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

Abstract

The present invention belongs to the technical field of underwater acoustic positioning, and specifically, relates to a multi-base multi-target positioning method based on a mobile platform, the method comprising: obtaining echo signals received by multiple 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 optimization cost function for target distribution according to the established sparse DPD vector signal model; and restoring the target distribution matrix according to the solution result of the above-mentioned optimization cost function to obtain multiple target distribution maps.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic positioning, and in particular, relates to a multi-base multi-target positioning method and system based on a mobile platform. Background Art

[0002] At present, underwater vehicles are widely used in many aspects such as marine rescue and salvage, deep-sea resource survey, offshore oil exploitation, underwater engineering construction, military and national defense construction, etc., which have produced huge economic and social benefits and have potential application prospects. With the development of acoustic stealth technology, the range of sonar equipment is constantly decreasing, and the corresponding target echo and noise intensity are decreasing. Single-base sonar systems can no longer meet the needs of practical applications. Therefore, it is of great significance to study and utilize the collaborative working system of multiple bases such as underwater vehicles and sea surface buoys to improve the performance of sonar systems, improve system stability and system concealment. The multi-base sonar system detects targets at close range through the transmitter installed on the underwater vehicle, and configures the receiver in a protected area far away from the target, so that the system has a long detection distance, high accuracy, and good concealment.

[0003] Target positioning has a wide range of applications in military and civilian fields, such as radar, sonar, wireless communication, satellites, aircraft, etc., and has always been a hot topic of research. In practical applications, target positioning is affected by size, weight, power, and cost constraints, which puts forward more stringent requirements on positioning algorithms. Positioning methods can be divided into two categories: the first category is usually called the two-step method. In the first step of the algorithm, the signal parameters such as direction of arrival (DOA), time of arrival (TOA), time difference of arrival (TDOA), frequency difference of arrival (FDOA), and received signal strength (RSS) are estimated. In the second step, the target position is determined using the estimated results. Since the two-step positioning method only needs to transmit the estimated parameters, this type of algorithm is suitable for systems with small data transmission volume, but in order to improve the positioning accuracy of the second step, it has higher requirements on the estimation accuracy of the parameters in the first step. Therefore, the first type of positioning method requires a very large signal storage space, and there is a mismatch problem in parameter allocation.

[0004] RSS-based positioning indicates that a two-dimensional or three-dimensional area can be divided into multiple grid points (GridPoints, GPs) and assigned to each grid point RSS parameter to form a target distribution map. The target distribution map shows the location and number of targets in the spatial dimension. The target points only occupy a small part of the target distribution map and can be regarded as sparse. However, the existing sparse positioning methods use parameters such as TOA, DOA, TDOA, RSS as measurement values, and do not directly use the original signal. Although the sparse method has significant effects in noise suppression and multi-target recognition, it still has the disadvantages of large signal storage space and parameter allocation mismatch of the two-step positioning method. The second type of method directly uses the receiving point (Access Points, APs) signal to estimate the target position. Weiss and Amar named this method Direct Position Determination (DPD). The DPD method brings signal transmission pressure to the system, but due to the rich information of the echo signal and the lack of signal sorting and parameter matching problems, this type of method can provide better positioning accuracy than the two-step method. However, in the actual application of the second type of algorithm, the echo data may be interfered by false targets and other sources. For multi-functional detection systems, the time allocated for positioning may be discontinuous, resulting in short or discontinuous positioning time. The small amount of data and discontinuous observation time lead to a decrease in the accuracy of the current second type of positioning method. Summary of the invention

[0005] In order to solve the above defects in the prior art, the present invention proposes a multi-base multi-target positioning method based on a mobile platform, which realizes compensation and extension of defective data through the method of the present invention, thereby improving positioning accuracy; the method of the present invention is used to construct an optimization cost function, and a fast algorithm is used to optimize and solve it, thereby realizing the noise suppression function. The method includes:

[0006] Acquire echo signals received by multiple moving receiving points AP to form an echo signal matrix, and establish a sparse DPD vector signal model based on the echo signal matrix;

[0007] According to the established sparse DPD vector signal model, an optimization cost function about the target distribution is constructed;

[0008] According to the solution result of the above optimization cost function, the target distribution matrix is ​​restored to obtain multiple target distribution maps.

[0009] As one of the improvements of the above technical solution, the echo signals received by 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; specifically, the method includes:

[0010] M moving receiving points AP are distributed in a two-dimensional or three-dimensional area, and the area is divided into N units by multiple grid points GP; each moving receiving point AP receives a defective and incomplete echo signal;

[0011] The position and velocity of the mth moving receiving point AP are p m and v m , m=1,2,…,M;

[0012] Q targets are randomly located on the grid points GP;

[0013] M moving receiving point APs transmit echo signals to each other through wired and wireless devices. Assuming that the time dimension transmission signal is s(t), the echo signal s received by the mth moving receiving point AP at time t is r,m (t) is:

[0014]

[0015] Among them, a m,q is the backscatter coefficient of the qth target toward the mth AP; j is n m (t) is the additive white noise of the mth moving receiving point AP; τ m,q is the delay between the qth target point and the mth moving receiving point AP;

[0016] τ m,q =2|p m -g q | / c (8)

[0017] Among them, p m is the position of the mth moving receiving point AP; g q is the position of the qth target; c is the propagation speed of the transmitted signal;

[0018] ω m,q is the Doppler shift between the qth target point and the mth moving receiving point AP;

[0019] ω m,q =2πf c v m T ·(p m -g q ) / c|p m -g q | (9)

[0020] Among them, f c is the carrier frequency of the transmitted signal; v m T is the speed of the mth moving receiving point AP;

[0021] When f s =1 / T s As the sampling frequency after sampling, where T s is the sampling time; the established signal model is

[0022] s r,m =Ψ m D m S m a m +n m (10)

[0023] Among them, s r,m is the echo signal matrix; m is the phase matrix of the echo signal; D m is the time shift matrix of the echo signal; S m is the transmit signal matrix; a m is the target distribution matrix; n m is the white noise matrix;

[0024] Based on the above signal model, multiple echo signals corresponding to multiple moving receiving points AP are obtained to form an echo signal vector matrix. Based on the echo signal vector matrix, a sparse DPD vector signal model is established:

[0025] S r =ΨDSA+N (11)

[0026] Among them, S r =[(s r,1 ) T ,(s r,2 ) T ,…,(s r,m ) T ,…,(s r,M ) T ] T ,S r ∈C MK×1 ;

[0027] A=[(a 1 ) T ,(a 2 ) T ,…,(a m ) T ,…,(a M ) T ] T ,A∈C MN×1 ;

[0028] S = diag{S 1 ,S 2 ,…,Sm ,…,S M},S∈C MNK×MN ;

[0029] D=diag{D 1 ,D 2 ,…,D m ,…,D M},D∈C MNK×MNK ;

[0030] Ψ=diag{Ψ 1 ,Ψ 2 ,…,Ψ m ,…,Ψ M},Ψ∈C MK×MNK ;

[0031] N=[(n 1 ) T ,(n 2 ) T ,…,(n m ) T ,…,(n M ) T ] T ,N∈C MK×1 ;

[0032] Where K = K m ; K m is the number of sampling points of the echo signal received by the mth moving receiving point AP.

[0033] As one of the improvements of the above technical solution, the optimization cost function for target distribution is constructed according to the established vector signal model; specifically including:

[0034] According to the established sparse DPD vector signal model:

[0035] S r =ΨDSA+N (12)

[0036] Let Θ = ΨDS, then the sorted sparse DPD vector signal model is:

[0037] S r =θA+N

[0038] According to the sorted sparse DPD vector signal model, an optimization cost function is constructed:

[0039]

[0040] Among them, J ε (A) is the objective function of the εth target distribution;

[0041] S′r =ZS r , indicating that S r Orthogonalization; Θ′=ZΘ, which means orthogonalization of Θ; ρ is the sparse coefficient; A EN (n) 2 =|a 1 (n)| 2 +|a 2 (n)| 2 +…+|a m (n)| 2 +…+|a M (n)| 2 ;∈=0.001 or∈=0.01.

[0042] As one of the improvements of the above technical solution, the target distribution matrix is ​​restored according to the solution result of the above optimization cost function to obtain multiple target distribution maps; specifically including:

[0043] According to the constructed optimization cost function:

[0044]

[0045] Among them, J ε (A) is the objective function of the εth target distribution;

[0046] S′ r =ZS r , indicating that S r Orthogonalization; Θ′=ZΘ, which means orthogonalization of Θ; ρ is the sparse coefficient; A EN (n) 2 =|a 1 (n)| 2 +|a 2 (n)| 2 +…+|a m (n)| 2 +…+|a M (n)| 2 ;∈=0.001 or∈=0.01;

[0047] The above optimization cost function is solved by using basis pursuit, gradient pursuit and orthogonal matching pursuit greedy algorithms; the target distribution vector A is obtained, and then the matrix of A is restored to obtain the target distribution matrix, and then multiple target distribution maps are obtained to complete multi-target positioning.

[0048] The present invention also provides a multi-base multi-target positioning system based on a mobile platform, the system comprising:

[0049] A model building module is used to obtain echo signals received by multiple moving receiving points AP, form an echo signal matrix, and build a sparse DPD vector signal model based on the echo signal matrix;

[0050] An optimization function building module, used to build an optimization cost function about a target distribution according to the established sparse DPD vector signal model; and

[0051] The data processing module is used to restore the target distribution matrix and obtain multiple target distribution maps according to the solution results of the above-mentioned optimization cost function.

[0052] The beneficial effects of the present invention compared with the prior art are:

[0053] The present invention directly utilizes the echo of the receiving point for positioning, does not need to estimate the intermediate parameters, avoids the signal sorting and parameter matching process required by the first type of positioning method of the two-step method, and can obtain a more accurate positioning result under a low signal-to-noise ratio; compared with the traditional direct positioning method, a mobile node data model is introduced to realize the expansion of the direct positioning method from fixed nodes to mobile nodes; utilizes the sparsity of target distribution and combines the echo information of the receiving point to restore the missing observation data, and then restores the target distribution map, solves the problem of data missing, improves positioning accuracy and suppresses noise; utilizes a fast algorithm to solve the problem of excessive data volume in the direct positioning algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a flow chart of a multi-base multi-target positioning method based on a mobile platform of the present invention;

[0055] Figure 2 It is a distribution diagram of APs and sampling points of a simulation experiment of a multi-base multi-target positioning method based on a mobile platform of the present invention;

[0056] Figure 3 It is a distribution diagram of APs and targets in a simulation experiment of a multi-base multi-target positioning method based on a mobile platform of the present invention;

[0057] Figure 4 It is a curve graph of the MSE of the multi-platform positioning method according to the present invention as the number of APs changes;

[0058] Figure 5 It is a curve diagram of the MSE changing with the SNR according to the positioning method of the present invention. DETAILED DESCRIPTION

[0059] The present invention will now be further described with reference to the accompanying drawings.

[0060] like Figure 1As shown, the present invention provides a multi-base multi-target positioning method based on a mobile platform. The method is a new direct positioning method for mobile node targets based on sparse priors. In a multi-platform target positioning environment, the target echo signal is directly processed by using the principle of compressed sensing to achieve high-precision multi-target positioning. In addition, the method of the present invention uses multi-platform defective data to achieve target positioning, and through data fusion, the positioning accuracy is improved and noise is suppressed. When there is irregular sampling, in order to enhance the positioning accuracy, the original echo signal information is used to solve ||A|| 2,1 norm optimization problem, and restore the target distribution map. The proposed multi-base sparse direct positioning method can jointly utilize the echo information of the receiving point to improve the positioning accuracy and noise suppression ability, and can provide more accurate target positioning accuracy compared with the single-base method.

[0061] The method specifically includes:

[0062] Acquire echo signals received by multiple moving receiving points AP to form an echo signal matrix, and establish a sparse DPD vector signal model based on the echo signal matrix;

[0063] Specifically, it is assumed 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 multiple grid points GP; it is assumed that each moving receiving point AP receives a defective and incomplete echo signal;

[0064] The position and velocity of the mth moving receiving point AP are p m and v m (m=1,2,…,M);

[0065] Q targets are randomly located on GP; the position of target q is represented by g q ;

[0066] M moving receiving point APs transmit echo signals to each other through wired and wireless devices. Assuming that the time dimension transmission signal is s(t), the echo signal s received by the mth moving receiving point AP at time t is r,m (t) is:

[0067]

[0068] Among them, a m,q is the backscatter coefficient of the qth target toward the mth AP; j is n m (t) is the additive white noise of the mth moving receiving point AP; τ m,q is the delay between the qth target point and the mth moving receiving point AP;

[0069] τm,q =2|p m -g q | / c (14)

[0070] Among them, p m is the position of the mth moving receiving point AP; g q is the position of the qth target; c is the propagation speed of the transmitted signal;

[0071] ω m,q is the Doppler shift between the qth target point and the mth moving receiving point AP;

[0072] ω m,q =2πf c v m T ·(p m -g q ) / c|p m -g q | (15)

[0073] Among them, f c is the carrier frequency of the transmitted signal; v m T is the speed of the mth moving receiving point AP;

[0074] When f s =1 / T s As the sampling frequency after sampling, where T s is the sampling time; the established signal model is

[0075] s r,m =Ψ m D m S m a m +n m (16)

[0076] Among them, s r,m is the echo signal matrix; m is the phase matrix of the echo signal; D m is the time shift matrix of the echo signal; S m is the transmit signal matrix; a m is the target distribution matrix; n m is the white noise matrix;

[0077] Based on the above signal model, the echo signals received by multiple moving receiving points AP are obtained to form an echo signal vector matrix. Based on the echo signal vector matrix, a sparse DPD vector signal model is established:

[0078] S r =ΨDSA+N (17)

[0079] where S r = [(s r,1 ) T , (s r,2 ) T , …, (s r,m ) T , …, (s r,M ) T ) T , S r ∈ C MK×1 ;

[0080] A = [(a 1 ) T , (a 2 ) T , …, (a m ) T , …, (a M ) T ) T , A ∈ C MN×1 ;

[0081] S = diag{S 1 , S 2 , …, S m , …, S M}], S ∈ C MNK×MN ;

[0082] D = diag{D 1 , D 2 , …, D m , …, D M}], D ∈ C MNK×MNK ;

[0083] Ψ = diag{Ψ 1 , Ψ 2 , …, Ψ m , …, Ψ M}], Ψ ∈ C MK×MNK ;

[0084] N = [(n 1 ) T , (n 2 ) T , …, (n m ) T , …, (n M ) T ) T , N ∈ C MK×1 ;

[0085] where K = K m ; K mis the number of sampling points of the echo signal received by the mth moving receiving point AP.

[0086] According to the established sparse DPD vector signal model, an optimization cost function about the target distribution is constructed;

[0087] Specifically, according to the established sparse DPD vector signal model:

[0088] S r =ΨDSA+N (18)

[0089] Let Θ = ΨDS, then the sorted sparse DPD vector signal model is:

[0090] S r =θA+N

[0091] According to the sorted sparse DPD vector signal model, an optimization cost function is constructed:

[0092]

[0093] Among them, J ε (A) is the objective function of the εth target distribution;

[0094] S′ r =ZS r , indicating that S r Orthogonalization; Θ′=ZΘ, which means orthogonalization of Θ; ρ is the sparse coefficient; A EN (n) 2 =|a 1 (n)| 2 +|a 2 (n)| 2 +…+|a m (n)| 2 +…+|a M (n)| 2 ;∈ is a small positive number, i.e.,∈=0.001 or∈=0.01;

[0095] According to the solution result of the above optimization cost function, the target distribution matrix is ​​restored to obtain multiple target distribution maps.

[0096] Specifically, according to the constructed optimization cost function:

[0097]

[0098] Among them, J ε (A) is the objective function of the εth target distribution;

[0099] S′ r =ZS r , indicating that S rOrthogonalization; Θ′=ZΘ, which means orthogonalization of Θ; ρ is the sparse coefficient; A EN (n) 2 =|a 1 (n)| 2 +|a 2 (n)| 2 +…+|a m (n)| 2 +…+|a M (n)| 2 ;∈ is a small positive number, i.e.,∈=0.001 or∈=0.01;

[0100] The above optimization cost function is solved using greedy algorithms such as basis pursuit, gradient pursuit and orthogonal matching pursuit. By solving the problem, the target distribution vector A can be obtained, and then the matrix of A can be restored to obtain the target distribution matrix, and then multiple target distribution maps can be obtained to complete multi-target positioning.

[0101] The present invention also provides a multi-base multi-target positioning system based on a mobile platform, the system comprising:

[0102] A model building module is used to obtain echo signals received by multiple moving receiving points AP, form an echo signal matrix, and build a sparse DPD vector signal model based on the echo signal matrix;

[0103] An optimization function building module, used to build an optimization cost function about a target distribution according to the established sparse DPD vector signal model; and

[0104] The data processing module is used to restore the target distribution matrix and obtain multiple target distribution maps according to the solution results of the above-mentioned optimization cost function.

[0105] Among them, the derivation process of establishing the signal model is as follows:

[0106] Assume 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 multiple grid points GP; Assume that each moving receiving point AP receives a defective and incomplete echo signal; Among them, the M moving receiving nodes are mobile and can be located at any position, and the target node is fixed and located on the grid point GP;

[0107] The position and velocity of the mth moving receiving point AP are p m and v m (m=1,2,…,M);

[0108] Q targets are randomly located on GP; the position of target q is represented by g q ;

[0109] M moving receiving point APs transmit echo signals to each other through wired and wireless devices. Assuming that the time dimension transmission signal is s(t), the echo signal s received by the mth moving receiving point AP at time t is r,m (t) is:

[0110]

[0111] Among them, a m,q is the backscatter coefficient of the qth target toward the mth AP; j is n m (t) is the additive white noise of the mth moving receiving point AP; τ m,q is the delay between the qth target point and the mth moving receiving point AP;

[0112] τ m,q =2|p m -g q | / c (20)

[0113] Among them, p m is the position of the mth moving receiving point AP; g q is the position of the qth target; c is the propagation speed of the transmitted signal;

[0114] ω m,q is the Doppler shift between the qth target point and the mth moving receiving point AP;

[0115] ω m,q =2πf c v m T ·(p m -g q ) / c|p m -g q | (21)

[0116] Among them, f c is the carrier frequency of the transmitted signal; v m T is the speed of the mth moving receiving point AP;

[0117] When f s =1 / T s As the sampling frequency after sampling, where T s is the sampling time; the established signal model is

[0118] s r,m =Ψ m D m S m a m +n m (twenty two)

[0119] Among them, s r,m is the echo signal matrix; m is the phase matrix of the echo signal; D m is the time shift matrix of the echo signal; S m is the transmit signal matrix; a m is the target distribution matrix; n m is the white noise matrix;

[0120] Among them, the echo signal matrix is ​​expressed as

[0121] s r,m =[s r,m (1T s ),s r,m (2T s ),…,s r,m (lT s ),…,s r,m (LT s )] T (twenty three)

[0122] Since the time allocated for positioning is discontinuous in a multifunctional system, the sampled echo signal may be discontinuous or incomplete.

[0123] Assume that the discontinuous echo signal has H m fragments, of which h m The fragment contains the sample sequence number w m,hm To the sampling sequence number w m,hm +K m,hm -1 K m,hm sampling points;

[0124] Discontinuous sampling sequence

[0125] 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].

[0126] There are K discontinuous echo signal vectors in total m =K m,1 +K m,2 +...+K m,Hm (K m <L) sampling points; where L is the number of sampling points of the complete echo signal vector;

[0127] Discontinuous sampling sequence w m ∈W m ; Among them, w m =[w m (1),w m (2),…,w m (K m )];

[0128] Discontinuous echo signal r,m Become a K m ×1 vector:

[0129] 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 (twenty four)

[0130] a m =[a m,1 ,a m,2 ,…,a m,n ,…,a m,N ] T ;

[0131] S m =diag{s m ,s m ,…,s m},S m ∈C KmN×N ;

[0132] Where C is the 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 ;

[0133] Here, the block diagonal matrix is ​​defined as

[0134]

[0135]

[0136] Where η is K m ×K m The permutation matrix of

[0137]

[0138] Among them, ξ m,n =τ m,n / T s is the power of the permutation matrix and is approximately an integer; τ m,n is the time delay between the mth moving receiving point AP and the nth grid point GP.

[0139] Ψ m =[ψ m,1 ,ψ m,2 ,…,ψ m,n ,…,ψ m,N ]

[0140] in,

[0141] 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 )]}

[0142] n m =[n m (1T s ),n m (2T s ),…,n m (lT s ),…,n m (LT s )] T

[0143] Based on the above signal model, the specific derivation process of constructing the sparse DPD vector signal model is as follows:

[0144] Based on the above signal model, that is, formula (4), multiple echo signals corresponding to multiple moving receiving points AP are obtained to form the echo signal vector matrix S r , based on the echo signal vector matrix S r , establish a sparse DPD vector signal model:

[0145] S r=ΨDSA+N (28)

[0146] Among them, S r =[(s r,1 ) T ,(s r,2 ) T ,…,(s r,m ) T ,…,(s r,M ) T ] T ,S r ∈C MK×1 ;

[0147] A=[(a 1 ) T ,(a 2 ) T ,…,(a m ) T ,…,(a M ) T ] T ,A∈C MN×1 ;

[0148] S = diag{S 1 ,S 2 ,…,S m ,…,S M},S∈C MNK×MN ;

[0149] D=diag{D 1 ,D 2 ,…,D m ,…,D M},D∈C MNK×MNK ;

[0150] Ψ=diag{Ψ 1 ,Ψ 2 ,…,Ψ m ,…,Ψ M},Ψ∈C MK×MNK ;

[0151] N=[(n 1 ) T ,(n 2 ) T ,…,(n m ) T ,…,(n M ) T ] T ,N∈C MK×1 ;

[0152] The above sparse DPD vector signal model is a MK linear formula;

[0153] If \(K\geq N\), \(A\) can be solved by the traditional least squares method; however, in actual situations, such as in the case of multi-functional or short-time observations, the time is very short, resulting in \(K < N\), which greatly increases the difficulty of solving \(A\). Therefore, it is necessary to find the optimal solution:

[0154] Let \(\Theta=\Psi D S\), and the sparse DPD vector signal model is modified to:

[0155] S r =\(\Theta A + N\)

[0156] According to the compressive sensing theory, if \(A\) is a sparse vector, the compression matrix \(\Theta\) conforms to the RIP criterion and can recover \(A\) from \(S\) with a very high probability. r

[0157] For multi-target positioning, since the number of target points is much smaller than the grid points in the target area, the two-dimensional or three-dimensional distribution of the target area is strongly sparse. The RIP performance is related to the incoherence of the compression matrix. To meet the RIP characteristics, it is necessary to orthogonalize \(\Theta\). After orthogonalization, the compression matrix \(\Theta\) and the measurement matrix \(S\) r become \(\Theta' = Z\Theta\) and \(S'\) r =\(ZS\) r respectively, where \(Z\) is the orthogonalization process. These characteristics provide prior information for recovering the target distribution by solving the optimization problem. Therefore, it is necessary to construct the norm \(\|A\|\) 2,1 :

[0158]

[0159] where \(A\) EN (n) 2 =\(\vert a\) 1 (n)\vert\) 2 +\(\vert a\) 2 (n)\vert\) 2 +\(\cdots+\vert a\) m (n)\vert\) 2 +\(\cdots+\vert a\) M (n)\vert\) 2 ;

[0160] It can be seen from the above formula that if there is a target located at the coordinate \(p\) q in the target distribution area, the target echo received by at least one moving receiving point \(A_p\) is not zero. The \(\|A\|\) 2,1 norm minimizes each \(p\) while ensuring the sparsity of the target distribution q ​energy, so that some strong 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 relatively weak or strong. In addition, if this optimization problem is not solved jointly, the wrong identification of the target position in a certain channel will lead to ||A|| 2,1 The norm term is improved, so other APs cannot recover the correct target position. Therefore, we construct the following optimization objective function to obtain different target distributions at the same time:

[0161]

[0162] Among them, ||·|| F is the F norm; ρ represents the sparse coefficient, which is used to balance the relationship between estimation error and sparsity; J(A) is the objective function; the optimization objective function in the above formula consists of two parts: A 2,1 represents that only a few elements in the target distribution are non-zero, corresponding to the sparsity of the target distribution; and The terms correspond to the accuracy of restoration and the degree of noise suppression.

[0163] Therefore, based on the above formula (12), the optimization objective function is improved as follows:

[0164]

[0165] Among them, J ε (A) is the objective function of the εth target distribution; ∈ is a small positive number;

[0166] Formula (13) is used as the final optimization objective function, that is, the optimization cost function.

[0167] After obtaining the optimized cost function, greedy algorithms such as basis pursuit, gradient pursuit and orthogonal matching pursuit are used to effectively solve the above optimized cost function. By solving it, the target distribution vector A can be obtained, and then the matrix of A can be restored to obtain the target distribution matrix, and then multiple target distribution maps can be obtained to complete multi-target positioning.

[0168] Among them, the prior information of A does not exist. In our algorithm, the initial value A 0 Obtained by conventional DPD method.

[0169] As u increases, the iteration process terminates when the following equation is satisfied:

[0170]

[0171] Among them, the constant δ is the iteration termination threshold. When the number of iterations reaches δ, the iteration is terminated.

[0172] In order to better illustrate the method of the present invention, a specific simulation experiment environment is given: Assume that a two-dimensional area of ​​10×10km is divided into N=100 grid points GP. Figure 2 As shown in the figure, M moving receiving points AP are distributed in the two-dimensional area, which is represented by "□"; Q targets are randomly distributed on the grid points, which are represented by "◇". Figure 2 In the figure, the x-direction distance and the y-direction distance form a two-dimensional area; Figure 2 The distribution of the corresponding moving receiving points and targets when M=8 and Q=9 is given. Table 1 shows the speed of the receiving points, as follows:

[0173]

[0174]

[0175] In the simulation experiment, the transmitted signal is a common LFM signal in engineering applications, with a center frequency of fc=1500 Hz, a signal propagation speed of 1500 m / s, a bandwidth of B=1000 Hz, a sampling frequency of 5 Hz, and a total number of sampling points for each AP of 96.

[0176] The following test shows the relationship between positioning accuracy and the number of target sampling points. AP = 4, the signal-to-noise ratio is 10dB, and the complete echo signal is randomly sampled. When the number of sampling points is 64, that is, L = 64, the results are as follows: Figure 3 shown.

[0177] like Figure 3 As shown, when the number of sampling points is 64, that is, L=64; the target estimated positions of the M moving receiving points AP obtained by adopting the positioning method of the present invention are completely consistent with the actual positions of the corresponding sampling points, that is, the target estimated positions of the moving receiving points AP represented by "○" are covered on the actual positions of the corresponding sampling points represented by "※"; according to the simulation experiment, it can be known that when the acquired echo signal is incomplete, the positioning method of the present invention can still be used to estimate the position of the sampling point from the incomplete echo signal, and the accuracy rate is above 90%.

[0178] In order to intuitively measure the target positioning accuracy, the MSE of the interval between the target estimated position obtained by AP and the actual position of the sampling point in 200 experiments is used as the accuracy measurement standard. When the signal-to-noise ratio is 5dB, the number of sampling points is 64, and the MSE curve with the number of AP points is as follows: Figure 4 As shown. Figure 4 It can be clearly seen that as the number of APs increases, the MSE gradually decreases, especially when the single platform is changed to the dual platform, the MSE decreases significantly. When AP=3, the MSE is almost 0. Figure 4The experiment further demonstrated that the multi-platform target estimation accuracy is much greater than that of the single-platform target estimation accuracy.

[0179] Next, we verify the noise resistance of the algorithm. The mean square error (MSE) between the estimated position and the actual position of 200 experiments is used as the accuracy measurement standard. When the number of sampling points is 64, AP=4, and the signal-to-noise ratio is -6-20dB, the curve of MSE changing with the signal-to-noise ratio (SNR) is as follows: Figure 5 As shown in the figure, with the increase of SNR, the target estimation error MSE gradually decreases. When SNR is greater than 5, the estimated target position is basically consistent with the original position, and the algorithm has a good noise suppression performance.

[0180] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A multi-base multi-target positioning method based on a mobile platform, the method comprising: Acquire echo signals received by multiple moving receiving points AP to form an echo signal matrix, and establish a sparse DPD vector signal model based on the echo signal matrix; According to the established sparse DPD vector signal model, an optimization cost function about the target distribution is constructed; According to the solution result of the above optimization cost function, the target distribution matrix is ​​restored to obtain multiple target distribution maps; The step of obtaining echo signals received by a plurality of moving receiving points AP to form an echo signal matrix and establishing a vector signal model based on the echo signal matrix specifically includes: M moving receiving points AP are distributed in a two-dimensional or three-dimensional area, and the area is divided into N units by multiple grid points GP; each moving receiving point AP receives a defective and incomplete echo signal; The position and velocity of the mth moving receiving point AP are p m and v m , m=1,2,…,M; Q targets are randomly located on the grid points GP; M moving receiving point APs transmit echo signals to each other through wired and wireless devices. Assuming that the time dimension transmission signal is s(t), the echo signal s received by the mth moving receiving point AP at time t is r,m (t) is: Among them, a m,q is the backscatter coefficient of the qth target toward the mth AP; j is n m (t) is the additive white noise of the mth moving receiving point AP; τ m,q is the delay between the qth target point and the mth moving receiving point AP; τ m,q J2|p m -g q | / c(2) Among them, p m is the position of the mth moving receiving point AP; g q is the position of the qth target; c is the propagation speed of the transmitted signal; ω m,q is the Doppler shift between the qth target point and the mth moving receiving point AP; oh m,q =2πf c v m T ·(p m -g q ) / c|p m -g q |(3) Among them, f c is the carrier frequency of the transmitted signal; v m T is the speed of the mth moving receiving point AP; When f s =1 / T s As the sampling frequency after sampling, where T s is the sampling time; the established signal model is s r,m =Ψ m D m S m a m +n m (4) Among them, s r,m is the echo signal matrix; m is the phase matrix of the echo signal; D m is the time shift matrix of the echo signal; S m is the transmit signal matrix; a m is the target distribution matrix; n m is the white noise matrix; Based on the above signal model, multiple echo signals corresponding to multiple moving receiving points AP are obtained to form an echo signal vector matrix. Based on the echo signal vector matrix, a sparse DPD vector signal model is established: S r =ΨDSA+N(5) in, 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 ; Where K = K m ; K m is the number of sampling points of the echo signal received by the mth moving receiving point AP; The method of constructing an optimization cost function for target distribution according to the established vector signal model specifically includes: According to the established sparse DPD vector signal model: S r =ΨDSA+N(6) Let Θ = ΨDS, then the sorted sparse DPD vector signal model is: S r =ΘA+N According to the sorted sparse DPD vector signal model, an optimization cost function is constructed: Among them, J ε (A) is the objective function of the εth target distribution; S′ r =ZS r , indicating that S r Orthogonalization; Θ′=ZΘ, which means orthogonalization of Θ; ρ is the sparse coefficient; A EN (n) 2 = |a1(n)| 2 + |a2(n)| 2 + … + |a m (n)| 2 + … + |a M (n)|²; ∈ = 0.001 or ∈ = 0.

01.

2. The multi-base multi-target positioning method based on a mobile platform according to claim 1, characterized in that: The method of restoring the target distribution matrix based on the solution of the above-mentioned optimization cost function to obtain multiple target distribution maps specifically includes: According to the constructed optimization cost function: Among them, J ε (A) is the objective function of the εth target distribution; S′ r =ZS r , indicating that S r Orthogonalization; Θ′=ZΘ, which means orthogonalization of Θ; ρ is the sparse coefficient; A EN (n) 2 = |a1(n)|2 + |a2(n)| 2 + … + |a m (n)| 2 + … + |a M (n)| 2 ; ∈ = 0.001 or ∈ = 0.01; The above optimization cost function is solved by using basis pursuit, gradient pursuit and orthogonal matching pursuit greedy algorithms; the target distribution vector A is obtained, and then the matrix of A is restored to obtain the target distribution matrix, and then multiple target distribution maps are obtained to complete multi-target positioning.

3. A system based on the multi-base multi-target positioning method based on a mobile platform according to claim 1, characterized in that: The system includes: A model building module is used to obtain echo signals received by multiple moving receiving points AP, form an echo signal matrix, and build a sparse DPD vector signal model based on the echo signal matrix; An optimization function building module, used to build an optimization cost function about a target distribution according to the established sparse DPD vector signal model; and The data processing module is used to restore the target distribution matrix and obtain multiple target distribution maps according to the solution results of the above-mentioned optimization cost function.

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