FDA-MIMO radar parameter estimation method based on GAMP algorithm

Abstract

The application provides an FDA-MIMO radar parameter estimation method based on a GAMP algorithm, a FDA-MIMO radar receiving signal model is established, and sparse expression of the FDA-MIMO radar receiving signal model is determined based on grid division results in the angle dimension and the distance dimension; the GAMP algorithm is used to replace the original SBL algorithm to form an SBL-GAMP algorithm, and parameter estimation of the FDA-MIMO radar is carried out according to the SBL-GAMP algorithm and the sparse expression of the FDA-MIMO radar receiving signal model, so that the E step calculation of the EM step in the SBL algorithm is replaced by the GAMP algorithm, the calculation complexity in the solving process of the SBL algorithm is reduced while the estimation performance is reserved, the target angle-distance two-dimensional joint estimation is effectively realized, and the parameter estimation efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of radar technology, and specifically to an FDA-MIMO radar parameter estimation method based on the GAMP algorithm. Background Technology

[0002] Traditional Sparse Bayesian Learning (SBL) algorithms, as a high-performance algorithm in compressed sensing, show good performance in radar direction of arrival (DOA) estimation. However, its solution process requires a large number of matrix inversion operations, resulting in high computational complexity, which increases exponentially with the data dimensionality. Therefore, SBL is not suitable for large datasets and high-dimensional data, hindering its application in many practical problems. Introducing SBL into the joint angle and range estimation of frequency diversity array (FDA)-multiple-input multiple-output (MIMO) radar requires dividing the angle and range dimensions into discrete grids. This results in a very large dictionary matrix dimension, which, due to computational complexity, may exceed the device's computational performance limits during the calculation process, leading to joint estimation failure. Summary of the Invention

[0003] To address the aforementioned problems in the existing technology, this invention provides a method for estimating FDA-MIMO radar parameters based on the GAMP algorithm. Specifically, it includes:

[0004] In a first aspect, the present invention provides an FDA-MIMO radar parameter estimation method based on the GAMP algorithm, comprising:

[0005] An FDA-MIMO radar received signal model is established, and the sparse representation of the FDA-MIMO radar received signal model is determined based on the grid partitioning results of the angle dimension and the range dimension.

[0006] The original SBL algorithm is replaced by the GAMP algorithm to form the SBL-GAMP algorithm, and the parameters of the FDA-MIMO radar are estimated based on the SBL-GAMP algorithm and the sparse representation of the FDA-MIMO radar received signal model.

[0007] Secondly, the present invention also provides a target localization method based on FDA-MIMO radar, comprising:

[0008] The parameter estimates of the FDA-MIMO radar are obtained according to any of the FDA-MIMO radar parameter estimation methods based on the GAMP algorithm provided in the first aspect.

[0009] The target location is determined based on the parameter estimation of the FDA-MIMO radar.

[0010] Thirdly, the present invention also provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0011] Memory, used to store computer programs;

[0012] A processor, when executing a program stored in memory, implements either the first aspect or the second aspect.

[0013] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements any of the methods provided in the first or second aspect.

[0014] Fifthly, the present invention provides a program product comprising computer program instructions that, when executed, can implement any of the methods provided in the first or second aspect.

[0015] The beneficial effects of this invention are:

[0016] The present invention provides a parameter estimation method for FDA-MIMO radar based on the GAMP algorithm. This method establishes an FDA-MIMO radar received signal model and determines its sparse representation based on the grid partitioning results of the angle and range dimensions. It replaces the original SBL algorithm with the GAMP algorithm to form the SBL-GAMP algorithm, and estimates the parameters of the FDA-MIMO radar based on the SBL-GAMP algorithm and the sparse representation of the FDA-MIMO radar received signal model. This method replaces the E-step calculation of the EM step in the SBL algorithm with the GAMP algorithm, reducing the computational complexity of the SBL algorithm while preserving estimation performance. It effectively achieves joint target angle-range estimation while improving parameter estimation efficiency.

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 A flowchart illustrating an FDA-MIMO radar parameter estimation method based on the GAMP algorithm provided by this invention;

[0019] Figure 2 A schematic diagram of the transmit and receive system structure of an FDA-MIMO radar provided by the present invention;

[0020] Figure 3 This invention provides a schematic diagram of a two-dimensional grid partitioning and rearrangement rule based on angular distance.

[0021] Figure 4 This is a schematic diagram of the amplitude of a sparse signal recovered by the GAMP algorithm provided by the present invention;

[0022] Figure 5 A schematic diagram of an angular dimension slice provided by the present invention;

[0023] Figure 6 A schematic diagram of a distance dimension slice provided by the present invention;

[0024] Figure 7 This invention provides a sparse signal power spectrum recovered using the GAMP algorithm.

[0025] Figure 8 A schematic diagram of an angle estimation error result provided by the present invention;

[0026] Figure 9 This is a schematic diagram of a distance estimation error result provided by the present invention. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0028] Frequency diversity arrays (FDAs), with their range-angle dependent transmit radiation patterns, have attracted widespread attention. Furthermore, combining them with multiple-input multiple-output (MIMO) architectures and separating the transmitted waveforms through matched filtering provides additional degrees of freedom in the range domain. Traditional subspace methods such as Multiple Signal Classification (MUSIC) and Estimating signal parameters via rotational invariance techniques (ESPRIT) can simultaneously estimate target range and angle, but require high signal-to-noise ratios and multi-frame scenarios. Compressed sensing algorithms, with their good performance in signal recovery, have been introduced into the field of radar signal arrival direction estimation. The SBL algorithm, as a compressed sensing algorithm, has demonstrated its performance in DOA estimation for array radars and can achieve good DOA estimation even with low frame rates. However, its application in target parameter estimation for FDA-MIMO radars often requires additional processing, such as transforming the steering vector matrix form and transmitting double-pulse signals to achieve angle-range decoupling.

[0029] To preserve the performance of the SBL algorithm while addressing the issue that its high computational complexity prevents direct joint estimation of target angle and range for FDA-MIMO radar, this invention proposes an improved FDA-MIMO sparse Bayesian parameter estimation method based on a message-passing algorithm. The method replaces the E-step calculation of the Expectation-Maximum (EM) step in the SBL algorithm with the Generalized Approximate Message Passing (GAMP) algorithm, thereby reducing the computational complexity of the SBL algorithm while preserving its estimation performance and effectively achieving two-dimensional joint estimation of target angle and range.

[0030] Figure 1 This is a flowchart illustrating an FDA-MIMO radar parameter estimation method based on the GAMP algorithm provided by the present invention, as shown below. Figure 1 As shown, the method includes:

[0031] S101. Establish the FDA-MIMO radar received signal model and determine the sparse representation of the FDA-MIMO radar received signal model based on the grid partitioning results of the angle dimension and the range dimension.

[0032] Optionally, the expression for the received signal model corresponding to the nth receiving element of the FDA-MIMO radar is:

[0033]

[0034] Where ξ represents the target scattering coefficient, M represents the total number of transmitting array elements, m represents the index of the transmitting array element, and f m This represents the carrier frequency of the m-th transmitting element. Let τ be the complex envelope of the narrowband signal corresponding to the m-th transmitting element. n,m The time required for the nth receiving element to capture the echo signal transmitted by the mth transmitting element is denoted by t, where t represents the time series and j represents the imaginary unit.

[0035] The sparse representation of the FDA-MIMO radar received signal model is expressed as follows:

[0036] y=Aξ+n

[0037] in, This represents the result after matched filtering of the received signal, where M represents the total number of transmitting array elements and N represents the total number of receiving array elements. This represents a complete matrix, where P represents the number of angle-dimensional grids and Q represents the number of distance-dimensional grids. ξ represents the scattering coefficient, a sparse vector of order PQ×1. The non-zero elements of ξ correspond to the angles and distances of the true target. Let Aξ represent the noise matrix after matched filtering, and let Aξ represent the noise-free output corresponding to the received signal after matched filtering.

[0038] Specifically, Figure 2 The present invention provides a schematic diagram of the transmission and reception system of an FDA-MIMO radar. The transmitting end is a uniform linear array composed of M omnidirectional antenna elements, and the receiving end is a uniform linear array composed of N elements, with the spacing between the elements being d.

[0039] At the transmitting end, taking the first element from the left as the reference element and its carrier frequency f1 as the reference carrier frequency, then the carrier frequency of the m-th transmitting element is:

[0040] f m =f1+(m-1)Δf,m=1,2,…M

[0041] The transmitted signal is in pulse signal form:

[0042]

[0043] Among them, T p The duration of the pulse. Let rect(t) be the complex envelope of the m-th narrowband signal.

[0044]

[0045] If the transmitted waveform of the FDA-MIMO radar is an orthogonal waveform, then the following condition must be met:

[0046]

[0047] Where τ is an arbitrary time delay.

[0048] Assume there exists a far-field target with an angle θ0 between it and the normal of the transmitting array, and a propagation distance of R0. After reflection from the target, the time required for the nth receiving element to capture the echo signal transmitted by the mth transmitting element is:

[0049]

[0050] Then the nth receiving element receives all the echo signals as follows:

[0051]

[0052] Where ξ is the target scattering coefficient.

[0053] MIMO radar systems require matched filtering at the receiver, while the frequency offset inherent in the FDA system leads to differences in the processing flow. It requires an additional digital mixing step before matched filtering to extract the extra information introduced by Δf. The overall operation flow is as follows:

[0054] Each receiver element has M matched filters, corresponding to M transmitted waveforms. The impulse function of the m-th matched filter is:

[0055]

[0056] The form of the m-th transmitted signal received by the n-th receiving element after matched filtering is:

[0057]

[0058] After completing the digital mixing and matched filtering of all array elements, the received signals are combined. The combined signal is:

[0059] y S =[y 11 ,y 12 ,…,y 1N ,y 21 ,…,y mn …,y MN ] T

[0060] The target transmission steering vector a(R0,θ0) and the reception steering vector b(θ0) are as follows:

[0061]

[0062]

[0063] The combined signal can then be written in the following form:

[0064]

[0065] in, Represents the Kronecker product. This is the virtual joint guidance vector for the FDA-MIMO radar.

[0066] Next, both the angle and distance dimensions are transformed into sparse representations, which requires meshing in the angle and distance dimensions, such as... Figure 3 As shown, assuming P grids are divided in the angle dimension and Q grids in the distance dimension, the two-dimensional discrete grids of angle and distance are rearranged and combined into a one-dimensional grid. The complete dictionary matrix is ​​written as follows.

[0067] Considering the presence of noise, the sparse representation of the received signal after matched filtering is as follows:

[0068] y=Aξ+n

[0069] in, For a complete matrix, The result of matched filtering of the received signal; It is a PQ×1 sparse vector, and the angles and distances corresponding to its non-zero elements represent the true target angles and distances; This represents the noise matrix after matched filtering.

[0070] S102. The original SBL algorithm is replaced by the GAMP algorithm to form the SBL-GAMP algorithm, and the parameters of the FDA-MIMO radar are estimated based on the SBL-GAMP algorithm and the sparse representation of the FDA-MIMO radar received signal model.

[0071] The SBL algorithm first treats the unknown parameter vector to be estimated as a random vector that conforms to a certain prior distribution, and determines the prior distribution based on previous knowledge of the parameter to be estimated; then, based on the sample information, it uses Bayes' rule to calculate the posterior probability distribution; finally, it combines the prior information and the posterior probability to make an inference about the unknown parameter.

[0072] SBL typically includes the following steps:

[0073] 1. Initialization: Initialize the model parameters, including noise variance, hyperparameters of the prior distribution of sparse coefficients, and other relevant parameters.

[0074] 2. Expectation-Maximization (EM) Iteration:

[0075] Step E: Given the current parameter estimates, estimate the sparse coefficients using Bayesian inference techniques.

[0076] M-step: Given the estimated sparse coefficients, update the model parameters using either maximum likelihood estimation or maximum a posteriori estimation.

[0077] 3. The E-step and M-step are performed alternately. The iteration stops when the convergence condition is met, and the relevant parameters are recovered.

[0078] In one possible implementation, the original SBL algorithm is replaced by the GAMP algorithm to form the SBL-GAMP algorithm. The parameters of the FDA-MIMO radar are estimated based on the sparse representation of the SBL-GAMP algorithm and the sparse representation of the FDA-MIMO radar received signal model. This includes: replacing the E step in the original SBL algorithm with the GAMP algorithm to form the SBL-GAMP algorithm; and, based on the sparse representation of the FDA-MIMO radar received signal model, alternately executing the GAMP algorithm and the M step in the SBL-GAMP algorithm until a preset convergence condition or maximum number of iterations is reached to complete the parameter estimation of the FDA-MIMO radar.

[0079] Optionally, the GAMP algorithm in the SBL-GAMP algorithm is executed based on the sparse representation of the FDA-MIMO radar received signal model, including:

[0080] 1. Update the noise-free output in the sparse representation of the FDA-MIMO radar receive signal model. The updated noise-free output is represented as follows:

[0081] z(t)=Aμ(t),

[0082] Where A represents the complete matrix, μ(t) represents the posterior mean of ξ, z(t) represents the noise-free output, t represents the number of iterations, and t represents the number of iterations.

[0083] 2. Based on the updated noise-free output, update the approximate value of the noise-free output. The updated approximate value of the noise-free output is expressed as:

[0084] h(t) = c(t-1) + τ h (t)Aμ(t),

[0085] Where h(t) represents an approximation of z(t), c(t-1) is an intermediate parameter, and τ h (t) represents the variance of h(t).

[0086] 3. Based on the updated approximate value of the noise-free output, update the preset target intermediate parameters and the variance of the preset target intermediate parameters. The updated preset target intermediate parameters are expressed as follows:

[0087] c(t)=g in (h(t),τ h (t)),

[0088] Among them, g in (·) indicates that the input is a scalar function. σ 2 This represents the variance of the noise.

[0089] 4. The variance of the updated target intermediate parameters is expressed as follows:

[0090] τ c (t)=τ h (t)g' in (h(t),τ h (t)),

[0091] Where, τ h (t) represents the variance of the noise-free output approximation, g' in (·) represents the derivative of the input scalar function.

[0092] 5. Based on the updated preset target intermediate parameters and the variance of the updated preset target intermediate parameters, update the approximate values ​​of the scattering coefficients and the variance of the approximate values ​​of the scattering coefficients in the sparse representation of the FDA-MIMO radar received signal model. The variance of the updated approximate values ​​of the scattering coefficients is expressed as:

[0093]

[0094] Here, ⊙ is the Hadamard operator, which indicates the multiplication of corresponding elements in the matrix.

[0095] The updated approximate value of the scattering coefficient is expressed as:

[0096] r(t)=μ(t)-τ r (t)A T c(t),

[0097] Among them, A T τ represents the transition to a complete matrix. r (t) is the variance of the approximate value of the updated scattering coefficient.

[0098] 6. Based on the variance and approximate values ​​of the updated scattering coefficients, the mean and variance of the scattering coefficients are obtained. The mean of the scattering coefficients is expressed as:

[0099] μ(t+1)=g out (r(t),τ r (t)),

[0100] Among them, g out(·) indicates that the output scalar function is used.

[0101] The variance of the scattering coefficient is expressed as:

[0102] τ μ (t+1)=τ r (t)g' out (r(t),τ r (t)),

[0103] Among them, g' out (·) represents the derivative of the output scalar function.

[0104] Correspondingly, the preset convergence conditions can be:

[0105]

[0106] Where ε represents the convergence threshold.

[0107] Optionally, before updating the noise-free output in the sparse representation of the FDA-MIMO radar receive signal model, the following steps are also included:

[0108] 1. Determine the likelihood function of the sparse representation of the FDA-MIMO radar received signal model. The likelihood function is expressed as:

[0109]

[0110] 2. Determine the hyperparameter vector α of the target scattering coefficient ξ and the hyperparameter vector σ of the noise n. 2 , and α and σ 2 An approximation of is expressed as:

[0111]

[0112] Where α=[α1,α2,…,α PQ ].

[0113] 3. The approximate true posterior distribution p(ξ|y,ρ) corresponding to the target scattering coefficient ξ is expressed as:

[0114]

[0115] in, This represents a complex Gaussian distribution.

[0116] 4. The approximate true posterior margin p(z|y,ρ) for noise-free output is expressed as:

[0117]

[0118] Where the noise-free output is represented by z = Aξ, h represents the approximate value of the noise-free output, and τh This represents the variance of h.

[0119] 5. Based on the approximate representation of the true posterior distribution corresponding to the target scattering coefficients and the approximation of the true posterior margin of the noise-free output, determine the input scalar function and its derivative, as well as the output scalar function and its derivative. The input scalar function is expressed as:

[0120]

[0121] The derivative of the input scalar function is expressed as:

[0122]

[0123] The output scalar function is represented as:

[0124]

[0125] The derivative of the output scalar function is expressed as:

[0126]

[0127] Specifically, GAMP is a Bayesian iterative technique with very low computational complexity. It mainly replaces the E-step in the EM step of the SBL algorithm, and finally obtains the mean and variance of ξ.

[0128] Assume the noise n follows a mean of 0 and a variance of σ. 2 The complex Gaussian distribution:

[0129]

[0130] Then the likelihood function of y can be written as

[0131]

[0132] Set α = [α1, α2, ..., α PQ ] is the hyperparameter vector of ξ, σ 2 Let n be the hyperparameter vector.

[0133] The idea behind the GAMP algorithm is to provide a posterior distribution p(ξ|y,α,σ). 2 The approximation of ξ is based on the premise that the prior distribution of ξ is known and the distribution of additive noise n is factorable. Therefore, it can be naturally embedded within the expectation maximization (EM) framework of the SBL algorithm to provide an approximate posterior distribution of ξ instead of the true posterior distribution. Combining GAMP with the SBL algorithm mainly involves replacing the E-step in the EM step. Therefore, the improved algorithm will include the hyperparameters {α, σ} in the GAMP calculation process. 2} is considered to be known and fixed, while {α,σ}2 The value can be updated in M ​​steps based on the approximate posterior distribution of ξ.

[0134] During the GAMP iteration process, relevant parameters need to be introduced for approximation. First, intermediate parameters r and τ are introduced. r , represent the approximation of the scattering coefficient ξ and the variance of its approximation r, respectively, updated in each GAMP iteration, and the explicit dependence on the iteration number t is abandoned in each EM algorithm iteration. Typically, in GAMP algorithm development, the values ​​of the two hyperparameters are approximated:

[0135] GAMP assumes posterior independence among latent variables ξ, and the true posterior distribution p(ξ|y,ρ) is approximated by the following formula:

[0136]

[0137] It can be seen that the approximate posterior distribution It also follows a complex Gaussian distribution.

[0138] Finally, the noiseless output z = Aξ is approximated as h, τ h Let h be the variance.

[0139] Here, the explicit dependence on the iteration number t is also abandoned in each iteration of the EM algorithm. Under additive white noise conditions, the GAMP approximate true posterior edge p(z|y,ρ) also follows a complex Gaussian distribution, expressed as:

[0140]

[0141] Based on the above approximation, we can now define two important scalar functions: the input and output functions. In the GAMP algorithm, g is used... in (·) and g out (·) serves as both the input and output of the likelihood function g(·). The input is a scalar function g. in (·) can be used to determine intermediate parameters c and τ c The update outputs the scalar function g. out (·) can update the posterior mean and variance of ξ.

[0142] The definition of the input function can be expressed as:

[0143]

[0144] Where the subscript i∈[1,2,…,MN] represents the i-th input function.

[0145] Further, we obtain the input scalar function:

[0146]

[0147] Input function g in (h,τ h The derivative of ) is expressed as:

[0148]

[0149] In MMSE mode, the output scalar function g is used. out (r,τ r Simply defined as the posterior mean μ of ξ ξ , is represented as:

[0150]

[0151] Output scalar function g out (r,τ r The derivative of ) is expressed as:

[0152]

[0153] Optionally, the M-step of the SBL-GAMP algorithm is performed based on the sparse representation of the FDA-MIMO radar received signal model, including:

[0154] 1. Based on the partial derivative of the Q function with respect to the hyperparameter α, the update rule for the hyperparameter α is obtained, expressed as:

[0155] α new =μ ξ 2 +τ ξ ,

[0156] Wherein, the Q function is represented as E ξ|y,ρ [lnp(ρ|ξ,y)],

[0157] 2. Based on the Q function relative to the noise variance σ 2 The partial derivatives are used to obtain the noise variance σ. 2 The update rule is represented as:

[0158]

[0159] Specifically, after completing the GAMP algorithm process, the M-step computation begins, through which hyperparameters are determined. The update requires updating the Q function E. ξ|y,ρ [lnp(ρ|ξ,y)]. Then, M steps are performed to calculate the hyperparameter α, and the partial derivatives of the Q function with respect to α are taken.

[0160]

[0161] Since the true posterior distribution of ξ cannot be obtained, an approximate posterior distribution of ξ obtained from the GAMP algorithm is used to replace the true posterior distribution. The update rule for α is given below:

[0162] α new =μ ξ 2 +τ ξ

[0163] Now we will calculate the noise hyperparameter σ. 2 The update, since the GAMP algorithm also provides an approximate posterior distribution for the noise-free output z, can simply treat z as a hidden variable when learning the noise variance, i.e.:

[0164]

[0165] Take the Q function with respect to σ 2 The partial derivatives yield the update rule as follows:

[0166]

[0167] The present invention provides a parameter estimation method for FDA-MIMO radar based on the GAMP algorithm. This method establishes an FDA-MIMO radar received signal model and determines its sparse representation based on the grid partitioning results of the angle and range dimensions. It replaces the original SBL algorithm with the GAMP algorithm to form the SBL-GAMP algorithm, and estimates the parameters of the FDA-MIMO radar based on the SBL-GAMP algorithm and the sparse representation of the FDA-MIMO radar received signal model. This method replaces the E-step calculation of the EM step in the SBL algorithm with the GAMP algorithm, reducing the computational complexity of the SBL algorithm while preserving estimation performance. It effectively achieves joint target angle-range estimation in two dimensions and improves parameter estimation efficiency.

[0168] Furthermore, the present invention also provides a target localization method based on FDA-MIMO radar, comprising: obtaining parameter estimates of FDA-MIMO radar according to the FDA-MIMO radar parameter estimation method based on the GAMP algorithm provided in any of the above embodiments; and determining the target position based on the parameter estimates of FDA-MIMO radar.

[0169] Specifically, after completing all EM iterations, the peak point of the posterior mean of ξ is searched, and its coordinates in the angular and distance dimensions correspond to the target position, thereby achieving target localization.

[0170] It should be noted that the target estimated in the first grid estimation is often not on the grid, requiring further grid refinement for precise target location estimation. The EM process needs to be performed on a one-dimensional grid, while target localization needs to be converted back to a two-dimensional grid. This invention further investigates the iterative process of grid refinement. After the previous algorithm finishes, the one-dimensional grid is rearranged into a two-dimensional grid, the target's coordinates on the grid are found, and the grid is refined in the angle and distance dimensions. Then, it is rearranged again into a one-dimensional matrix for the next algorithm iteration, until the grid is very small and the iteration stops.

[0171] To further demonstrate the beneficial effects of the present invention, two sets of simulation experimental data are also provided, as follows:

[0172] A uniform linear array of M=N=8 was constructed to evaluate the estimation performance of angles and distances. The root mean square error (RMSE) of the angle and distance estimation results was used for performance evaluation and compared with the Cramé-Rao boundary (CRB).

[0173] Experiment 1: Set the target angle to 5.5°, distance to 2600m, transmit signal reference frequency f0 = 10GHz, frequency increment Δf = 30kHz, and signal-to-noise ratio to 20dB. Figure 4 The amplitude distribution of the sparse signal recovered by the GAMP algorithm in the angle-distance two-dimensional domain is given. Figure 5 For the angular dimension, the amplitude of the sparse signal is tangent. Figure 6 For the amplitude of a sparse signal, the cross-section in the distance dimension. Figure 7 The power spectrum of the sparse signal is a two-dimensional distribution. It can be seen that the amplitude and the peak of the power spectrum fall at the target location. In other words, the GAMP algorithm can effectively achieve two-dimensional joint parameter estimation of FDA-MIMO radar targets.

[0174] Experiment 2: Target and radar parameters remain constant, with a signal-to-noise ratio ranging from -10dB to 20dB. Figure 8 These are the RMSE and CRB variation curves for angle estimation. Figure 9 These are the RMSE and CRB curves for distance estimation. It can be seen that the RMSE curve is close to the CRB curve at high signal-to-noise ratios, which means that the estimation result is close to the lower bound of the performance, achieving high-precision estimation.

[0175] This invention also provides a schematic diagram of the structure of an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus.

[0176] Memory, used to store computer programs;

[0177] When a processor executes a program stored in memory, it implements the steps provided in the above method embodiments.

[0178] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0179] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps provided in the above-described method embodiments.

[0180] The present invention also provides a program product comprising computer program instructions, which, when executed, can implement the steps provided in the above method embodiments.

[0181] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for estimating FDA-MIMO radar parameters based on the GAMP algorithm, characterized in that, include: An FDA-MIMO radar received signal model is established, and the sparse representation of the FDA-MIMO radar received signal model is determined based on the grid partitioning results of the angle dimension and the range dimension. The original SBL algorithm is replaced by the GAMP algorithm to form the SBL-GAMP algorithm. Parameter estimation for the FDA-MIMO radar is then performed based on the SBL-GAMP algorithm and the sparse representation of the FDA-MIMO radar received signal model. Specifically, this includes: replacing the E-step in the original SBL algorithm with the GAMP algorithm to form the SBL-GAMP algorithm; and, based on the sparse representation of the FDA-MIMO radar received signal model, alternately executing the GAMP algorithm and the M-step in the SBL-GAMP algorithm until a preset convergence condition or maximum number of iterations is reached to complete the parameter estimation for the FDA-MIMO radar. The original E-step estimates the sparse coefficients using Bayesian inference given the current parameter estimates; the M-step updates the model parameters using maximum likelihood estimation or maximum a posteriori estimation given the estimated sparse coefficients.

2. The method according to claim 1, characterized in that, FDA-MIMO radar's first The expression for the received signal model corresponding to each receiving array element is: ， in, Represents the target scattering coefficient. This indicates the total number of elements in the transmitting array. Indicates the index of the transmitting array element. Indicates the first The carrier frequency of each transmitting element For the first The complex envelope of the narrowband signal corresponding to each transmitting element Indicates the first The first receiver element captured the first The time required for each transmitting element to transmit an echo signal Representing a time series, Represents the imaginary unit; The sparse expression of the FDA-MIMO radar received signal model is as follows: ， in, This represents the result of matched filtering of the received signal. This indicates the total number of elements in the transmitting array. This represents the total number of receiving array elements. Representing a complete matrix, For the FDA-MIMO radar, the virtual joint guidance vector for transmission and reception. For FDA launch guidance vector, For MIMO receiver steering vector; Represents the number of grid cells in the angular dimension. Indicates the number of grid cells in the distance dimension. Represents the scattering coefficient, which is 1st order sparse vector, The non-zero elements represent the actual target angle and distance. This represents the noise matrix after matched filtering. This indicates the noise-free output corresponding to the received signal after matched filtering.

3. The method according to claim 2, characterized in that, The GAMP algorithm in the SBL-GAMP algorithm is executed based on the sparse representation of the FDA-MIMO radar received signal model, including: Update the noise-free output in the sparse representation of the FDA-MIMO radar received signal model to the noise-free output of the first sparse representation. Taking the next iteration as an example, the updated noiseless output is represented as follows: ， in, Representing a complete matrix, express The posterior mean, This indicates no noise output. Indicates the number of iterations; Based on the updated noise-free output, the approximate value of the noise-free output is updated, and the updated approximate value of the noise-free output is expressed as follows: ， in, express Approximate value, For intermediate parameters, express The variance; Based on the updated approximation of the noise-free output, the preset target intermediate parameters and the variance of the preset target intermediate parameters are updated. The updated preset target intermediate parameters are expressed as follows: ， in, Indicates that the input is a scalar function. , Represents the variance of the noise; The variance of the updated target intermediate parameters is expressed as: ， in, The variance of the approximate value of the noise-free output. This represents the derivative of the input scalar function; Based on the updated preset target intermediate parameters and the variance of the updated preset target intermediate parameters, the approximate values ​​of the scattering coefficients in the sparse representation of the FDA-MIMO radar received signal model and the variance of the approximate values ​​of the scattering coefficients are updated. The variance of the updated approximate values ​​of the scattering coefficients is expressed as: ， in, This is the Hadamard operator, which indicates the multiplication of corresponding elements in a matrix. The updated approximate value of the scattering coefficient is expressed as: ， in, Represents the transpose of a complete matrix. The variance of the updated approximate value of the scattering coefficient; Based on the variance of the updated approximation of the scattering coefficients and the updated approximation of the scattering coefficients, the mean and variance of the scattering coefficients are obtained. The mean of the scattering coefficients is expressed as: ， in, This indicates that the output is a scalar function. The variance of the scattering coefficient is expressed as: ， in, This represents the derivative of the output scalar function.

4. The method according to claim 3, characterized in that, Before updating the noise-free output in the sparse representation of the FDA-MIMO radar received signal model, the method further includes: Determine the likelihood function of the sparse representation of the FDA-MIMO radar received signal model, wherein the likelihood function is expressed as: ； Determine the target scattering coefficient hyperparameter vector and noise variance ,as well as and The approximate values ​​of these parameters together constitute the hyperparameter set, which is expressed as: ， in, ; Approximate representation of target scattering coefficient The corresponding true posterior distribution , represented as: ； Approximate representation of the true posterior margins of noise-free output , represented as: ， Wherein, noiseless output is represented as , This represents an approximate value for noise-free output. express The variance; Based on the approximate representation of the true posterior distribution corresponding to the target scattering coefficients and the approximation of the true posterior margin of the noise-free output, the input scalar function and its derivative, as well as the output scalar function and its derivative, are determined. The input scalar function is expressed as: ， The derivative of the input scalar function is expressed as: ， The output scalar function is expressed as: ， The derivative of the output scalar function is expressed as: 。 5. The method according to claim 4, characterized in that, The M step of the SBL-GAMP algorithm is performed based on the sparse representation of the FDA-MIMO radar received signal model, including: Based on the Q function relative to hyperparameters The partial derivatives are used to obtain the hyperparameters. The update rules are expressed as follows: ， in, Let ξ be the posterior mean of the scattering coefficients ξ output by the GAMP. for The posterior variance; the Q function is expressed as , ; Based on the Q function relative to the noise variance The partial derivatives are used to obtain the noise variance. The update rule is represented as: in, express The Middle One element, express The Middle Each element.

6. A target localization method based on FDA-MIMO radar, characterized in that, include: The parameter estimates of the FDA-MIMO radar are obtained according to any of the FDA-MIMO radar parameter estimation methods based on the GAMP algorithm provided in claims 1-5. The target location is determined based on the parameter estimation of the FDA-MIMO radar.

7. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the method of any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method described in any one of claims 1-6.

9. A program product, characterized in that, The program product includes computer program instructions, which, when executed, enable the implementation of the method as described in any one of claims 1-6.

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