructed restoration signal.

[0100] The tensor reconstruction algorithm includes: based on the core tensor and three factor matrices obtained by tensor decomposition operation, the signal is reconstructed by tensor product operation; the three factor matrices correspond to the three modal dimensions of the signal respectively, and the reconstruction of the original high-dimensional signal is realized by dimension-by-dimension tensor product operation; the reconstruction result is expanded into the original signal format. Specifically, the tensor reconstruction algorithm includes: performing modulo-n product operation on the core tensor and the three factor matrices in sequence, and completing three tensor product calculations in the order of the first mode, the second mode and the third mode; optimizing the calculation order by using the associative law of tensor product to reduce the storage overhead of the intermediate results; rearranging the final tensor product result into the same data structure as the original signal to obtain the reconstructed signal. By analyzing the size of each modal dimension and selecting the optimal tensor product calculation order, the computational complexity is effectively reduced. In particular, by utilizing the associative law characteristics of the tensor product operation, the generation of large-scale intermediate results is avoided, and the computational efficiency and storage efficiency of the algorithm are improved. Compared with the traditional fixed order reconstruction, this reconstruction method based on modal optimization can better adapt to the signal processing requirements of different dimensional features.

[0101] Preferably, the present invention adopts a dual criterion mechanism of the signal reconstruction model to evaluate the reconstruction effect in two dimensions: time domain and frequency domain. In the time domain, the overall reconstruction quality of the signal is evaluated based on the root mean square error. In the frequency domain, the spectral consistency of the signal is evaluated by the mutual correlation coefficient. This multi-dimensional evaluation method avoids the one-sidedness that may be caused by a single indicator. Through the comprehensive evaluation of time domain features and frequency domain features, the quality of the reconstructed signal is fully controlled, providing a reliable signal basis for subsequent processing.

[0102] S2: Input the reconstructed restoration signal into the Kalman filter to estimate the platform motion parameters and construct the motion compensation parameter matrix;

[0103] Furthermore, based on the reconstructed signal, the radial distance, Doppler frequency shift and azimuth angle data of the target relative to the radar platform are obtained as the observation input of the Kalman filter; specifically, the distance dimension analysis of the reconstructed signal is performed to obtain the radial distance value, the frequency shift value is obtained through Doppler spectrum analysis, and the angle information is obtained by azimuth signal processing; these three parameters are combined into an observation vector to constitute the input of the filter. The observation vector contains three basic parameters: radial distance, Doppler frequency shift and azimuth angle of the target. These parameters are extracted from the reconstructed signal through a signal processing algorithm. The signal processing algorithm is a prior art and will not be described in detail here.

[0104] Furthermore, the three-dimensional position coordinates and three-dimensional velocity components of the target are estimated by the Kalman filter, and the acceleration components and turning rate parameters are calculated based on the motion model equations, and the state equation and observation equation are established. The calculation formula is as follows:

[0105] ;

[0106] in, is the number of filter iterations, is the state vector, containing position and velocity information, is the state transfer matrix, is the process noise, is the observation matrix, The filter estimates the target motion parameters through two stages: prediction and update. On this basis, the motion model equations are used to calculate the acceleration components and turning rate parameters of the target, which reflect the maneuvering characteristics of the target.

[0107] Furthermore, a relative motion relationship model between the radar platform and the target is established based on the target motion state vector, and a motion compensation parameter matrix is ​​constructed through the line of sight angle change rate matrix;

[0108] Specifically, the three-dimensional position coordinates, three-dimensional velocity components, acceleration components and turning rate parameters of the target are first combined into a complete motion state vector; based on the state vector, a relative motion relationship model between the radar platform and the target is established, and the variation characteristics of the line of sight angle over time are calculated. The calculation formula is as follows:

[0109] ;

[0110] in, is the line of sight angle change rate matrix, , , are radial angle, azimuth angle and elevation angle respectively, and t is a continuous time variable;

[0111] Construct the motion compensation parameter matrix, the calculation formula is as follows:

[0112] ;

[0113] in, To compensate for the time series, is the motion compensation parameter matrix, Distance dimension compensation coefficient, is the azimuth dimension compensation coefficient, are the Doppler dimension compensation coefficients; these compensation coefficients are calculated by the line of sight angle change rate and are used to compensate for the signal distortion caused by target motion; this matrix fully considers the impact of target motion on radar signals in the distance dimension, azimuth dimension and Doppler dimension, and realizes all-round motion compensation. The compensation coefficient relationship formula is as follows:

[0114] ;

[0115] Where T is the transformation matrix, It is the vectorized form of the line of sight angle change rate matrix.

[0116] S3: Perform dynamic compensation processing on the reconstructed restoration signal according to the motion compensation parameter matrix and output the target positioning parameters.

[0117] Furthermore, the dynamic compensation processing includes: analyzing the signal distortion effect caused by the target motion, including the range unit migration effect, the azimuth Doppler frequency modulation effect, and the signal envelope broadening effect caused by complex motion; establishing a mapping relationship between the target motion and the signal distortion, expressing the compensation model in matrix form, correcting the original signal through the compensation parameter matrix, and outputting the target positioning parameters. The calculation formula is as follows:

[0118] ;

[0119] Among them, ξ is the time series index of compensation processing, is the target positioning parameter after multi-dimensional compensation, is the compensation weight coefficient of each dimension, is the compensation matrix of each dimension, To reconstruct the restored signal, is the Doppler frequency, is the time delay factor, is the reference signal power, is the current signal power, Represents three dimensions, (distance dimension , Azimuth dimension , Doppler dimension ).

[0120] The better one is that in terms of the distance-to-distance unit migration effect, the radial motion of the target causes the echo signal to migrate in the distance dimension, and the migration amount is positively correlated with the motion speed and the pulse repetition period; the accelerated motion of the target causes the energy dispersion in the distance dimension, so that the width of the main lobe of the range image widens with the increase of acceleration, and is proportional to the square of the observation time. This migration effect directly affects the distance measurement accuracy; in terms of the azimuth Doppler frequency modulation effect, the tangential motion of the target causes the instantaneous Doppler frequency of the echo signal to have time-varying characteristics, forming a Doppler frequency modulation effect, and the frequency modulation slope is proportional to the tangential velocity; the non-uniform motion causes the frequency modulation rate to show nonlinear changes, and the modulation depth is dynamically adjusted with the curvature of the motion trajectory, resulting in the frequency The spectrum is broadened and the azimuth parameter estimation accuracy is reduced; in terms of the signal envelope broadening effect caused by complex motion, the radial and tangential motion coupling produced by the three-dimensional motion of the target leads to dynamic changes in the scattering characteristics, the scattering center migrates with the change of attitude, and the electromagnetic scattering characteristics show obvious observation angle correlation; the target micro-motion modulation causes envelope fluctuations, and the complex motion trajectory may cause Doppler blurring; in terms of the influence of environmental factors, atmospheric propagation causes phase disturbances, the ionospheric scintillation effect produces signal modulation, the terrain and objects cause multipath propagation, and the propagation loss changes under different meteorological conditions will aggravate the degree of signal distortion; the combined effect of these environmental factors makes the signal distortion show complex time-varying characteristics. By establishing a multi-dimensional coupling mechanism analysis system, the quantitative mapping of motion parameters and signal distortion is realized, and the interaction law of distortion effects in each dimension is clarified; this systematic distortion analysis method provides a theoretical basis for the establishment of subsequent compensation models, and also provides a quantitative basis for evaluating the compensation effect.

[0121] Example 2, reference Figure 2-Figure 3 , which is the second embodiment of the present invention, this embodiment also provides an independent positioning and navigation system based on synthetic aperture radar, including:

[0122] The signal reconstruction module is used to collect echo signals using synthetic aperture radar, and perform sparse reconstruction processing on the echo signals through a double-layer sparse reconstruction unit to obtain a reconstructed and restored signal;

[0123] The compensation evaluation module is used to input the reconstructed restoration signal into the Kalman filter to estimate the platform motion parameters and construct the motion compensation parameter matrix;

[0124] The signal compensation module is used to perform dynamic compensation processing on the reconstructed restoration signal according to the motion compensation parameter matrix and output the target positioning parameters.

[0125] This embodiment also provides a computer device, which may be a terminal, and its internal structure diagram may be as shown in FIG. Figure 3As shown. The computer device includes a processor, a memory, a communication interface, a display screen and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, NFC (near field communication) or other technologies. When the computer program is executed by the processor, a non-supported positioning and navigation system based on synthetic aperture radar is realized. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, or a button, trackball or touchpad set on the computer device shell, or an external keyboard, touchpad or mouse, etc.

[0126] This embodiment further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:

[0127] The synthetic aperture radar is used to collect echo signals, and the echo signals are sparsely reconstructed through a double-layer sparse reconstruction unit to obtain a reconstructed and restored signal;

[0128] The reconstructed signal is input into the Kalman filter to estimate the platform motion parameters and construct the motion compensation parameter matrix;

[0129] The reconstructed signal is dynamically compensated according to the motion compensation parameter matrix and the target positioning parameters are output.

[0130] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

[0131] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The schemes in the embodiments of the present application may be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0132] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0133] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0134] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0135] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0136] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A non-supported positioning and navigation system based on synthetic aperture radar, characterized in that: The following steps are included: Using synthetic aperture radar to collect echo signals, and performing sparse reconstruction processing on the echo signals through a double-layer sparse reconstruction unit to obtain a reconstructed restoration signal; Inputting the reconstructed restoration signal into a Kalman filter to estimate platform motion parameters and construct a motion compensation parameter matrix; Performing dynamic compensation processing on the reconstructed restoration signal according to the motion compensation parameter matrix, and outputting target positioning parameters; The motion compensation process comprises: Compensate for the range unit migration effect caused by target motion, the Doppler frequency modulation effect in azimuth, and the signal envelope broadening effect caused by complex motion; Establish a mapping relationship between target motion and signal distortion; The compensation parameter matrix is ​​used to correct the original signal and output the target positioning parameters. The calculation formula is as follows: ； Among them, ξ is the time series index of compensation processing, is the target positioning parameter after multi-dimensional compensation, is the compensation weight coefficient of each dimension, is the compensation matrix of each dimension, To reconstruct the restored signal, is the Doppler frequency, is the time delay factor, is the reference signal power, is the current signal power, For three dimensions, the distance dimension , Azimuth dimension , Doppler dimension .

2. The independent positioning and navigation system based on synthetic aperture radar as claimed in claim 1, characterized in that: The collecting of echo signals comprises: Synthetic aperture radar is used to transmit detection signals to the target area and receive echo signals reflected by the target; Convert the echo signal into a digital baseband signal through a high-speed analog-to-digital converter, and perform noise reduction preprocessing on the digital baseband signal; The echo signal includes: an interference echo signal, a target echo signal and a noise signal; wherein the interference echo signal includes ground clutter echo, meteorological clutter echo and electromagnetic interference signal, the target echo signal includes the main lobe echo signal and the side lobe echo signal of the target, and the noise signal includes thermal noise inside the radar system and external environmental noise; The characteristics of the target echo signal include: signal amplitude characteristics, frequency characteristics, phase characteristics, polarization characteristics and Doppler characteristics; the signal amplitude characteristics are used to characterize the size of the target reflection cross-sectional area; the frequency characteristics are used to characterize the radial motion speed of the target; the phase characteristics are used to characterize the spatial position information of the target; the polarization characteristics are used to characterize the geometric shape and material properties of the target; the Doppler characteristics are used to characterize the motion state of the target; The characteristics of the interference echo signal include: random fluctuation characteristics, spatial distribution characteristics, spectrum characteristics and time-varying characteristics; the random fluctuation characteristics are used to express the random changes in signal amplitude and phase; the spatial distribution characteristics are used to express the distribution law of the interference source in space; the spectrum characteristics are used to express the energy distribution of the interference signal in the frequency domain; the time-varying characteristics are used to express the change law of the interference signal intensity over time.

3. The independent positioning and navigation system based on synthetic aperture radar as claimed in claim 2, characterized in that: The sparse reconstruction process includes: Based on the signal energy to noise variance ratio and the signal amplitude to noise standard deviation criteria, marking the signal segment that meets the criteria as a valid signal segment; Constructing a measurement matrix based on orthogonal basis functions, applying the measurement matrix to a valid signal segment for compression sampling, and obtaining a sampled signal after dimensionality reduction; Constructing a three-dimensional tensor structure to perform multi-dimensional reorganization on the sampled signal, wherein the three-dimensional tensor structure consists of a distance dimension, an azimuth dimension, and a Doppler dimension; Calculating a proportional relationship between a tensor rank of the three-dimensional tensor and a minimum dimension value, and when the tensor rank is less than one third of the minimum dimension value, performing a core tensor decomposition operation on the three-dimensional tensor to obtain a core tensor and three factor matrices; The core tensor and factor matrix obtained by the tensor decomposition operation are used to restore the signal through a signal reconstruction model to obtain a reconstructed and restored signal.

4. The independent positioning and navigation system based on synthetic aperture radar as claimed in claim 3, characterized in that: The obtained core tensor and three factor matrices include, Constructing a three-dimensional tensor structure to perform multi-dimensional reorganization on the sampled signal, wherein the three-dimensional tensor structure consists of a distance dimension, an azimuth dimension, and a Doppler dimension; The multi-dimensional reorganization includes distance dimension reorganization, azimuth dimension reorganization and Doppler dimension reorganization; the distance dimension reorganization divides the sampling interval based on the distance resolution of the radar system, and arranges the sampling data of each range gate into a distance vector; the azimuth dimension reorganization divides the sampling interval based on the angle increment of the antenna rotation, and arranges the sampling data of different azimuth angles into an azimuth vector; the Doppler dimension reorganization divides the sampling interval based on the inverse of the pulse repetition period, and arranges the sampling data at different times into a Doppler vector; The proportional relationship between the tensor rank and the minimum dimension value of the three-dimensional tensor is calculated. When the tensor rank is less than one third of the minimum dimension value, the low rank property is satisfied. The core tensor decomposition operation is performed on the three-dimensional tensor that satisfies the low rank condition to obtain a core tensor and three factor matrices.

5. The independent positioning and navigation system based on synthetic aperture radar as claimed in claim 4, characterized in that: The satisfying the low-rank property comprises: extracting distance dimension value, azimuth dimension value and Doppler dimension value from the structure of the three-dimensional tensor, and selecting the minimum dimension value therefrom; Expand the three-dimensional tensor into matrices along three dimensions to obtain three expanded matrices; Compute the singular values ​​of the three unfolded matrices; Count the number of singular values ​​in each unfolded matrix that are greater than a given threshold; The maximum number of valid singular values ​​of the three unfolded matrices is defined as the tensor rank; Calculate the ratio of the tensor rank to the minimum dimension value. When the ratio is less than one-third, the three-dimensional tensor satisfies the low-rank property. The expansion matrix includes a distance dimension expansion matrix, an azimuth dimension expansion matrix and a Doppler dimension expansion matrix; The execution of core tensor decomposition includes: establishing a Tucker decomposition model and initializing three factor matrices; The core tensor is calculated by iterative optimization using the alternating least squares method; Extract the main elements from the core tensor as signal features; The Tucker decomposition model is established to represent a three-dimensional tensor as the product of a core tensor and three factor matrices; Initialize the three factor matrices by performing singular value decomposition on the three unfolded matrices respectively, and take the first R left singular vectors as the initial factor matrix; By using the alternating least squares method to iterate and fix two factor matrices, the third factor matrix is ​​updated; the three factor matrices are updated cyclically until convergence; The calculation of the core tensor is to project the original tensor into the space formed by three factor matrices. The calculation formula is as follows: ； in, is the position in the core tensor The elements at is the index of the distance dimension, is the index of the orientation dimension, is the index of the Doppler dimension, is the position in the original three-dimensional tensor The elements at is the index of the original distance dimension, is the index of the original orientation dimension, is the index of the original Doppler dimension, is the element in the dth row and ith column of the distance dimension factor matrix, is the element in the ath row and jth column of the orientation dimension factor matrix, is the element in the mth row and kth column of the Doppler dimension factor matrix, is the distance dimension size of the original tensor, is the azimuth dimension of the original tensor, is the Doppler dimension size of the original tensor.

6. The independent positioning and navigation system based on synthetic aperture radar as claimed in claim 5, characterized in that: The constructing of the motion compensation parameter matrix comprises: A relative motion relationship model between the radar platform and the target is established based on the target motion state vector; A motion compensation parameter matrix is ​​constructed through a line of sight angle change rate matrix, wherein the motion compensation parameter matrix includes a distance dimension compensation coefficient, an azimuth dimension compensation coefficient, and a Doppler dimension compensation coefficient.

7. The independent positioning and navigation system based on synthetic aperture radar according to any one of claims 1 to 6, characterized in that: Also includes, The signal reconstruction module is used to collect echo signals using synthetic aperture radar, and perform sparse reconstruction processing on the echo signals through a double-layer sparse reconstruction unit to obtain a reconstructed restoration signal; The compensation evaluation module is used to input the reconstructed restoration signal into the Kalman filter to estimate the platform motion parameters and construct a motion compensation parameter matrix; The signal compensation module is used to perform dynamic compensation processing on the reconstructed restoration signal according to the motion compensation parameter matrix and output target positioning parameters.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the independent positioning and navigation system based on synthetic aperture radar as described in any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the independent positioning and navigation system based on synthetic aperture radar as described in any one of claims 1 to 6 are implemented.

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