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CN-116338622-B - Low-complexity target DOD-DOA and Doppler frequency joint estimation algorithm based on space-time nested sampling

CN116338622BCN 116338622 BCN116338622 BCN 116338622BCN-116338622-B

Abstract

The invention provides a low-complexity target DOD-DOA and Doppler frequency joint estimation algorithm based on space-time nested sampling, which comprises the following steps of 1, configuring a bistatic MIMO radar system as a space-time nested sampling model, sampling a received signal { x q (l) }, 2, carrying out multistage delay sampling on the received signal { x q (l) } to obtain { y (l) }, 3, carrying out matched filtering on the received signal { y (l) } to obtain { y (t) }, 4, solving an echo signal covariance matrix R of a target, 5, vectorizing and removing redundancy on the target signal covariance matrix, and obtaining the target signal according to the vector Obtaining the observation signal Step 6, for the new observation signal And 7, carrying out triple Toeplitz matrix iterative reconstruction to obtain an equivalent covariance matrix R xx of the virtual domain, and solving DOD-DOA and Doppler frequency parameters of the target by using an improved multidimensional ESPRIT algorithm.

Inventors

  • ZHAN CHENGHONG
  • HU GUOPING
  • PAN XIAOMIN
  • ZHAO FANGZHENG
  • ZHOU HAO

Assignees

  • 中国人民解放军空军工程大学

Dates

Publication Date
20260512
Application Date
20230423

Claims (7)

  1. 1. The low-complexity target DOD-DOA and Doppler frequency joint estimation algorithm based on space-time nested sampling is characterized by comprising the following steps of: Step 1, configuring a bistatic MIMO radar system as a space-time nested sampling model, and sampling a received signal by using the space-time nested sampling model ; Step 2, adopting a nested Q-level delay receiver to receive the received signal Performing multistage delay sampling, receiving with Q stage delay, and representing the received data in vector form to obtain ; Step 3, using matched filter to delay the received signal Performing matched filtering to obtain echo signals ; Step 4, according to the echo signal Establishing covariance matrix of target echo signals ; Step 5, vectorizing covariance matrix of target echo signal Realizing the secondary expansion of the time-space degree of freedom, namely representing as a data vector Data vector by using multi-linear mapping method Redundancy and rearrangement are carried out to obtain an observation signal ; Step 6, for the new observation signal Performing triple Toeplitz matrix iterative reconstruction to obtain an equivalent covariance matrix of the virtual domain ; Step 7, applying the improved multidimensional ESPRIT algorithm to the equivalent covariance matrix Performing feature decomposition, constructing an expression of the emission angle, the receiving angle and the Doppler frequency of the target, and further obtaining estimated values of the emission angle, the receiving angle and the Doppler frequency of the target; receiving a signal The sampling process of (a) is specifically as follows: step 101, in a space-time nested sampling model, a transmitting array and a receiving array are both second-order nested arrays, and the number of array elements of the transmitting array is The array element number of the receiving array is The delayer is configured to Let the array element spacing of unit array element be The set of physical array element positions for transmit-receive display is expressed as: (1) Step 102, assuming existence of A far-field narrowband incoherent target, 、 And , DOD, DOA and Doppler frequencies, respectively, of the target, the transmit array transmitting A different orthogonal pulse signal, at the first Under the secondary transmitting pulse, the echo signal model of the receiving end is expressed as: (2) Wherein, the , Represents the Khatri-Rao product, , Represent the first The scattering coefficient of the individual objects is determined, In order to transmit the repetition period of the pulse, Mean value 0 and variance 0 A kind of electronic device A wigaussian white noise vector, and: (3) (4) (5) And The steering vectors representing the transmit and receive arrays, respectively, are expressed as: (6) (7) step 103, adopting a nested Q-level delay receiver to receive the received signal Performing delay sampling processing, assuming that DOD, DOA and Doppler frequency parameters of the target remain unchanged during the delay time, then The echo signal after the stage delay is expressed as: (8) Wherein, the , ; For new observation signals The method for performing the triple Toeplitz matrix iterative reconstruction comprises the following specific processes: Step 601, first observe vector Division into rows The number of matrix blocks is one, each matrix block comprises Line elements, if Represent the first A matrix block, wherein According to matrix blocks The following Toeplitz matrix was constructed for the basic elements: (23) Step 602, then matrix block ( ) Division into rows Each matrix block, assuming Represent the first A matrix block, wherein To As basic element, matrix block The elements in (a) are constructed as a Toeplitz matrix: (24) step 603. Finally, matrix block , Division into rows Line elements, assuming Representing matrix blocks Middle (f) A row element in which To As basic element, matrix block Expressed as a Toeplitz matrix: (25) each matrix block is assembled using a Toeplitz process of formula (24) Such Toeplitz operation is performed, and then the Toeplitz operation procedure of the formula (25) is applied to each element in the Toeplitz matrix after the above operation This will result in an equivalent multi-sample snapshot, i.e., a virtual domain equivalent covariance matrix As can be seen from the formula (25), Is one A dimension matrix, which can be expressed as: (26) Wherein, the , , 。
  2. 2. The low complexity target DOD-DOA and doppler frequency joint estimation algorithm based on space-time nested sampling of claim 1, wherein the received signal The expression of (2) is: (9) Wherein, the (10) (11) Is the doppler steering vector of the target, And Referred to as airspace-directed vectors.
  3. 3. The joint estimation algorithm of low complexity target DOD-DOA and doppler frequency based on space-time nested sampling according to claim 2, wherein in the above step 3, the echo signal The expression of (2) is as follows: (12) Wherein, the , Information vectors constructed for the scattering coefficients and doppler parameters, A white noise signal vector is maintained; representing the joint steering vector of the received signal.
  4. 4. A low complexity target DOD-DOA and doppler frequency joint estimation algorithm based on space-time nested sampling as recited in claim 3, wherein in said step 4, the covariance matrix of the target echo signal can be expressed as (13) Wherein, the As a result of the objective covariance matrix, Is the power level of the signal.
  5. 5. The joint estimation algorithm of low complexity target DOD-DOA and doppler frequency based on space-time nested sampling as recited in claim 4, wherein in said step 5, data vectors are represented The expression of (2) is (14) Wherein, the Signal power representing K targets; (15) As is known from the formula (15), Can be expressed as: (16)。
  6. 6. the low complexity target DOD-DOA and doppler frequency joint estimation algorithm based on spatio-temporal nest sampling of claim 5, characterized by data vectors The specific process of redundancy and rearrangement is as follows: From the structure of formula (16), the vector The sum and difference joint space-time structure is satisfied on the space-time structure, and the set of the virtual array element and the time domain virtual sampling point is set as Then it can be expressed as: (17) in equation (17), the difference joint array of the nested arrays Has the following characteristics of A plurality of virtual array elements are arranged in the array, Has the following characteristics of Difference joint structure of virtual array elements and time domain sampling Has the following components The virtual sampling points are integrated because the sum-joint structure in the formula (17) consists of three different parameters The spatio-temporal joint degrees of freedom of (c) can be expressed as: (18) Order the , , Then the virtual space-time steering vector ranges from To the point of ; The unique needed virtual array element can be indexed out from the one-dimensional matrix after vectorization according to the position and is the same as the vectorization matrix structure formed by the uniform array, Namely: (19) In the formula, Representation of Dimension vector, and Representing virtual joint steering vectors, there are , wherein, (20) (21) (22)。
  7. 7. The joint estimation algorithm of DOD-DOA and Doppler frequency for low complexity targets based on space-time nested sampling of claim 6, wherein in said step 7, the process of obtaining DOD-DOA and Doppler frequency parameters for targets comprises: Step 701, equivalent covariance matrix Performing feature decomposition to obtain a single product Signal subspace formed by individual eigenvalues , Order-making Front of (2) The matrix of row elements is Rear (back) The matrix of row elements is Based on virtual space-time steering vectors The following is true: (27) Wherein, the Representing the generalized inverse of the solution matrix, As the rotation invariant factor of the doppler domain, in combination with (27), And Are all complex matrices And satisfy the following (28) Wherein, the The scale factor is represented by a scale factor, For column permutation matrix, space-time virtual guide vector is obtained directly by the following method Is a function of the estimated value of (a): (29) obtaining extended virtual space-time steering vectors Estimate of (2) ; Step 702, obtaining an estimated value Then, according to the internal structure, the joint estimation of the emission angle DOD, the receiving angle DOA and the Doppler frequency of the target is obtained through the following three expressions; (30) (31) (32) From the same virtual space-time steering vector through the three formulas Estimate of (2) The estimated values of the target receiving and transmitting angle and the Doppler frequency are obtained, and the three parameters are estimated from the same space-time virtual guide vector, so that the obtained DOD, DOA and Doppler frequency are automatically paired.

Description

Low-complexity target DOD-DOA and Doppler frequency joint estimation algorithm based on space-time nested sampling Technical Field The invention belongs to the technical field of radar signal processing, and particularly relates to a low-complexity target DOD-DOA and Doppler frequency joint estimation algorithm based on space-time nested sampling. Background Bistatic Multiple-Input Multiple-Output (MIMO) radars have the potential advantages of anti-scout, anti-interference, anti-stealth, and anti-reverse missile, and have been of great interest and research in recent years. The bistatic MIMO radar can fully utilize the space-time information to realize joint estimation of parameters such as the wave-leaving direction angle (Direction of Departure, DOD) and the wave-reaching direction angle (Direction of Arrival, DOA) of a target, doppler frequency and the like. After the MIMO radar obtains the target wave separation angle, the wave arrival angle and the Doppler frequency parameter, the target can be positioned and tracked in a crossing way. Most of the existing algorithms are joint estimation of DOD, DOA, doppler frequency and the like of targets by applying a traditional super-resolution algorithm on the basis of a radar with a conventional array structure, such as a two-dimensional MUSIC algorithm, a multi-dimensional ESPRIT algorithm and some improved algorithms thereof, but when multi-dimensional parameter joint estimation is carried out on a plurality of targets, the algorithms are extremely complex and are not beneficial to implementation or have poor precision. In order to reduce algorithm complexity, document [1] proposes a dimension-reducing MUSIC algorithm (RD MUSIC), which converts two-dimensional spectral peak search into two-dimensional spectral peak search, thereby well reducing algorithm complexity and completing DOD and DOA joint estimation of a target. The algorithm can realize the joint estimation of the target DOD and DOA, but does not consider the Doppler frequency joint estimation, and along with the advancement of research, a subsequent learner expands the receiving-transmitting angle joint estimation to the receiving-transmitting angle and Doppler frequency joint estimation, the complexity of the algorithm is further increased due to the increase of the parameters to be estimated, and the accuracy of the estimated parameters is also more difficult to ensure. The documents [2] and [3] realize joint estimation of the receiving and transmitting angles and Doppler frequencies of the targets by constructing a space-time model of the received signals and utilizing a multidimensional ESPRIT algorithm, but the algorithm has low complexity and precision and requires an additional pairing algorithm for parameter estimation. Document [4] proposes a bistatic MIMO radar receiving and transmitting angle and Doppler frequency joint estimation algorithm based on parallel factor analysis, which fully utilizes all information of a receiving end, adopts a least square iteration method to obtain a target value to be estimated, and can realize automatic parameter pairing. The algorithm has lower complexity and higher parameter estimation accuracy than the multidimensional ESPRIT algorithm. Document [5] expands a uniform linear array into a uniform rectangular array, and provides a four-dimensional angle and Doppler frequency joint estimation algorithm by using a tensor decomposition technology, wherein parameter pairing and multi-dimensional search are not needed in the algorithm, but the algorithm is slow in convergence speed, easy to converge to local optimum, and high in algorithm complexity, and an optimal solution is needed to be found through a plurality of groups of initial values. For the parallel factor method, the transmitting coefficient is required to be taken as priori knowledge, and document [6] proposes a four-wire decomposition algorithm which does not need the priori knowledge, and the algorithm obtains the receiving and transmitting angle and Doppler frequency of a target through a four-wire alternating least square iteration (Quadrilinear ALTERNATING LEAST square, QALS) method and does not need spectral peak searching and parameter additional pairing. In order to achieve higher accuracy of parameter estimation and higher degrees of freedom, sparse arrays are introduced into the joint estimation of target DOD, DOA and doppler frequency, e.g. minimal redundant arrays, nested arrays and reciprocal arrays are proposed successively in view of achieving larger array aperture, lower mutual coupling effect and higher degrees of freedom of the arrays. Document [7] proposes a target receiving and transmitting angle and Doppler frequency joint estimation algorithm based on a minimum redundant array MIMO radar, the algorithm utilizes a virtual array formed by the minimum redundant array and non-uniform delay sampling to realize the secondary expansion of the aperture degrees of freedom of a t