Target three-dimensional positioning method and system based on compressed sensing

Abstract

The invention provides a target three-dimensional positioning method and system based on compressed sensing. The method comprises the steps that S1, parameter initialization setting is conducted on all radio stations; s2, performing compressed sampling on the transmission signal by using an AIC compressed sampling method to obtain a compressed signal; s3, reconstructing the compressed signal by adopting a matching pursuit and sparse reconstruction algorithm to obtain a frequency domain signal, and performing Fourier inversion on the frequency domain signal to obtain a time domain signal after the sampling rate is recovered; and S4, based on the time domain signal after sampling rate recovery, obtaining a target position estimation result of the signal, and finally obtaining 3D positioning of the target through a TDOA distance measurement method.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a method and system for three-dimensional target positioning based on compressed sensing. Background Art

[0002] As an important military communication equipment, radio is of great significance in military communication and communication under special environment. Due to the complexity and diversity of battlefield communication requirements, traditional radio communication systems face huge challenges in spectrum utilization, network adaptability and anti-interference ability. Relatively high-dimensional original signals and other characteristics.

[0003] According to the Nyquist sampling theorem, traditional signal processing requires a sampling rate that is more than twice the highest frequency of the original signal. However, in the face of increasingly tight spectrum resources and the trend of increasing signal bandwidth, in order to restore the original signal, a large amount of sampled data needs to be obtained. The high sampling rate will place extremely high demands on the hardware conditions of existing equipment. But in fact, for some specific signals, complete data acquisition is unnecessary.

[0004] Sheng Jinfeng, Li Ning, Guo Yan, Chen Cheng, Li Huajing, Journal of University of Chinese Academy of Sciences, Passive multi-target positioning method based on phase offset based on compressed sensing, is a passive positioning method based on phase offset designed under the framework of compressed sensing, with the phase offset value of the received signal as the observation data, but the final positioning effect is only two-dimensional, which has no application capability in the actual real environment;

[0005] Zuo Xunhe, Wang Zixiong, Ma Chuang, Yu Jinlong, and Jiang Yang, Journal of Chongqing University of Posts and Telecommunications, Performance analysis of integrated visible light communication and positioning system based on compressed sensing, is to use OMP reconstruction algorithm for compressed sensing in OFDM system, combined with TOA algorithm, to achieve integrated visible light communication and positioning.

[0006] Zhang Yang and Qin Ningning, Journal of Sensor Technology, The fingerprint information density condensation positioning algorithm integrated with compressed sensing is a fusion of compressed sensing and fingerprint positioning technology, which has significant value in indoor positioning.

[0007] "Xi'an University of Electronic Science and Technology", the frequency domain sparse compression and recovery technology of monitoring data for TDOA positioning is based on a distributed radar system as a model, uses dual-satellite time-frequency difference for joint positioning, and makes full use of the frequency domain sparse compression method of positioning perception data to estimate the time difference and frequency difference, and finally obtains the target positioning.

[0008] In view of the tight spectrum resources in battlefield environments and the urgent need for accurate timing and positioning, the existing technology lacks corresponding technical methods, and the positioning results obtained are of poor accuracy and high algorithm complexity. Summary of the invention

[0009] In view of the defects in the prior art, the object of the present invention is to provide a method and system for three-dimensional target positioning based on compressed sensing.

[0010] A method for three-dimensional positioning of a target based on compressed sensing provided by the present invention includes:

[0011] Step S1: Initialize parameters for all radio stations;

[0012] Step S2: using the AIC compression sampling method to compress and sample the transmission signal to obtain a compressed signal;

[0013] Step S3: reconstructing the compressed signal using matching pursuit and sparse reconstruction algorithms to obtain a frequency domain signal, and performing inverse Fourier transform on the frequency domain signal to obtain a time domain signal after sampling rate recovery;

[0014] Step S4: Based on the time domain signal after sampling rate recovery, the target position estimation result of the signal is obtained, and the 3D positioning of the target is finally obtained through the TDOA ranging method.

[0015] Preferably, the step S2 comprises:

[0016] Step S2.1: The signal to be detected x t (n) and the pseudo-random sampling signal p c (t) is multiplied to obtain the modulated signal;

[0017] Step S2.2: low-pass filter the modulated signal through an integrator to obtain a processed signal;

[0018] Step S2.3: The processed signal is sampled at a rate lower than the Nyquist sampling rate to obtain a compressed sampling signal y t (n).

[0019] Preferably, the step S2 comprises:

[0020] y t (n) = Φx t (n)

[0021] Among them, x t (n) is a sparse vector of dimension N×1, which represents the sampled signal obtained by sampling at the Nyquist sampling rate; y t (n) is M×1, indicating a compressed sampling signal; Φ is an M×N (M<<N) dimensional compressed sampling matrix.

[0022] Preferably, step S3 comprises:

[0023] Step S3.1: Convert the compressed signal y in the time domain t (n) Perform Fourier transform to obtain the spectrum representation y of the compressed signalt (f);

[0024] Step S3.2: Divide the spectrum representation of the compressed signal into frequency bands to generate a dictionary matrix [y t (f)]

[0025] Step S3.3: Use matching pursuit and sparse reconstruction algorithm to reconstruct the dictionary matrix [y t (f)] to obtain the reconstructed signal and the frequency domain signal x after sampling rate recovery. t (f);

[0026] Step S3.4: Restore the sampling rate to the frequency domain signal x t (f) Perform Fourier transform to obtain a time domain signal after sampling rate recovery, wherein the time domain signal after sampling rate recovery is a sampling signal x at the Nyquist sampling rate. t (n).

[0027] Preferably, the step S3.3 comprises: converting the dictionary matrix [y t (f)] Based on the matching pursuit and sparse reconstruction algorithm, after two iterations, including: the first iteration convolves the observed data with the current estimated sparse vector to obtain the reconstructed signal, and then calculates the residual between the observed signal and the reconstructed signal; the second iteration uses the least squares method to solve the optimization problem, updates the estimated sparse vector, and obtains the frequency domain signal x after the sampling rate is restored t (f);

[0028] The sparse representation signal s can be reconstructed by solving the following l0-norm convex optimization problem. By solving the l0-norm optimization problem, a sparse solution is obtained:

[0029]

[0030] stΦΨs=y

[0031] Because of y t (n) = Φx t (n), so x=Ψs

[0032] Among them, y represents the dictionary matrix in the frequency domain [y t (f)]; ||s||1 represents the l0 norm of the sparse representation signal s, and the definition of ||s||1 is as follows:

[0033]

[0034] x=Ψs

[0035] Wherein, s is an N×1 dimensional vector, representing the sparse representation of the Nyquist sampling signal x in the frequency domain under the sparse representation matrix Ψ, and the number of non-zero elements is Ls×N; finally, the Nyquist sampling signal X in the frequency domain is obtained.

[0036] Preferably, the step S4 adopts:

[0037] Step S4.1: Based on the time domain signal after sampling rate recovery, calculate each anchor node (x i ,y i ,z i ) to the target node (x,y,z) i and the distance difference R i ;

[0038] R i =t i ×c

[0039] Where c represents the speed of light;

[0040] Step S4.2: 3D modeling using TDOA method;

[0041]

[0042] Step S4.3: Use the Chan algorithm to solve and obtain the positioning result (x, y, z) of the target node.

[0043] A target three-dimensional positioning system based on compressed sensing provided by the present invention includes:

[0044] Module M1: Initialize parameters for all radio stations;

[0045] Module M2: Use the AIC compression sampling method to compress the transmission signal to obtain a compressed signal;

[0046] Module M3: Use matching pursuit and sparse reconstruction algorithms to reconstruct the compressed signal to obtain the frequency domain signal, and perform inverse Fourier transform on the frequency domain signal to obtain the time domain signal after the sampling rate is restored;

[0047] Module M4: Based on the time domain signal after sampling rate recovery, the target position estimation result of the signal is obtained, and the 3D positioning of the target is finally obtained through the TDOA ranging method.

[0048] Preferably, the module M2 comprises:

[0049] Module M2.1: The signal to be detected x t (n) and the pseudo-random sampling signal p c (t) is multiplied to obtain the modulated signal;

[0050] Module M2.2: low-pass filter the modulated signal through an integrator to obtain a processed signal;

[0051] Module M2.3: The processed signal is sampled at a rate lower than the Nyquist sampling rate to obtain a compressed sampling signal y t (m); the module M2 comprises:

[0052] y t (n) = Φx t (n)

[0053] Among them, x t (n) is a sparse vector of dimension N×1, which represents the sampled signal obtained by sampling at the Nyquist sampling rate; y t (n) is M×1, indicating a compressed sampling signal; Φ is an M×N (M<<N) dimensional compressed sampling matrix.

[0054] Preferably, the module M3 comprises:

[0055] Module M3.1: Convert the compressed signal y in the time domain t (n) Perform Fourier transform to obtain the spectrum representation y of the compressed signal t (f);

[0056] Module M3.2: Divide the spectrum representation of the compressed signal into frequency bands to generate a dictionary matrix [y t (f)]

[0057] Module M3.3: Reconstruct the dictionary matrix [y t (f)] to obtain the reconstructed signal and the frequency domain signal x after sampling rate recovery. t (f);

[0058] Module M3.4: Restore the sampling rate to the frequency domain signal x t (f) Perform Fourier transform to obtain a time domain signal after sampling rate recovery, wherein the time domain signal after sampling rate recovery is a sampling signal x at the Nyquist sampling rate. t (n);

[0059] The module M3.3 includes: converting the dictionary matrix [y t (f)] Based on the matching pursuit and sparse reconstruction algorithm, after two iterations, including: the first iteration convolves the observed data with the current estimated sparse vector to obtain the reconstructed signal, and then calculates the residual between the observed signal and the reconstructed signal; the second iteration uses the least squares method to solve the optimization problem, updates the estimated sparse vector, and obtains the frequency domain signal x after the sampling rate is restored t (f);

[0060] The sparse representation signal s can be reconstructed by solving the following l0-norm convex optimization problem. By solving the l0-norm optimization problem, a sparse solution is obtained:

[0061]

[0062] stΦΨs=y

[0063] Because of y t (n) = Φx t (n), so x=Ψs

[0064] Among them, y represents the dictionary matrix in the frequency domain [y t (f)]; ||s||1 represents the l0 norm of the sparse representation signal s, and the definition of ||s||1 is as follows:

[0065]

[0066] x=Ψs

[0067] Wherein, s is an N×1 dimensional vector, representing the sparse representation of the Nyquist sampling signal x in the frequency domain under the sparse representation matrix Ψ, and the number of non-zero elements is Ls×N; finally, the Nyquist sampling signal X in the frequency domain is obtained.

[0068] Preferably, the module M4 adopts:

[0069] Module M4.1: Based on the time domain signal after sampling rate recovery, calculate each anchor node (x i ,y i ,z i ) to the target node (x,y,z) i and the distance difference R i ;

[0070] R i =t i ×c

[0071] Where c represents the speed of light;

[0072] Module M4.2: Three-dimensional modeling using TDOA method;

[0073]

[0074] Module M4.3: Use the Chan algorithm to solve and obtain the positioning result (x, y, z) of the target node.

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] 1. The present invention uses both compressed sensing technology and delay information to measure the distance and locate the target, which improves the spectrum utilization of the signal compared with the traditional positioning technology;

[0077] 2. The present invention improves the accuracy of positioning and greatly reduces the amount of data to be processed and transmitted by the target node radio station, which has forward-looking significance for future broadband battlefields;

[0078] 3. The transition from traditional narrowband signals to broadband transmission signals in modern battlefields brings pressure on the target radio station to receive a large amount of data transmitted from each anchor node. At the same time, high-speed sampling brings practical problems such as excessive sampling data redundancy, wasted hardware system resources and expensive high-speed sampling receiver costs. For this reason, the present invention uses a compressed sensing algorithm to compress the original sampling signal to reduce the amount of transmitted data;

[0079] 4. Different from the traditional narrowband compressed sensing dictionary matrix, the present invention performs Fourier transform on the received broadband compressed signal and generates a dictionary matrix by frequency band, which can solve the problem that the traditional narrowband transmission signal cannot be applied to the current broadband signal positioning;

[0080] 5. The present invention provides a timing positioning technology based on compressed sensing, which combines the signal delay information of the radio station and specific compressed sensing features to improve the accuracy of position measurement and reduce the complexity of the algorithm;

[0081] 6. Compared with the traditional ranging positioning method, the present invention has higher frequency efficiency and spectrum utilization, and can more accurately estimate the location information of the target while reducing the complexity of the positioning algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0083] Figure 1 This is a flow chart of the target three-dimensional positioning method based on compressed sensing.

[0084] Figure 2 This is the AIC compression sampling flow chart.

[0085] Figure 3 Reconstruct the flow graph for the compressed signal.

[0086] Figure 4 This is the flow chart of the three-dimensional positioning algorithm. DETAILED DESCRIPTION

[0087] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0088] Example 1

[0089] According to the present invention, a method and system for three-dimensional target positioning based on compressed sensing includes: using a radio station to realize signal transmission and reception, wherein the transmitted signal is a narrowband signal that is not easily detected on the battlefield; however, with the development of modern information warfare, broadband radio stations have become an increasingly obvious trend; the signal has the following characteristics, by constructing a joint coefficient positioning model, sparsely representing the transmitted signal, selecting a measurement matrix to compress the sparse signal, and obtaining a subsequent compressed signal. After receiving the signal, a sparse reconstruction algorithm is used to reconstruct the compressed signal to obtain a preliminary constructed original signal. The target position estimation result and sparse vector estimation result of the signal are obtained therein, and the 3D positioning of the target is finally obtained through the TDOA ranging method.

[0090] The target three-dimensional positioning method based on compressed sensing is as follows: Figure 1 As shown, including:

[0091] Step 1: Initialize parameters for all radio stations and debug sending and receiving signals;

[0092] Step 2: All anchor node radio stations receive and record the signal from the target node radio station;

[0093] Step 3: Use the AIC compression sampling method to compress and sample the received analog signal;

[0094] Step 3 is as follows Figure 2 As shown, the following steps are included:

[0095] Step 3.1: Set the signal to be detected x t (n) and the pseudo-random sampling signal p c (t) is multiplied to obtain the modulated signal;

[0096] Step 3.2: low-pass filter the modulated signal through an integrator to obtain a processed signal;

[0097] Step 3.3: The processed signal is sampled at a rate lower than the Nyquist sampling rate to obtain the compressed sampling signal y t (n);

[0098] The above specific implementation process is expressed by the calculation formula: The mathematical representation of AIC compression sampling is as follows:

[0099] y t (n) = Φx t (n)

[0100] Among them, x t (n) is an N×1-dimensional sparse vector, representing the sampled signal obtained by sampling at the Nyquist sampling rate. t (n) is M×1, indicating a compressed sampling signal. Φ is a compressed sampling matrix of M×N (M<<N) dimensions. In order to ensure that effective delay information of the signal can be obtained from the compressed signal for subsequent positioning, Φ uses the Hadamard compression matrix, which is originally an N×N square matrix consisting of only ±1. The rows of the matrix are orthogonal to each other, and an M×N (M<<N) matrix consisting of M rows of elements is selected from it.

[0101] Step 4: Matching pursuit and sparse signal reconstruction algorithm, the algorithm flow is as follows Figure 3 As shown, the following steps are included:

[0102] Step 4.1: Receive the compressed sampled signal y t (n), and perform Fourier transform on the signal into the frequency domain.

[0103] Step 4.2: Generate a dictionary matrix by frequency band. The dictionary matrix includes a matrix of multiple basis vectors, and each basis vector includes the delay information of the signal.

[0104] Step 4.3: Solving equations (4) and (5) through matching pursuit and sparse signal reconstruction algorithm requires two iterations: the first iteration convolves the observed data with the current estimated sparse vector to obtain the reconstructed signal, and then calculates the residual between the observed signal and the reconstructed signal; the second iteration uses the least squares method to solve the optimization problem, updates the estimated sparse vector, and obtains the frequency domain signal after the sampling rate is restored.

[0105] Therefore, the whole process can be understood as reconstructing the Nyquist sampling signal x from the compressed sampling signal y as a problem of solving an underdetermined equation.

[0106] The sparse representation signal s can be reconstructed by solving the following l0-norm convex optimization problem. By solving the l0-norm optimization problem, a sparse solution is obtained:

[0107]

[0108] stΦΨs=y(4)

[0109] Because of y t (n) = Φx t(n), so x=Ψs

[0110] Among them, y represents the dictionary matrix in the frequency domain [y t (f)]; ||s||1 represents the l0 norm of the sparse representation signal s, and the definition of ||s||1 is as follows:

[0111]

[0112] x=Ψs

[0113] Wherein, s is an N×1 dimensional vector, representing the sparse representation of the Nyquist sampling signal x under the sparse representation matrix Ψ, and the number of non-zero elements is Ls×N.

[0114] Step 4.4: Perform inverse Fourier transform on the solved frequency domain signal to convert it into a time domain signal after the sampling rate is restored.

[0115] Step 5: The data center of the edge node radio station uses the recovered time domain signal to calculate the 3D positioning algorithm. The specific process is as follows: Figure 4 shown.

[0116] Step 5.1: The data center of the edge node radio uses the time domain signal recovered in step 4.

[0117] Step 5.2: Calculate each anchor node (x i ,y i ,z i ) to the target node (x,y,z) i and the distance difference R i . Where c is the speed of light, as shown in equation (6).

[0118] R i =t i ×c (6)

[0119] Step 5.3: Use TDOA method to perform three-dimensional modeling. The simultaneous equations are as follows:

[0120]

[0121] Step 5.4: Use Chan algorithm to solve equation (7) and obtain the positioning result (x, y, z) of the target node.

[0122] The present invention also provides a target three-dimensional positioning system based on compressed sensing. The target three-dimensional positioning system based on compressed sensing can be implemented by executing the process steps of the target three-dimensional positioning method based on compressed sensing, that is, those skilled in the art can understand the target three-dimensional positioning method based on compressed sensing as a preferred implementation of the target three-dimensional positioning system based on compressed sensing.

[0123] Example 2

[0124] Embodiment 2 is a preferred embodiment of Embodiment 1

[0125] The present invention provides a target three-dimensional positioning method based on compressed sensing. Assume that there are 4 wide-band radio stations as anchor nodes and the target edge node radio station as the measured radio station. The application scenarios include Gaussian and suburban areas. Here is the Gaussian scenario. The simulation parameters and positioning results are as follows:

[0126]

[0127]

[0128] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0129] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A three-dimensional target positioning method based on compressed sensing, characterized in that: include: Step S1: Initialize parameters for all radio stations; Step S2: using the AIC compression sampling method to compress and sample the transmission signal to obtain a compressed signal; Step S3: reconstructing the compressed signal using matching pursuit and sparse reconstruction algorithms to obtain a frequency domain signal, and performing inverse Fourier transform on the frequency domain signal to obtain a time domain signal after sampling rate recovery; Step S4: Based on the time domain signal after sampling rate recovery, the target position estimation result of the signal is obtained, and the 3D positioning of the target is finally obtained through the TDOA ranging method.

2. The method for three-dimensional target positioning based on compressed sensing according to claim 1, characterized in that: The step S2 comprises: Step S2.1: The signal to be detected x t (n) and the pseudo-random sampling signal p c (t) is multiplied to obtain the modulated signal; Step S2.2: low-pass filter the modulated signal through an integrator to obtain a processed signal; Step S2.3: The processed signal is sampled at a rate lower than the Nyquist sampling rate to obtain a compressed sampling signal y t (m).

3. The method for three-dimensional target positioning based on compressed sensing according to claim 1, characterized in that: The step S2 comprises: y t (n)=Φx t (n) Among them, x t (n) is a sparse vector of dimension N×1, which represents the sampled signal obtained by sampling at the Nyquist sampling rate; y t (n) is M×1, indicating a compressed sampling signal; Φ is an M×N (M<<N) dimensional compressed sampling matrix.

4. The method for three-dimensional target positioning based on compressed sensing according to claim 1, characterized in that: The step S3 comprises: Step S3.1: Convert the compressed signal y in the time domain t (n) Perform Fourier transform to obtain the spectrum representation y of the compressed signal t (f); Step S3.2: Divide the spectrum representation of the compressed signal into frequency bands to generate a dictionary matrix [y t (f)] Step S3.3: Use matching pursuit and sparse reconstruction algorithm to reconstruct the dictionary matrix [y t (f)] to obtain the reconstructed signal and the frequency domain signal x after sampling rate recovery. t (f); Step S3.4: Restore the sampling rate to the frequency domain signal x t (f) Perform Fourier transform to obtain a time domain signal after sampling rate recovery, wherein the time domain signal after sampling rate recovery is a sampling signal x at the Nyquist sampling rate. t (n).

5. The method for three-dimensional target positioning based on compressed sensing according to claim 4, characterized in that: The step S3.3 comprises: converting the dictionary matrix [y t (f)] Based on the matching pursuit and sparse reconstruction algorithm, after two iterations, including: the first iteration convolves the observed data with the current estimated sparse vector to obtain the reconstructed signal, and then calculates the residual between the observed signal and the reconstructed signal; the second iteration uses the least squares method to solve the optimization problem, updates the estimated sparse vector, and obtains the frequency domain signal x after the sampling rate is restored t (f); The sparse representation signal s can be reconstructed by solving the following l0-norm convex optimization problem. By solving the l0-norm optimization problem, a sparse solution is obtained: stΦΨs=y Because of y t (n) = Φx t (n), so x=Ψs Among them, y represents the dictionary matrix in the frequency domain [y t (f)]; ||s||1 represents the l0 norm of the sparse representation signal s, and the definition of ||s||1 is as follows: x=Ψs Wherein, s is an N×1 dimensional vector, representing the sparse representation of the Nyquist sampling signal x in the frequency domain under the sparse representation matrix Ψ, and the number of non-zero elements is Ls×N; finally, the Nyquist sampling signal X in the frequency domain is obtained.

6. The method for three-dimensional target positioning based on compressed sensing according to claim 1, characterized in that: The step S4 adopts: Step S4.1: Based on the time domain signal after sampling rate recovery, calculate each anchor node (x i ,y i ,z i ) to the target node (x,y,z) i and the distance difference R i ; R i =t i ×c Where c represents the speed of light; Step S4.2: 3D modeling using TDOA method; Step S4.3: Use the Chan algorithm to solve and obtain the positioning result (x, y, z) of the target node.

7. A three-dimensional target positioning system based on compressed sensing, characterized in that: include: Module M1: Initialize parameters for all radio stations; Module M2: Use the AIC compression sampling method to compress the transmission signal to obtain a compressed signal; Module M3: Use matching pursuit and sparse reconstruction algorithms to reconstruct the compressed signal to obtain the frequency domain signal, and perform inverse Fourier transform on the frequency domain signal to obtain the time domain signal after the sampling rate is restored; Module M4: Based on the time domain signal after sampling rate recovery, the target position estimation result of the signal is obtained, and the 3D positioning of the target is finally obtained through the TDOA ranging method.

8. The target three-dimensional positioning system based on compressed sensing according to claim 7, characterized in that: The module M2 comprises: Module M2.1: The signal to be detected x t (n) and the pseudo-random sampling signal p c (t) is multiplied to obtain the modulated signal; Module M2.2: low-pass filter the modulated signal through an integrator to obtain a processed signal; Module M2.3: The processed signal is sampled at a rate lower than the Nyquist sampling rate to obtain a compressed sampling signal y t (m); The module M2 comprises: y t (n)=Φx t (n) Among them, x t (n) is a sparse vector of dimension N×1, which represents the sampled signal obtained by sampling at the Nyquist sampling rate; y t (n) is M×1, indicating a compressed sampling signal; Φ is an M×N (M<<N) dimensional compressed sampling matrix.

9. The target three-dimensional positioning system based on compressed sensing according to claim 7, characterized in that: The module M3 comprises: Module M3.1: Convert the compressed signal y in the time domain t (n) Perform Fourier transform to obtain the spectrum representation y of the compressed signal t (f); Module M3.2: Divide the spectrum representation of the compressed signal into frequency bands to generate a dictionary matrix [y t (f)] Module M3.3: Reconstruct the dictionary matrix [y t (f)] to obtain the reconstructed signal and the frequency domain signal x after sampling rate recovery. t (f); Module M3.4: Restore the sampling rate to the frequency domain signal x t (f) Perform Fourier transform to obtain a time domain signal after sampling rate recovery, wherein the time domain signal after sampling rate recovery is a sampling signal x at the Nyquist sampling rate. t (n); The module M3.3 includes: converting the dictionary matrix [y t (f)] Based on the matching pursuit and sparse reconstruction algorithm, after two iterations, including: the first iteration convolves the observed data with the current estimated sparse vector to obtain the reconstructed signal, and then calculates the residual between the observed signal and the reconstructed signal; the second iteration uses the least squares method to solve the optimization problem, updates the estimated sparse vector, and obtains the frequency domain signal x after the sampling rate is restored t (f); The sparse representation signal s can be reconstructed by solving the following l0-norm convex optimization problem. By solving the l0-norm optimization problem, a sparse solution is obtained: stΦΨs=y Because of y t (n) = Φx t (n), so x=Ψs Among them, y represents the dictionary matrix in the frequency domain [y t (f)]; ||s||1 represents the l0 norm of the sparse representation signal s, and the definition of ||s||1 is as follows: x=Ψs Wherein, s is an N×1 dimensional vector, representing the sparse representation of the Nyquist sampling signal x in the frequency domain under the sparse representation matrix Ψ, and the number of non-zero elements is Ls×N; finally, the Nyquist sampling signal X in the frequency domain is obtained.

10. The target three-dimensional positioning system based on compressed sensing according to claim 7, characterized in that: The module M4 adopts: Module M4.1: Based on the time domain signal after sampling rate recovery, calculate each anchor node (x i ,y i ,z i ) to the target node (x,y,z) i and the distance difference R i ; R i =t i ×c Where c represents the speed of light; Module M4.2: Three-dimensional modeling using TDOA method; Module M4.3: Use the Chan algorithm to solve and obtain the positioning result (x, y, z) of the target node.

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