CN114384529A - Multi-base multi-target positioning method and system based on mobile platform - Google Patents

Abstract

The invention belongs to the technical field of underwater sound positioning, and particularly relates to a multi-base multi-target positioning method based on a mobile platform, which comprises the following steps: obtaining echo signals received by a plurality of moving receiving points AP to form an echo signal matrix, and establishing a sparse DPD vector signal model based on the echo signal matrix; constructing an optimized cost function related to target distribution according to the established sparse DPD vector signal model; and restoring the target distribution matrix according to the solution result of the optimization cost function to obtain a plurality of target distribution maps.

Description

Multi-base multi-target positioning method and system based on mobile platform

Technical Field

The invention belongs to the technical field of underwater sound positioning, and particularly relates to a multi-base multi-target positioning method and system based on a mobile platform.

Background

At present, an underwater vehicle is widely applied to various aspects such as marine rescue and salvage, deep sea resource investigation, marine oil exploitation, underwater engineering construction, military affairs and national defense construction, and huge economic benefits and social benefits are generated, so that the underwater vehicle has potential application prospects. With the development of the acoustic stealth technology, the working distance of sonar equipment is continuously reduced, and corresponding target echoes and noise intensity are reduced. The single-base sonar system has difficulty meeting the practical application requirements. Research has therefore utilized multiple bases such as: the cooperative working system of the underwater vehicle and the sea surface buoy has very important significance in improving the performance of the sonar system and improving the stability and the concealment of the system. The multi-base sonar system detects a target in a short distance through a transmitter arranged on an underwater vehicle, and a receiver is arranged in a protected area far away from the target, so that the system has a long detection distance, high precision and good concealment.

Target positioning is widely applied to military and civil fields, such as radar, sonar, wireless communication, satellites, airplanes and the like, and is always a hot point of research. In practical application, target positioning is affected by size, weight, power and cost constraints, and more rigorous requirements are put on a positioning algorithm. Positioning methods can be divided into two categories: the first type is generally called a two-step method, and in the first step Of the algorithm, parameters such as a Direction Of Arrival (DOA), Time Of Arrival (TOA), Time Difference Of Arrival (TDOA), Frequency Difference Of Arrival (FDOA), and Signal Strength (RSS) are estimated, and in the second step, the target position is determined using the estimated result. The two-step method positioning only needs to transmit the estimated parameters, so the algorithm is suitable for a system with small data transmission quantity, but has higher requirements on the parameter estimation precision of the first step in order to improve the positioning precision of the second step. Therefore, the first positioning method requires a very large signal storage space and has a mismatch problem in parameter allocation.

RSS-based localization indicates that a two-dimensional or three-dimensional region can be mapped to a target profile by dividing it into Grid Points (GPs) and assigning RSS parameters to each Grid point. The target distribution graph indicates the position and number of targets in the spatial dimension. The target points, which are only a small fraction of the target profile, may be considered sparse. However, the existing sparse positioning method takes parameters such as TOA, DOA, TDOA, RSS, etc. as measurement values, and does not directly utilize original signals, and although the sparse method has significant effects in noise suppression, multi-target identification, etc., the sparse method still has the disadvantages of large signal storage space and parameter allocation mismatch of the two-step positioning method. The second method directly estimates the target Position by using Access Points (APs) signals, and Weiss and Amar names this method as Direct Position estimation (DPD). The DPD method puts signal transmission pressure on the system, but because of the rich information of the echo signals and the lack of signal sorting and parameter matching problems, this kind of method can provide better positioning accuracy than the two-step method. However, in practical applications of the second type of algorithm, echo data may be interfered by false targets and other sources, and for a multifunctional detection system, the time allocated for positioning may be discontinuous, which results in short or discontinuous positioning time, and the accuracy of the current second type of positioning method is reduced due to the small data volume and discontinuous observation time.

Disclosure of Invention

In order to solve the defects in the prior art, the invention provides a multi-base multi-target positioning method based on a mobile platform, and the compensation and continuation of defect data are realized by the method, so that the positioning precision is improved; the method of the invention is used for constructing an optimized cost function, and the fast algorithm is used for optimizing and solving, so that the noise suppression function is realized. The method comprises the following steps:

obtaining echo signals received by a plurality of moving receiving points AP to form an echo signal matrix, and establishing a sparse DPD vector signal model based on the echo signal matrix;

constructing an optimized cost function related to target distribution according to the established sparse DPD vector signal model;

and restoring the target distribution matrix according to the solution result of the optimization cost function to obtain a plurality of target distribution maps.

As one improvement of the above technical solution, the echo signals received by the multiple moving receiving points AP are obtained to form an echo signal matrix, and a vector signal model is established based on the echo signal matrix; the method specifically comprises the following steps:

the M moving receiving points AP are distributed in a two-dimensional or three-dimensional area, and the area is divided into N units by a plurality of grid points GP; each moving receiving point AP receives a defective and incomplete echo signal;

the position and speed of the m-th moving receiving point AP are p_mAnd v_m，m＝1,2,…,M；

Q targets are randomly positioned on grid points GP;

echo signals are mutually transmitted among M moving receiving points AP through wired and wireless equipment, a time dimension transmitting signal is assumed to be s (t), and the echo signal s received by the M moving receiving point AP at the t moment is assumed to be s (t)_r,m(t) is:

wherein, a_m,qThe backscattering coefficient of the qth target to the mth AP direction; j is

n_m(t) additive white noise of the mth moving receiving point AP; tau is_m,qThe time delay between the qth target point and the mth moving receiving point AP is obtained;

τ_m,q＝2|p_m-g_q|/c (8)

wherein p is_mThe position of the receiving point AP for the mth movement; g_qIs the location of the qth target; c is the propagation speed of the transmitted signal;

ω_m,qis the doppler shift between the qth target point and the mth moving receiver point AP;

ω_m,q＝2πf_cv_m ^T·(p_m-g_q)/c|p_m-g_q| (9)

wherein f is_cIs the carrier frequency of the transmitted signal; v. of_m ^TThe velocity of the m-th moving receiving point AP;

when is given by f_s＝1/T_sAfter sampling as a sampling frequency, wherein T_sIs the sampling time; the signal model is established as

s_r,m＝Ψ_mD_mS_ma_m+n_m (10)

Wherein s is_r,mIs an echo signal matrix; Ψ_mA phase matrix which is an echo signal; d_mA time shift matrix for the echo signal; s_mIs a transmit signal matrix; a is_mA target distribution matrix is obtained; n is_mIs a white noise matrix;

based on the signal model, obtaining a plurality of echo signals correspondingly received by a plurality of moving receiving points AP to form an echo signal vector matrix, and based on the echo signal vector matrix, establishing a sparse DPD vector signal model:

S_r＝ΨDSA+N (11)

wherein S is_r＝[(s_r,1)^T,(s_r,2)^T,…,(s_r,m)^T,…,(s_r,M)^T]^T,S_r∈C^MK×1；

A＝[(a₁)^T,(a₂)^T,…,(a_m)^T,…,(a_M)^T]^T,A∈C^MN×1；

S＝diag{S₁,S₂,…,S_m,…,S_M},S∈C^MNK×MN；

D＝diag{D₁,D₂,…,D_m,…,D_M},D∈C^MNK×MNK；

Ψ＝diag{Ψ₁,Ψ₂,…,Ψ_m,…,Ψ_M},Ψ∈C^MK×MNK；

N＝[(n₁)^T,(n₂)^T,…,(n_m)^T,…,(n_M)^T]^T,N∈C^MK×1；

Wherein K is K_m；K_mThe number of sampling points of the echo signal received by the m-th moving receiving point AP.

As one improvement of the above technical solution, the optimization cost function about the target distribution is constructed according to the established vector signal model; the method specifically comprises the following steps:

according to the established sparse DPD vector signal model:

S_r＝ΨDSA+N (12)

let Θ be Ψ DS, the organized sparse DPD vector signal model is:

S_r＝ΘA+N

according to the sorted sparse DPD vector signal model, an optimized cost function is constructed:

wherein, J_ε(A) An objective function distributed for an epsilon-th object;

S′_r＝ZS_rdenotes a pair S_rOrthogonalizing; Θ' ═ Z Θ, meaning orthogonalizing Θ; rho is a sparse coefficient; a. the_EN(n)²＝|a₁(n)|²+|a₂(n)|²+…+|a_m(n)|²+…+|a_M(n)|²(ii) a E is 0.001 or 0.01.

As an improvement of the above technical solution, the target distribution matrix is restored according to a result of solving the optimization cost function to obtain a plurality of target distribution maps; the method specifically comprises the following steps:

according to the constructed optimization cost function:

wherein, J_ε(A) An objective function distributed for an epsilon-th object;

S′_r＝ZS_rdenotes a pair S_rOrthogonalizing; Θ' ═ Z Θ, meaning orthogonalizing Θ; rho is a sparse coefficient; a. the_EN(n)²＝|a₁(n)|²+|a₂(n)|²+…+|a_m(n)|²+…+|a_M(n)|²；∈＝0.001 or e is 0.01;

solving the optimization cost function by using a greedy algorithm of basis tracking, gradient tracking and orthogonal matching tracking; and obtaining a target distribution vector A, restoring the A to obtain a target distribution matrix, and further obtaining a plurality of target distribution maps to finish multi-target positioning.

The invention also provides a multi-base multi-target positioning system based on the mobile platform, which comprises the following components:

the model establishing module is used for obtaining echo signals received by a plurality of moving receiving points AP, forming an echo signal matrix and establishing a sparse DPD vector signal model based on the echo signal matrix;

the optimization function building module is used for building an optimization cost function related to target distribution according to the built sparse DPD vector signal model; and

and the data processing module is used for restoring the target distribution matrix according to the solution result of the optimization cost function to obtain a plurality of target distribution maps.

Compared with the prior art, the invention has the beneficial effects that:

the method directly utilizes the echo positioning of the receiving point without estimating intermediate parameters, avoids the signal sorting and parameter pairing processes required by the first positioning method of a two-step method, and can obtain a positioning result with higher precision under the condition of low signal-to-noise ratio; compared with the traditional direct positioning method, the mobile node data model is introduced, and the extension of the direct positioning method from a fixed node to a mobile node is realized; the target distribution sparsity is utilized, the defective observation data are recovered by jointly utilizing the echo information of the receiving points, and then a target distribution map is recovered, so that the problem of data defect is solved, the positioning accuracy is improved, and the noise is suppressed; the problem of overlarge data volume in a direct positioning algorithm is solved by using a quick algorithm.

Drawings

FIG. 1 is a flow chart of a multi-base multi-target positioning method based on a mobile platform according to the present invention;

FIG. 2 is a distribution diagram of AP and sampling points of a simulation experiment of a multi-base multi-target positioning method based on a mobile platform according to the present invention;

FIG. 3 is a distribution diagram of AP and targets of a simulation experiment of a multi-base multi-target positioning method based on a mobile platform according to the present invention;

FIG. 4 is a graph of MSE as a function of the number of APs for a multi-platform based positioning method embodying the present invention;

fig. 5 is a plot of MSE versus SNR for a positioning method of the present invention.

Detailed Description

The invention will now be further described with reference to the accompanying drawings.

As shown in fig. 1, the present invention provides a multi-base multi-target positioning method based on a mobile platform, which is a new mobile node target direct positioning method based on sparse prior; under the multi-platform target positioning environment, a compressed sensing principle is utilized to directly process target echo signals, and high-precision multi-target positioning is realized. In addition, the method of the invention realizes target positioning by utilizing multi-platform defect data, and realizes the improvement of positioning precision and noise suppression through data fusion. In order to enhance the positioning accuracy under the condition of irregular sampling, original echo signal information is utilized to solve the problem of counting the (| | A |)_2,1And (5) performing norm optimization, and recovering the target distribution diagram. The multi-base sparse direct positioning method can jointly utilize echo information of the receiving points, improve positioning accuracy and noise suppression capability, and can provide more accurate target positioning accuracy compared with a single-base method.

The method specifically comprises the following steps:

obtaining echo signals received by a plurality of moving receiving points AP to form an echo signal matrix, and establishing a sparse DPD vector signal model based on the echo signal matrix;

specifically, it is assumed that M moving receiving points AP are distributed in a two-dimensional or three-dimensional region, and the region is divided into N cells by a plurality of grid points GP; assuming that each moving receiving point AP receives a defective, incomplete echo signal;

the position and speed of the m-th moving receiving point AP are p_mAnd v_m(m＝1,2,…,M)；

Q targets are randomly positioned on GP; wherein the position of the target q is denoted as g_q；

Echo signals are mutually transmitted among M moving receiving points AP through wired and wireless equipment, a time dimension transmitting signal is assumed to be s (t), and the echo signal s received by the M moving receiving point AP at the t moment is assumed to be s (t)_r,m(t) is:

wherein, a_m,qThe backscattering coefficient of the qth target to the mth AP direction; j is

n_m(t) additive white noise of the mth moving receiving point AP; tau is_m,qThe time delay between the qth target point and the mth moving receiving point AP is obtained;

τ_m,q＝2|p_m-g_q|/c (14)

wherein p is_mThe position of the receiving point AP for the mth movement; g_qIs the location of the qth target; c is the propagation speed of the transmitted signal;

ω_m,qis the doppler shift between the qth target point and the mth moving receiver point AP;

ω_m,q＝2πf_cv_m ^T·(p_m-g_q)/c|p_m-g_q| (15)

wherein f is_cIs the carrier frequency of the transmitted signal; v. of_m ^TThe velocity of the m-th moving receiving point AP;

when is given by f_s＝1/T_sAfter sampling as a sampling frequency, wherein T_sIs the sampling time; the signal model is established as

s_r,m＝Ψ_mD_mS_ma_m+n_m (16)

Wherein s is_r,mIs an echo signal matrix; Ψ_mA phase matrix which is an echo signal; d_mA time shift matrix for the echo signal; s_mIs a transmit signal matrix; a is_mA target distribution matrix is obtained; n is_mIs a white noise matrix;

based on the signal model, obtaining echo signals received by a plurality of moving receiving points AP to form an echo signal vector matrix, and based on the echo signal vector matrix, establishing a sparse DPD vector signal model:

S_r＝ΨDSA+N (17)

wherein S is_r＝[(s_r,1)^T,(s_r,2)^T,…,(s_r,m)^T,…,(s_r,M)^T]^T,S_r∈C^MK×1；

A＝[(a₁)^T,(a₂)^T,…,(a_m)^T,…,(a_M)^T]^T,A∈C^MN×1；

S＝diag{S₁,S₂,…,S_m,…,S_M},S∈C^MNK×MN；

D＝diag{D₁,D₂,…,D_m,…,D_M},D∈C^MNK×MNK；

Ψ＝diag{Ψ₁,Ψ₂,…,Ψ_m,…,Ψ_M},Ψ∈C^MK×MNK；

N＝[(n₁)^T,(n₂)^T,…,(n_m)^T,…,(n_M)^T]^T,N∈C^MK×1；

Wherein K is K_m；K_mThe number of sampling points of the echo signal received by the m-th moving receiving point AP.

Constructing an optimized cost function related to target distribution according to the established sparse DPD vector signal model;

specifically, according to the established sparse DPD vector signal model:

S_r＝ΨDSA+N (18)

let Θ be Ψ DS, the organized sparse DPD vector signal model is:

S_r＝ΘA+N

according to the sorted sparse DPD vector signal model, an optimized cost function is constructed:

wherein, J_ε(A) An objective function distributed for an epsilon-th object;

S′_r＝ZS_rdenotes a pair S_rOrthogonalizing; Θ' ═ Z Θ, meaning orthogonalizing Θ; rho is a sparse coefficient; a. the_EN(n)²＝|a₁(n)|²+|a₂(n)|²+…+|a_m(n)|²+…+|a_M(n)|²(ii) a E is a smaller positive number, namely e is 0.001 or 0.01;

and restoring the target distribution matrix according to the solution result of the optimization cost function to obtain a plurality of target distribution maps.

Specifically, according to the constructed optimization cost function:

wherein, J_ε(A) An objective function distributed for an epsilon-th object;

S′_r＝ZS_rdenotes a pair S_rOrthogonalizing; Θ' ═ Z Θ, meaning orthogonalizing Θ; rho is a sparse coefficient; a. the_EN(n)²＝|a₁(n)|²+|a₂(n)|²+…+|a_m(n)|²+…+|a_M(n)|²(ii) a E is a smaller positive number, namely e is 0.001 or 0.01;

solving the optimization cost function by utilizing greedy algorithms such as basis tracking, gradient tracking, orthogonal matching tracking and the like; through solving, a target distribution vector A can be obtained, then the A is restored to the matrix to obtain a target distribution matrix, and then a plurality of target distribution maps are obtained to complete multi-target positioning.

The invention also provides a multi-base multi-target positioning system based on the mobile platform, which comprises the following components:

the model establishing module is used for obtaining echo signals received by a plurality of moving receiving points AP, forming an echo signal matrix and establishing a sparse DPD vector signal model based on the echo signal matrix;

the optimization function building module is used for building an optimization cost function related to target distribution according to the built sparse DPD vector signal model; and

and the data processing module is used for restoring the target distribution matrix according to the solution result of the optimization cost function to obtain a plurality of target distribution maps.

The derivation process for establishing the signal model is specifically as follows:

supposing that M moving receiving points AP are distributed in a two-dimensional or three-dimensional area, and the area is divided into N units by a plurality of grid points GP; assuming that each moving receiving point AP receives a defective, incomplete echo signal; the M moving receiving nodes are mobile and can be located at any position, and the target node is fixed and is located on a grid point GP;

the position and speed of the m-th moving receiving point AP are p_mAnd v_m(m＝1,2,…,M)；

Q targets are randomly positioned on GP; wherein the position of the target q is denoted as g_q；

Echo signals are mutually transmitted among M moving receiving points AP through wired and wireless equipment, a time dimension transmitting signal is assumed to be s (t), and the echo signal s received by the M moving receiving point AP at the t moment is assumed to be s (t)_r,m(t) is:

wherein, a_m,qBackward scattering of the qth target to the mth APA coefficient of radiation; j is

n_m(t) additive white noise of the mth moving receiving point AP; tau is_m,qThe time delay between the qth target point and the mth moving receiving point AP is obtained;

τ_m,q＝2|p_m-g_q|/c (20)

wherein p is_mThe position of the receiving point AP for the mth movement; g_qIs the location of the qth target; c is the propagation speed of the transmitted signal;

ω_m,qis the doppler shift between the qth target point and the mth moving receiver point AP;

ω_m,q＝2πf_cv_m ^T·(p_m-g_q)/c|p_m-g_q| (21)

wherein f is_cIs the carrier frequency of the transmitted signal; v. of_m ^TThe velocity of the m-th moving receiving point AP;

when is given by f_s＝1/T_sAfter sampling as a sampling frequency, wherein T_sIs the sampling time; the signal model is established as

s_r,m＝Ψ_mD_mS_ma_m+n_m (22)

Wherein s is_r,mIs an echo signal matrix; Ψ_mA phase matrix which is an echo signal; d_mA time shift matrix for the echo signal; s_mIs a transmit signal matrix; a is_mA target distribution matrix is obtained; n is_mIs a white noise matrix;

wherein the echo signal matrix is expressed as

s_r,m＝[s_r,m(1T_s),s_r,m(2T_s),…,s_r,m(lT_s),…,s_r,m(LT_s)]^T (23)

Since in a multifunction system the time allocated for positioning is discontinuous, the sampled echo signals may be discontinuous or incomplete.

Suppose that the discontinuous echo signal has H_mA fragment of which_mEach segment containing a sequence number w from the sample_m,hmTo the sampling sequence number w_m,hm+K_m,hmK of-1_m,hmSampling points;

non-consecutive sampling sequence

W_m＝[w_m,1,w_m,1+K_m,1-1]∪[w_m,2,w_m,2+K_m,2-1]∪…[w_m,Hm,w_m,Hm+K_m,Hm-1]。

Total number of discontinuous echo signal vectors is K_m＝K_m,1+K_m,2+...+K_m,Hm(K_m< L) sampling points; wherein, L is the number of sampling points of the complete echo signal vector;

discontinuous sampling sequence w_m∈W_m(ii) a Wherein, w_m＝[w_m(1),w_m(2),…,w_m(K_m)]；

Discontinuous echo signal s_r,mBecome a K_mVector of x 1:

s_r,m＝[s_r,m(w_m(1)T_s),s_r,m(w_m(2)T_s),…,s_r,m(w_m(K_m)T_s)]^T (24)

a_m＝[a_m,1,a_m,2,…,a_m,n,…,a_m,N]^T；

S_m＝diag{s_m,s_m,…,s_m},S_m∈C^KmN×N；

wherein C is a complex matrix space; s_m＝[s(w_m(1)T_s),s(w_m(2)T_s),…,s(w_m(K_m)T_s)]^T；

Wherein the block diagonal matrix is defined as

Wherein eta is K_m×K_mCan be defined as

Wherein ξ_m,n＝τ_m,n/T_sIs a power of the permutation matrix and is approximated as an integer; tau is_m,nIs the time delay between the m-th moving reception point AP and the n-th grid point GP.

Ψ_m＝[ψ_m,1,ψ_m,2,…,ψ_m,n,…,ψ_m,N]

Wherein the content of the first and second substances,

ψ_m,n＝diag{exp[jω_m,n(W_m(1)T_s)],exp[jω_m,n(W_m(2)T_s)],$$…,exp[jω_m,n(W_m(K_m)T_s)]}

n_m＝[n_m(1T_s),n_m(2T_s),…,n_m(lT_s),…,n_m(LT_s)]^T

based on the signal model, the specific derivation process for constructing the sparse DPD vector signal model is as follows:

based on the signal model, i.e. formula (4), a plurality of echo signals received by a plurality of moving receiving points AP are obtained to form an echo signal vector matrix S_rBased on the echo signal vector matrix S_rEstablishing a sparse DPD vector signal model:

S_r＝ΨDSA+N (28)

wherein S is_r＝[(s_r,1)^T,(s_r,2)^T,…,(s_r,m)^T,…,(s_r,M)^T]^T,S_r∈C^MK×1；

A＝[(a₁)^T,(a₂)^T,…,(a_m)^T,…,(a_M)^T]^T,A∈C^MN×1；

S＝diag{S₁,S₂,…,S_m,…,S_M},S∈C^MNK×MN；

D＝diag{D₁,D₂,…,D_m,…,D_M},D∈C^MNK×MNK；

Ψ＝diag{Ψ₁,Ψ₂,…,Ψ_m,…,Ψ_M},Ψ∈C^MK×MNK；

N＝[(n₁)^T,(n₂)^T,…,(n_m)^T,…,(n_M)^T]^T,N∈C^MK×1；

The sparse DPD vector signal model is an MK linear formula;

if K is more than or equal to N, A can be solved by a traditional least square method; however, in practical situations, such as multi-functional or short-time observation, the time is short, which results in K < N, and thus the difficulty of solving a is greatly increased, and therefore, an optimal solution needs to be found:

let Θ be Ψ DS, the sparse DPD vector signal model is modified as:

S_r＝ΘA+N

according to the compressed sensing theory, if A is a sparse vector, the compression matrix Θ conforms to the RIP criterion, and can be represented by S with a great probability_rRecovering A.

For the positioning of multiple targets, the number of target points is far less than the number of grid points of the target area, so that the two-dimensional or three-dimensional distribution of the target area is sparse. The RIP performance is related to the non-correlation of the compression matrix, and it is necessary to orthogonalize Θ to satisfy the RIP characteristics. Orthogonalized compression matrix theta and measurement matrix S_rBecome Θ ' ═ Z Θ and S ', respectively '_r＝ZS_rWherein Z is orthogonalAnd (5) a chemical process. These characteristics provide a priori information for recovering the target distribution by solving the optimization problem, and therefore, the norm a survival is required to be constructed_2,1：

Wherein A is_EN(n)²＝|a₁(n)|²+|a₂(n)|²+…+|a_m(n)|²+…+|a_M(n)|²；

As can be seen from the above equation, if there is an object located at the coordinate p in the object distribution area_qIn the above, the target echo received by at least one moving receiving point AP is not zero. | A | non-conducting phosphor_2,1Norm minimizes each p while ensuring sparsity of target distribution_qSuch that some strong scattering points or weak scattering points in a certain channel can be suppressed or enhanced, if the scattering coefficients of these target points in other channels are weaker or stronger, and if this optimization problem is not solved jointly, in a certain channel if the target position is identified incorrectly, this may result in a i_2,1The norm term is increased, so that other APs cannot recover the correct target position, therefore, the following optimization objective function is constructed to obtain different target distributions at the same time:

wherein | · | purple sweet_FIs the F norm; rho represents a sparse coefficient for balancing the relationship between estimation error and sparsity; j (A) is an objective function; the optimization objective function in the above equation comprises two parts: a. the_2,1Representing that only a few elements in the target distribution are nonzero, corresponding to the sparsity of the target distribution; and

the term corresponds to the accuracy of the recovery and the degree of noise suppression.

Therefore, based on the above formula (12), the optimization objective function is improved, specifically:

wherein, J_ε(A) An objective function distributed for an epsilon-th object; e is a small positive number;

equation (13) is taken as the final optimization objective function, i.e. the optimization cost function.

After the optimization cost function is obtained, the optimization cost function is effectively solved by a greedy algorithm such as basis tracking, gradient tracking and orthogonal matching tracking. Through solving, a target distribution vector A can be obtained, then the A is restored to the matrix to obtain a target distribution matrix, and then a plurality of target distribution maps are obtained to complete multi-target positioning.

Where a priori information for a is not present, in our algorithm, an initial value a is used⁰Obtained by the conventional DPD method.

As u increases, the iterative process terminates when the following equation is satisfied:

wherein the constant delta is an iteration termination threshold, and when the iteration number reaches delta, the iteration is also terminated.

In order to better illustrate the method of the invention, a specific and simulated experimental environment is specified: assume that a two-dimensional area of 10 × 10km is divided into N-100 grid points GP. As shown in fig. 2, M moving reception points AP are distributed in the two-dimensional area, which is denoted by "□"; the Q targets are randomly distributed over the grid points, denoted by "o". Wherein, in fig. 2, the x-direction distance and the y-direction distance constitute a two-dimensional area; fig. 2 shows the distribution of the corresponding receiving points and targets of the motion when M is 8 and Q is 9, and table one is the velocity of the receiving point, which is as follows:

in a simulation test, a transmitting signal is an LFM signal which is common in engineering application, the center frequency is fc-1500 Hz, the signal propagation speed is 1500m/s, the bandwidth is B-1000 Hz, the sampling frequency is 5Hz, and the total sampling point number of each AP is 96.

Next, the relationship between the positioning accuracy and the target sampling point is tested, where AP is 4, the signal-to-noise ratio is 10dB, and the complete echo signal is randomly extracted, and the sampling point is 64, that is, L is 64, and the obtained result is shown in fig. 3.

As shown in fig. 3, when the number of sampling points is 64, i.e., L is 64; the target estimation positions of the M moving receiving points AP obtained by the positioning method of the present invention are completely consistent with the actual positions of the corresponding sampling points, that is, the target estimation positions of the APs of the moving receiving points represented by "∘" are covered by the actual positions of the corresponding sampling points represented by "; according to the simulation experiment, when the acquired echo signals are incomplete, the positioning method can still be used for estimating the positions of the sampling points from the incomplete echo signals, and the accuracy is over 90 percent.

In order to intuitively measure the target positioning accuracy, the MSE obtained by using the AP in 200 experiments and the actual position interval of the sampling point is used as the standard for measuring the accuracy, when the signal-to-noise ratio is 5dB, the number of sampling points is 64, and a graph showing the variation curve of the MSE along with the number of AP points is shown in fig. 4. As is apparent from fig. 4, as the number of APs increases, the MSE gradually decreases, especially from a single platform to a dual platform, and from AP being equal to 3, the MSE is almost 0, and the experiment of fig. 4 further illustrates that the multi-platform target estimation accuracy is much higher than the single-platform target estimation accuracy.

The anti-noise performance of the algorithm is verified below, Mean Square Error (MSE) of the interval between the estimated position and the actual position of 200 experiments is used as a standard for precision measurement, when the number of sampling points is 64, AP is 4, and Signal-to-noise ratio is-6-20 dB, a variation curve of MSE with Signal-to-noise ratio (SNR) is shown in fig. 5, as the SNR increases, the target estimation error MSE gradually decreases, and when the SNR is greater than 5, the target estimation position is substantially consistent with the original position, and the algorithm has good noise suppression performance.

Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (5)

1. A multi-base multi-target positioning method based on a mobile platform comprises the following steps:

obtaining echo signals received by a plurality of moving receiving points AP to form an echo signal matrix, and establishing a sparse DPD vector signal model based on the echo signal matrix;

constructing an optimized cost function related to target distribution according to the established sparse DPD vector signal model;

and restoring the target distribution matrix according to the solution result of the optimization cost function to obtain a plurality of target distribution maps.

2. The multi-base multi-target positioning method based on the mobile platform as claimed in claim 1, wherein the echo signals received by the plurality of moving receiving points AP are obtained to form an echo signal matrix, and a vector signal model is established based on the echo signal matrix; the method specifically comprises the following steps:

the M moving receiving points AP are distributed in a two-dimensional or three-dimensional area, and the area is divided into N units by a plurality of grid points GP; each moving receiving point AP receives a defective and incomplete echo signal;

the position and speed of the m-th moving receiving point AP are p_mAnd v_m，m＝1,2,…,M；

Q targets are randomly positioned on grid points GP;

echo signals are mutually transmitted among M moving receiving points AP through wired and wireless equipment, a time dimension transmitting signal is assumed to be s (t), and the echo signal s received by the M moving receiving point AP at the t moment is assumed to be s (t)_r,m(t) is:

wherein, a_m，qThe backscattering coefficient of the qth target to the mth AP direction; j is

n_m(t) additive white noise of the mth moving receiving point AP; tau is_m,qThe time delay between the qth target point and the mth moving receiving point AP is obtained;

τ_m,q＝2|p_m-g_q|/c (2)

wherein p is_mThe position of the receiving point AP for the mth movement; g_qIs the location of the qth target; c is the propagation speed of the transmitted signal;

ω_m,qis the doppler shift between the qth target point and the mth moving receiver point AP;

ω_m,q＝2πf_cv_m ^T·(p_m-g_q)/c|p_m-g_q| (3)

wherein f is_cIs the carrier frequency of the transmitted signal; v. of_m ^TThe velocity of the m-th moving receiving point AP;

when is given by f_s＝1/T_sAfter sampling as a sampling frequency, wherein T_sIs the sampling time; the signal model is established as

s_r,m＝Ψ_mD_mS_ma_m+n_m (4)

Wherein s is_r,mIs an echo signal matrix; Ψ_mA phase matrix which is an echo signal; d_mA time shift matrix for the echo signal; s_mIs a transmit signal matrix; a is_mA target distribution matrix is obtained; n is_mIs a white noise matrix;

based on the signal model, obtaining a plurality of echo signals correspondingly received by a plurality of moving receiving points AP to form an echo signal vector matrix, and based on the echo signal vector matrix, establishing a sparse DPD vector signal model:

S_r＝ΨDSA+N (5)

wherein S is_r＝[(s_r,1)^T,(s_r,2)^T,…,(s_r,m)^T,…,(s_r,M)^T]^T,S_r∈C^MK×1；

A＝[(a₁)^T,(a₂)^T,…,(a_m)^T,…,(a_M)^T]^T,A∈C^MN×1；

S＝diag{S₁,S₂,…,S_m,…,S_M},S∈C^MNK×MN；

D＝diag{D₁,D₂,…,D_m,…,D_M},D∈C^MNK×MNK；

Ψ＝diag{Ψ₁,Ψ₂,…,Ψ_m,…,Ψ_M},Ψ∈C^MK×MNK；

N＝[(n₁)^T,(n₂)^T,…,(n_m)^T,…,(n_M)^T]^T,N∈C^MK×1；

Wherein K is K_m；K_mThe number of sampling points of the echo signal received by the m-th moving receiving point AP.

3. The multi-base multi-target positioning method based on the mobile platform as claimed in claim 2, wherein an optimized cost function about target distribution is constructed according to the established vector signal model; the method specifically comprises the following steps:

according to the established sparse DPD vector signal model:

S_r＝ΨDSA+N (6)

let Θ be Ψ DS, the organized sparse DPD vector signal model is:

S_r＝ΘA+N

according to the sorted sparse DPD vector signal model, an optimized cost function is constructed:

wherein, J_ε(A) An objective function distributed for an epsilon-th object;

S′_r＝ZS_rdenotes a pair S_rOrthogonalizing; Θ' ═ Z Θ, meaning orthogonalizing Θ; rho is a sparse coefficient; a. the_EN(n)²＝|a₁(n)|²+|a₂(n)|²+…+|a_m(n)|²+…+|a_M(n)|²(ii) a E is 0.001 or 0.01.

4. The multi-base multi-target positioning method based on the mobile platform as claimed in claim 3, wherein the target distribution matrix is restored according to the solution result of the optimization cost function to obtain a plurality of target distribution maps; the method specifically comprises the following steps:

according to the constructed optimization cost function:

wherein, J_ε(A) An objective function distributed for an epsilon-th object;

S′_r＝ZS_rdenotes a pair S_rOrthogonalizing; Θ' ═ Z Θ, meaning orthogonalizing Θ; rho is a sparse coefficient; a. the_EN(n)²＝|a₁(n)|²+|a₂(n)|²+…+|a_m(n)|²+…+|a_M(n)|²(ii) a E is 0.001 or 0.01;

solving the optimization cost function by using a greedy algorithm of basis tracking, gradient tracking and orthogonal matching tracking; and obtaining a target distribution vector A, restoring the A to obtain a target distribution matrix, and further obtaining a plurality of target distribution maps to finish multi-target positioning.

5. A multi-base multi-target positioning system based on a mobile platform is characterized by comprising:

the model establishing module is used for obtaining echo signals received by a plurality of moving receiving points AP, forming an echo signal matrix and establishing a sparse DPD vector signal model based on the echo signal matrix;

the optimization function building module is used for building an optimization cost function related to target distribution according to the built sparse DPD vector signal model; and

and the data processing module is used for restoring the target distribution matrix according to the solution result of the optimization cost function to obtain a plurality of target distribution maps.

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