A multi-target position and velocity theoretical estimation accuracy calculation method and device

Abstract

The application relates to a multi-target position and velocity theoretical estimation precision calculation method and device. The method comprises the following steps: based on the time delay-Doppler coupling effect existing in the peak point position of the output result of linear frequency modulation (LFM) signal matching filtering, a first intermediate vector is constructed for a first FIM matrix model of an unknown parameter vector in a direct method measurement model, which is used for determining the root CRLB lower bound of each target position and velocity estimation; a second intermediate vector is introduced for a peak point measurement value model in a time domain, which is used for determining the root SLB lower bound of each target position and velocity estimation, and the CRLB and the SLB are combined to determine a multi-target position and velocity theoretical estimation precision result. The application gives a theoretical performance lower bound of target position and velocity parameter estimation by only using the time delay-Doppler coupling effect of an LFM signal, and quantitatively describes the influence of a signal sampling rate on target parameter estimation precision.

Description

Technical Field

[0001] This application relates to the field of radar technology, and in particular to a method and apparatus for calculating the accuracy of theoretical estimation of the position and velocity of multiple targets. Background Technology

[0002] Distributed MIMO radar is a novel radar system where the transceiver nodes are widely distributed in space. It fully utilizes spatial / angular diversity to enhance the system's target detection, tracking, and acquisition capabilities, while also possessing stronger survivability and resilience compared to traditional monostatic radars. Therefore, distributed MIMO radar has gained widespread attention in recent years and shows promising application and development prospects.

[0003] From a signal processing perspective, distributed MIMO radar can be categorized into coherent and incoherent processing. Coherent processing requires system time and phase synchronization, which places stringent demands on the hardware system and typically results in high construction costs. In contrast, incoherent processing only requires system time synchronization, making it easier to implement in hardware and offering a cost advantage. Target parameter estimation is one of the fundamental tasks of distributed MIMO radar. Existing target parameter estimation methods can be broadly classified into indirect and direct methods. Indirect methods estimate target parameters in two steps: first, obtaining specific intermediate measurement data about the target in different transmit-receive channels, such as time delay and Doppler shift; second, using this intermediate measurement data to solve for the target parameters. Direct methods, on the other hand, directly estimate target parameters using the received echo signal. Because these two methods employ different measurement models, their theoretical estimation performance also differs. Extensive research has investigated the theoretical estimation accuracy of target parameters under indirect and direct method measurement models. A typical approach is to calculate the Cramér-Rao Lower Bound (CRLB) of the parameter estimates under the corresponding models to obtain the lower bound of the estimation variance. In the indirect measurement model, CRLB calculation starts directly from intermediate measurements, requiring relatively few derivation steps. However, the direct measurement model's CRLB calculation needs to consider factors such as signal type, target model, and noise model, making the derivation process more complex. For the direct method, most current research focuses on continuous signal models, with limited consideration of multi-target scenarios. Since signals in practical applications are sampled in discrete form, it is necessary to investigate the theoretical estimation accuracy of target parameters under discrete-time signal models. Summary of the Invention

[0004] Therefore, it is necessary to provide a method, apparatus, computer equipment, and storage medium for calculating the theoretical estimation accuracy of multi-target position and velocity under discrete-time signal models, which can be applied to address the above-mentioned technical problems.

[0005] A method for calculating the accuracy of theoretical estimation of multi-target position and velocity, the method comprising:

[0006] A direct measurement model for estimating the position and velocity parameters of multiple targets is constructed based on the output results of the matched filtering of linear frequency modulated signals in all transmit-receive channels of the distributed MIMO radar; however, the output results of the matched filtering of the linear frequency modulated signals exhibit a time delay-Doppler coupling effect at the peak point.

[0007] A first FIM matrix model of the unknown parameter vector in the direct method measurement model is constructed. Based on the time delay-Doppler coupling effect at the peak point position of the output result of the linear frequency modulated signal matched filtering, a first intermediate vector is constructed. The unknown parameter vector includes multi-target position and velocity parameter vectors. The first intermediate vector contains parameter vectors characterizing the relationship between the peak point position and time delay and Doppler frequency shift. The time delay and Doppler frequency shift are related to the multi-target position and velocity.

[0008] Based on the chain rule, the first FIM matrix model is solved using the intermediate vector to determine the root CRLB lower bound for the position and velocity estimation of each target.

[0009] For the discrete form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect existing at the peak point position in the output result of the matched filtering of the linear frequency modulated signal, a peak point measurement model in the time domain is constructed, and a second intermediate vector is introduced according to the peak point measurement model; the second intermediate vector contains parameter vectors of time delay and Doppler frequency shift; the time delay and Doppler frequency shift are related to the position and velocity of multiple targets;

[0010] Based on the chain rule, the second FIM matrix model of the multi-target position and velocity parameter vectors is solved by the second intermediate vector to determine the root SLB lower bound of the position and velocity estimation for each target.

[0011] The root mean square error lower bound of the position and velocity estimation of each target is obtained based on the root CRLB lower bound and the root SLB lower bound, and the theoretical estimation accuracy of the multi-target position and velocity of the direct method measurement model is determined.

[0012] A device for calculating the theoretical estimation accuracy of multi-target position and velocity, the device comprising:

[0013] The parameter estimation module is used to construct a direct measurement model for estimating the position and velocity parameters of multiple targets based on the output results of the matched filtering of the linear frequency modulated signals in all transmit-receive channels of the distributed MIMO radar; the output results of the matched filtering of the linear frequency modulated signals exhibit a time delay-Doppler coupling effect at the peak point position;

[0014] The first intermediate vector construction module is used to construct the first FIM matrix model of the unknown parameter vector in the direct method measurement model. Based on the time delay-Doppler coupling effect existing at the peak point position of the output result of the linear frequency modulated signal matched filtering, the first intermediate vector is constructed. The unknown parameter vector includes multi-target position and velocity parameter vectors. The first intermediate vector contains parameter vectors characterizing the relationship between the peak point position and the time delay and Doppler frequency shift. The time delay and Doppler frequency shift are related to the multi-target position and velocity.

[0015] The CRLB determination module is used to solve the first FIM matrix model based on the chain rule through the intermediate vector, and determine the root CRLB lower bound for the position and velocity estimation of each target respectively;

[0016] The second intermediate vector determination module is used to construct a time-domain peak point measurement model for the discrete form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect present at the peak point position of the output result of the matched filtering of the linear frequency modulated signal, and to introduce a second intermediate vector according to the peak point measurement model; the second intermediate vector contains parameter vectors of time delay and Doppler frequency shift; the time delay and Doppler frequency shift are related to the position and velocity of multiple targets;

[0017] The SLB determination module is used to solve the second FIM matrix model of the multi-target position and velocity parameter vectors based on the chain rule through the second intermediate vector, and determine the root SLB lower bound for the position and velocity estimation of each target respectively.

[0018] The estimation accuracy determination module is used to obtain the root mean square error lower bound of the position and velocity estimation of each target based on the root CRLB lower bound and the root SLB lower bound, and to determine the theoretical estimation accuracy result of the multi-target position and velocity of the direct method measurement model.

[0019] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:

[0020] A direct measurement model for estimating the position and velocity parameters of multiple targets is constructed based on the output results of the matched filtering of linear frequency modulated signals in all transmit-receive channels of the distributed MIMO radar; however, the output results of the matched filtering of the linear frequency modulated signals exhibit a time delay-Doppler coupling effect at the peak point.

[0021] A first FIM matrix model of the unknown parameter vector in the direct method measurement model is constructed. Based on the time delay-Doppler coupling effect at the peak point position of the output result of the linear frequency modulated signal matched filtering, a first intermediate vector is constructed. The unknown parameter vector includes multi-target position and velocity parameter vectors. The first intermediate vector contains parameter vectors characterizing the relationship between the peak point position and time delay and Doppler frequency shift. The time delay and Doppler frequency shift are related to the multi-target position and velocity.

[0022] Based on the chain rule, the first FIM matrix model is solved using the intermediate vector to determine the root CRLB lower bound for the position and velocity estimation of each target.

[0023] For the discrete form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect existing at the peak point position in the output result of the matched filtering of the linear frequency modulated signal, a peak point measurement model in the time domain is constructed, and a second intermediate vector is introduced according to the peak point measurement model; the second intermediate vector contains parameter vectors of time delay and Doppler frequency shift; the time delay and Doppler frequency shift are related to the position and velocity of multiple targets;

[0024] Based on the chain rule, the second FIM matrix model of the multi-target position and velocity parameter vectors is solved by the second intermediate vector to determine the root SLB lower bound of the position and velocity estimation for each target.

[0025] The root mean square error lower bound of the position and velocity estimation of each target is obtained based on the root CRLB lower bound and the root SLB lower bound, and the theoretical estimation accuracy of the multi-target position and velocity of the direct method measurement model is determined.

[0026] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0027] A direct measurement model for estimating the position and velocity parameters of multiple targets is constructed based on the output results of the matched filtering of linear frequency modulated signals in all transmit-receive channels of the distributed MIMO radar; however, the output results of the matched filtering of the linear frequency modulated signals exhibit a time delay-Doppler coupling effect at the peak point.

[0028] A first FIM matrix model of the unknown parameter vector in the direct method measurement model is constructed. Based on the time delay-Doppler coupling effect at the peak point position of the output result of the linear frequency modulated signal matched filtering, a first intermediate vector is constructed. The unknown parameter vector includes multi-target position and velocity parameter vectors. The first intermediate vector contains parameter vectors characterizing the relationship between the peak point position and time delay and Doppler frequency shift. The time delay and Doppler frequency shift are related to the multi-target position and velocity.

[0029] Based on the chain rule, the first FIM matrix model is solved using the intermediate vector to determine the root CRLB lower bound for the position and velocity estimation of each target.

[0030] For the discrete form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect existing at the peak point position in the output result of the matched filtering of the linear frequency modulated signal, a peak point measurement model in the time domain is constructed, and a second intermediate vector is introduced according to the peak point measurement model; the second intermediate vector contains parameter vectors of time delay and Doppler frequency shift; the time delay and Doppler frequency shift are related to the position and velocity of multiple targets;

[0031] Based on the chain rule, the second FIM matrix model of the multi-target position and velocity parameter vectors is solved by the second intermediate vector to determine the root SLB lower bound of the position and velocity estimation for each target.

[0032] The root mean square error lower bound of the position and velocity estimation of each target is obtained based on the root CRLB lower bound and the root SLB lower bound, and the theoretical estimation accuracy of the multi-target position and velocity of the direct method measurement model is determined.

[0033] The aforementioned method, apparatus, computer equipment, and storage medium for calculating the theoretical estimation accuracy of multi-target position and velocity, based on the constructed direct method measurement model for multi-target position and velocity parameter estimation, and considering the time delay-Doppler coupling effect at the peak point position in the output result of the linear frequency modulated signal matched filtering, constructs a first intermediate vector containing parameter vectors characterizing the relationship between peak point position and time delay and Doppler frequency shift for the first FIM matrix model of the unknown parameter vector in the direct method measurement model. This first intermediate vector is used to solve the first FIM matrix and determine the root CRLB lower bound for the estimation of each target position and velocity. A second intermediate vector containing parameter vectors of time delay and Doppler frequency shift is introduced into the peak point measurement model in the time domain. This second intermediate vector is used to solve the second FIM matrix and determine the root SLB lower bound for the estimation of each target position and velocity. The theoretical estimation accuracy result of multi-target position and velocity in the direct method measurement model is determined based on the root CRLB lower bound and the root SLB lower bound. This invention provides a theoretical lower bound for estimating target position and velocity parameters using only the time delay-Doppler coupling effect of LFM signals in the absence of phase information. It considers the influence of discrete sampling errors and quantitatively describes the impact of signal sampling rate on the accuracy of target parameter estimation. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating a method for calculating the theoretical estimation accuracy of multi-target position and velocity in one embodiment;

[0035] Figure 2This is a flowchart illustrating the method for calculating the accuracy of theoretical estimation of multi-target position and velocity in another embodiment;

[0036] Figure 3 This is a schematic diagram of a simulation experiment scenario in one embodiment;

[0037] Figure 4 This is a comparison chart of the theoretical estimation accuracy and the optimal estimation result of the target 1 position calculated in one embodiment;

[0038] Figure 5 A comparison chart showing the theoretical estimation accuracy and optimal estimation results of the target 2 position calculated in one embodiment;

[0039] Figure 6 A comparison chart of the theoretical estimation accuracy and the optimal estimation result of the target 3 position calculated in one embodiment;

[0040] Figure 7 This is a comparison chart of the theoretical estimation accuracy and the optimal estimation result of the velocity of target 1 calculated in one embodiment;

[0041] Figure 8 A comparison chart showing the theoretical estimation accuracy and optimal estimation results of the target 2 velocity calculated in one embodiment;

[0042] Figure 9 A comparison chart showing the theoretical estimation accuracy and optimal estimation results of the target 3 velocity calculated in one embodiment;

[0043] Figure 10 This is a structural block diagram of a multi-target position and velocity theoretical estimation accuracy calculation device in one embodiment;

[0044] Figure 11 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0046] In one embodiment, such as Figure 1 As shown, a method for calculating the accuracy of theoretical estimation of the position and velocity of multiple targets is provided, including the following steps:

[0047] Step 102: Construct a direct method measurement model for estimating the position and velocity parameters of multiple targets based on the output results of the matched filtering of the linear frequency modulated signals of all transmit-receive channels of the distributed MIMO radar.

[0048] The output of the matched filter for a linear frequency modulated signal exhibits a time delay-Doppler coupling effect at the peak point.

[0049] Consider a radar system in a two-dimensional scene consisting of M transmitters and N receivers. Each transmitter emits orthogonal LFM signals with energy E, and each signal consists of P (P≥1) independent pulses with different characteristics. For the m-th transmitter, the normalized waveform of its p-th pulse is written as:

[0050]

[0051] in For pulse width, For bandwidth, For frequency modulation, and for positive frequency modulation, For positive frequency modulation, The value is negative. The term Δf represents the frequency spacing parameter, which is used to maintain the approximate orthogonality between signals from different transmitters. Let the received signal of the p-th pulse at the n-th receiver be... It consists of the superposition of echoes from M transmitted signals reflected by K targets, and can be expressed as:

[0052]

[0053]

[0054] Where α mnk τ mnk and f mnk Let M and N represent the complex scattering coefficient, time delay, and Doppler shift of the k-th target in the mn-th transmit-receive channel, respectively. Let be the thermal noise of the nth receiver, which is modeled as a white complex Gaussian random process. PRI stands for Pulse Repetition Interval. At time t... c Receive signal and signal The output of the matched filter between them is expressed as:

[0055]

[0056] in For output noise, The original form of the matched filter associated with the k-th target is, i.e.

[0057]

[0058] Since phase information cannot be used under incoherent conditions, therefore, it is defined as follows: Its parsing expression can be written as:

[0059]

[0060] Where Δτ mnk =|t c -τ mnk |. We can see Its time-domain response exhibits narrow pulse characteristics, and its peak appears at... Place, that is This indicates the presence of a time-delay-Doppler coupling effect at the peak location. In other words, the peak location simultaneously contains both target position and velocity information.

[0061] The direct method measurement model for estimating the position and velocity parameters of multiple targets is a measurement model based on the time delay-Doppler coupling effect at the peak point position.

[0062] This direct method measurement model determines the parameter search space for target position and velocity based on the distributed MIMO radar detection scenario. The parameter search space is then divided into grids to determine the grid parameter vectors. Based on the output results of matched filtering of the linear frequency modulated signals from all transmit and receive channels of the distributed MIMO radar, the grid energy values ​​of the parameter search space are defined.

[0063]

[0064] in Represents the parameter vector The determined time-domain projection time, i.e.

[0065]

[0066] in and They are respectively The corresponding target position and velocity have time delay and Doppler frequency shift in the mn-th transmit-receive channel. The time delay and Doppler frequency shift are related to the position and velocity of multiple targets.

[0067] Construct an original solution model containing all grid energy values, and solve it to determine the position and velocity estimates of multiple targets.

[0068] Step 104: Construct the first FIM matrix model of the unknown parameter vector in the direct method measurement model. Based on the time delay-Doppler coupling effect of the output result of the linear frequency modulated signal matched filtering at the peak point, construct the first intermediate vector.

[0069] The unknown parameter vector includes multi-target position and velocity parameter vectors; the first intermediate vector contains parameter vectors representing the relationship between peak point position and time delay and Doppler frequency shift; time delay and Doppler frequency shift are related to multi-target position and velocity.

[0070] In practice, continuous signals are sampled into discrete signals using an ADC (Analog-to-Digital Converter). Let the sampling rate be f. s Therefore, the received signal can be rewritten as:

[0071]

[0072] i = 1, 2, ..., I

[0073] where i, i mnk I and t and τ are respectively mnk and The sampling index, f mnk [i] = (i / f s )f mnk For discrete-time Doppler frequency shift, and To ensure that the discrete-time signal is still normalized, the received discrete signal can be written in matrix form as follows:

[0074]

[0075] in

[0076]

[0077] S = blkdiag(S1,…,S) N ),S n =[S 1n ,…,S Mn ],S mn =[s mn1 ,…,s mnK ],

[0078]

[0079]

[0080]

[0081]

[0082] make Let be a vector of unknown parameters, where

[0083]

[0084] And u k and v k These are the position and velocity parameters of the k-th target, respectively. and Let α be the real part and α be the imaginary part, respectively. Then, given θ, the joint probability density function of r can be expressed as:

[0085]

[0086] in Let ω be the covariance matrix. Indicates the numerical value of the diagonal elements, I NIP Denotes an identity matrix of size NIP×NIP, det(Σ ω ) represents Σ ω The determinant of .

[0087] According to the definition of CRLB, for a parameter vector θ, its arbitrary unbiased estimator The lower bound of the variance of the i-th element is

[0088]

[0089] Where J(θ) is the FIM (Fisher Information Matrix) of θ, that is, the first FIM matrix model of the unknown parameter vector.

[0090]

[0091] in This represents the expected value. Since the position and velocity parameters of multiple targets are not directly related to the received signal, directly calculating J(θ) is difficult. Therefore, a common approach is to construct a suitable intermediate parameter vector and then solve it based on the chain rule. Because the model under consideration utilizes the time delay-Doppler coupling effect, its coupling mode (i.e., the relationship between the peak position of the matched filter output and the time delay and Doppler frequency shift) can be determined by the parameter vector. If we perform representation, then we can construct intermediate vectors. That is, the first intermediate vector, where

[0092]

[0093]

[0094]

[0095]

[0096] Step 106: Solve the first FIM matrix model using the intermediate vector based on the chain rule, and determine the root CRLB lower bound for the position and velocity estimation of each target respectively.

[0097] J(θ) can be rewritten as:

[0098]

[0099] in It can be written in block matrix form, that is

[0100]

[0101] in 0 2MNK×MNKP Let H represent a 2MNK×MNKP matrix of all zeros. The expressions for each element in matrix H can be calculated according to the definition. Next, we calculate FIM J(ζ), which can also be written in the form of a block matrix, i.e.

[0102]

[0103] in

[0104]

[0105]

[0106]

[0107] In the above expression, each block represents a submatrix related to the combination of the corresponding two parts of J(ζ) and vector ζ. According to the expression for the joint probability density function p(r|θ), the elements of J(ζ) can be calculated as follows:

[0108]

[0109] Where ζ q Let represent the q-th element of ζ. Based on the above formula, the values ​​of each element in J(ζ) can be obtained. Combining the above analysis and using some simple operations, J(θ) can be expressed as:

[0110]

[0111] The CRLB matrix is ​​then calculated as follows:

[0112] C CRLB (θ)=[J(θ)] -1

[0113] According to the matrix inversion lemma, C CRLB (θ) can be further expressed as:

[0114]

[0115] in

[0116]

[0117]

[0118] Since we only need to focus on the estimated target position and velocity, we only need to calculate matrix B1 here. For the k-th target, its position and velocity estimate RCRLB (Root CRLB) is expressed as:

[0119]

[0120]

[0121] Step 108: For the discrete form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect of the output result of the linear frequency modulated signal matched filtering at the peak point position, construct the peak point measurement model in the time domain, and introduce a second intermediate vector according to the peak point measurement model.

[0122] The second intermediate vector contains parameter vectors for time delay and Doppler frequency shift; the time delay and Doppler frequency shift are related to the position and velocity of multiple targets.

[0123] In the discrete-time signal model under consideration, the performance of target parameter estimation is also limited by sampling errors, and SLB describes this performance boundary. It represents the theoretical estimation accuracy when all observations are affected only by discrete sampling errors. In this case, the peak point measurements in the time domain... Modeled as:

[0124]

[0125] in This represents rounding to the nearest integer, and ε represents the measurement error. For ease of analysis, it is assumed that ε follows a distribution. And the probability p(-1 / 2f) s ≤ε≤1 / 2f s The approximation is 0.9. Based on the above assumptions, we can obtain... The SLB is defined as the target parameter estimate CRLB under this measurement model. Since the peak point measurement value is determined by the target's time delay and Doppler frequency shift, an intermediate parameter vector ζ is introduced for ease of solution. T =[τ T ,f T ] T That is, the second intermediate vector.

[0126] Step 110: Based on the chain rule, solve the second FIM matrix model of the multi-target position and velocity parameter vectors using the second intermediate vector, and determine the root SLB lower bound for the position and velocity estimation of each target. Parameter vector θ T The FIM (i.e., the second FIM matrix model) can be represented as:

[0127]

[0128] in

[0129]

[0130] In addition, J(ζ) T The elements in ) can be written as:

[0131]

[0132] q,q′=1,2,...,2MNK

[0133] Where ζ Tq Represents ζ T The q-th element. Based on the above formula and the vector... The definition of J(ζ) T It can be represented in block matrix form, i.e.

[0134]

[0135] Where D is a diagonal matrix with the following elements:

[0136]

[0137] q=((n-1)×M+m-1)×K+k,

[0138] n=1,...,N,m=1,...,M,k=1,...,K

[0139] Will and J(ζ) T Substitute the parameter vector θ T The FIM calculation expression can be obtained.

[0140]

[0141] D(·) and F(·) are both coefficient matrices in the solution results, and both are diagonal matrices.

[0142]

[0143]

[0144] Where q represents the index of an element in the matrix, [D] q,q and [F] q,q Let represent the elements in the q-th row and q-th column of matrices D and F, respectively.

[0145] Therefore, θ T The CRLB matrix is ​​represented as follows:

[0146] CCRLB (θ T )=[J(θ T )] -1

[0147] For the k-th target, its position and velocity estimate RSLB (Root SLB) is calculated as follows:

[0148]

[0149] Step 112: Obtain the root mean square error lower bound of the position and velocity estimation for each target based on the root CRLB lower bound and the root SLB lower bound, and determine the theoretical estimation accuracy of the multi-target position and velocity of the direct method measurement model.

[0150] Based on the calculation results of CRLB and SLB, the lower bound of the position and velocity estimation RMSE (Root Mean Square Error) for the k-th target is expressed as follows:

[0151]

[0152] In the aforementioned method for calculating the theoretical estimation accuracy of multi-target position and velocity, based on the constructed direct method measurement model for multi-target position and velocity parameter estimation, and considering the time delay-Doppler coupling effect at the peak point position in the output result of the matched filtering of the linear frequency modulated signal, a first intermediate vector containing parameter vectors characterizing the relationship between the peak point position and time delay and Doppler frequency shift is constructed for the first FIM matrix model of the unknown parameter vector in the direct method measurement model. This first intermediate vector is used to solve the first FIM matrix and determine the root CRLB lower bound for each target position and velocity estimation. A second intermediate vector containing parameter vectors with time delay and Doppler frequency shift is introduced into the peak point measurement model in the time domain. This second intermediate vector is used to solve the second FIM matrix and determine the root SLB lower bound for each target position and velocity estimation. The theoretical estimation accuracy of multi-target position and velocity in the direct method measurement model is determined based on the root CRLB lower bound and the root SLB lower bound. This invention provides a theoretical performance lower bound for target position and velocity parameter estimation using only the time delay-Doppler coupling effect of the LFM signal without phase information, considering the influence of discrete sampling error, and quantitatively describing the impact of signal sampling rate on the accuracy of target parameter estimation.

[0153] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0154] In one embodiment, such as Figure 2 This paper provides a method for calculating the accuracy of theoretical estimation of the position and velocity of multiple targets, including:

[0155] Step 202: Reasonably model the signal measurement error and the complex scattering coefficient of the target under different transmit-receive channels, and calculate the position and velocity estimates CRLB of different targets based on the given radar system parameters and target parameters;

[0156] Step 204: Model the discrete sampling error of the signal reasonably, and calculate the position and velocity estimates (SLB) of different targets based on the given radar system parameters and target parameters.

[0157] Step 206: Combine CRLB and SLB to obtain the theoretical estimation accuracy of the system for the position and velocity parameters of multiple targets.

[0158] In one embodiment, the method of the present invention is further verified by simulation. The main system parameters are given in Table 1, and a schematic diagram of the simulation scenario is shown below. Figure 3 It is displayed in the middle.

[0159] Table 1

[0160]

[0161]

[0162] In the simulation, K = 3 moving targets are set, and their positions are set to u1 = [-319, 98]. T m, u2 = [-279, -321] T m, u3 = [341, 260] T m, speed set to v1 = [29.7, 30.0] T m / s, v2 = [-30.0, -29.6] T m / s, v3 = [20.0, 29.8] T m / s. For each target, its complex scattering coefficients in different channels are based on the distribution. Generate, where the variance ratio is set to Furthermore, the value remains fixed after generation. For ease of description, the simulation defines SNR (Signal-to-Noise Ratio) based on the first objective, written as:

[0163]

[0164] In addition, the LFM waveforms corresponding to different transmitters and pulses in the simulation alternate between positive and negative frequency modulation to alleviate the ambiguity effect. Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 and Figure 9 The results show the position and velocity estimates RCRLB and RSLB of the three targets as a function of SNR. Additionally, the figures also present the target position and velocity estimates RMSE of the optimal grid search method, based on results from 2000 Monte Carlo trials. To reduce the computational complexity of the optimal grid search method, several simplifications were employed in the simulation. Specifically, the method uses echo signals generated independently for each target, and the different signals have the same noise level, which reduces the search dimension from 4... K Reduced to 4. Furthermore, the search range for the position and velocity of each target is limited to a circular area centered on the true value with radii of 60m and 20m / s, respectively, while the search grid size for position and velocity is set to 20×20m. 2 and 10×10m 2 / s 2 .from Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 and Figure 9 As can be seen, the estimation results of the optimal grid search method generally approach the derived lower bound of parameter estimation accuracy. However, it can also be observed that the method's velocity estimation RMSE exhibits a threshold phenomenon in the low signal-to-noise ratio region, meaning the estimation error significantly deviates from the derived theoretical lower bound of accuracy. This phenomenon is quite common in the estimation results of nonlinear estimators. Furthermore, the method's estimation RMSE fails to perfectly match the theoretical lower bound of accuracy in some high signal-to-noise ratio conditions, which is caused by grid scale errors present during the search process.

[0165] In one embodiment, such as Figure 10 As shown, a device for calculating the theoretical estimation accuracy of multi-target position and velocity is provided, comprising: a parameter estimation module 1002, a first intermediate vector construction module 1004, a CRLB determination module 1006, a second intermediate vector determination module 1008, an SLB determination module 1010, and an estimation accuracy determination module 1012, wherein:

[0166] The parameter estimation module 1002 is used to construct a direct measurement model for estimating the position and velocity parameters of multiple targets based on the output results of the matched filtering of the linear frequency modulated signals in all transmit-receive channels of the distributed MIMO radar; the output results of the matched filtering of the linear frequency modulated signals have a time delay-Doppler coupling effect at the peak point position;

[0167] The first intermediate vector construction module 1004 is used to construct the first FIM matrix model of the unknown parameter vector in the direct method measurement model. Based on the time delay-Doppler coupling effect of the output of the linear frequency modulated signal matched filter at the peak point position, the first intermediate vector is constructed. The unknown parameter vector includes multi-target position and velocity parameter vectors. The first intermediate vector contains parameter vectors characterizing the relationship between the peak point position and time delay and Doppler frequency shift. Time delay and Doppler frequency shift are related to the multi-target position and velocity.

[0168] The CRLB determination module 1006 is used to solve the first FIM matrix model based on the chain rule through the intermediate vector, and to determine the root CRLB lower bound for the position and velocity estimation of each target respectively.

[0169] The second intermediate vector determination module 1008 is used to construct a time-domain peak point measurement model for the discrete form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect existing at the peak point position of the output result of the linear frequency modulated signal matched filtering, and to introduce a second intermediate vector according to the peak point measurement model; the second intermediate vector contains parameter vectors of time delay and Doppler frequency shift; the time delay and Doppler frequency shift are related to the position and velocity of multiple targets;

[0170] SLB determination module 1010 is used to solve the second FIM matrix model of multi-target position and velocity parameter vectors based on the chain rule and the second intermediate vector, and to determine the root SLB lower bound for the position and velocity estimation of each target respectively.

[0171] The estimation accuracy determination module 1012 is used to obtain the root mean square error lower bound of the position and velocity estimation of each target based on the root CRLB lower bound and the root SLB lower bound, and to determine the theoretical estimation accuracy results of the multi-target position and velocity of the direct method measurement model.

[0172] The first intermediate vector construction module 1004 is also used to construct the first FIM matrix model of the unknown parameter vector in the direct method measurement model:

[0173]

[0174] in, For an unknown parameter vector, u k and v kThese are the position and velocity parameters of the k-th target, respectively. and Let be the real and imaginary parts of the complex scattering coefficient vector α of the distributed MIMO radar received signal, respectively. Let p(r|θ) represent the expectation, and let p(r|θ) represent the joint probability density function of r given θ, where r is the discrete form of the received signal from the distributed MIMO radar.

[0175] The first intermediate vector construction module 1004 is also used to construct the first intermediate vector based on the time delay-Doppler coupling effect present at the peak point of the output result of the matched filter of the linear frequency modulated signal:

[0176]

[0177] in:

[0178]

[0179]

[0180]

[0181]

[0182] A parameter vector characterizing the relationship between peak location and time delay and Doppler frequency shift. for The element vector, for The element vector, for The element vector, for The element, f mnk τ represents the Doppler frequency shift of the k-th target in the mn-th transmit-receive channel. mnk This represents the time delay of the k-th target under the mn-th transmit-receive channel. To adjust the frequency.

[0183] CRLB determination module 1006 is also used to rewrite the first FIM matrix based on the intermediate vector according to the chain rule:

[0184]

[0185] Solving for each term on the right side of the above equation, we get:

[0186]

[0187] in, J UL J URJ UR and J LR To express J(ζ) as a block matrix element, M is the number of distributed MIMO radar transmitters, N is the number of distributed MIMO radar receivers, K is the total number of targets, and P represents that the distributed MIMO radar system transmits mutually orthogonal LFM signals consisting of P (P≥1) independent pulses with different characteristics.

[0188] The lower bound of the CRLB obtained for the estimation of the unknown parameter vector is:

[0189]

[0190] in,

[0191] The root CRLB lower bound for the position and velocity estimates of each target is determined as follows:

[0192]

[0193]

[0194] Where q represents the index of an element in the matrix, [B1] q,q This represents the element in the q-th row and q-th column of matrix B1.

[0195] The second intermediate vector determination module 1008 is also used to construct a time-domain peak point measurement model for the discrete form received signal of distributed MIMO radar, based on the time delay-Doppler coupling effect present at the peak point position of the output result of the linear frequency modulated signal matched filtering:

[0196]

[0197] Among them, f s The sampling rate represents how a continuously received signal is sampled as a discrete received signal. This indicates rounding to the nearest integer, where ε is the measurement error, and we can assume that ε follows a distribution. And the probability p(-1 / 2f) s ≤ε≤1 / 2f s Approximately 0.9, we get I MNKP This represents an identity matrix of size MNKP×MNKP.

[0198] The second intermediate vector determination module 1008 is also used to introduce a second intermediate vector based on the peak point measurement model:

[0199] ζ T =[τ T ,f T ] T

[0200] Where τ represents the vector consisting of the time delays of all targets in all channels, and f represents the vector consisting of the Doppler frequency shifts of all targets in all channels.

[0201] The SLB determination module 1010 is also used to rewrite the second FIM matrix model of the multi-target position and velocity parameter vectors based on the chain rule and the second intermediate vector as follows:

[0202]

[0203] Solving for each term on the right side of the above equation, we get:

[0204]

[0205] Where D(·) is the coefficient matrix and F(·) is the coefficient matrix.

[0206] The root SLB lower bound for the position and velocity estimation of each target is determined as follows:

[0207]

[0208]

[0209] Among them, C CRLB (θ T )=[J(θ T )] -1 .

[0210] The estimation accuracy determination module 1012 is also used to obtain the root mean square error lower bound of each target position and velocity estimate based on the root CRLB lower bound and the root SLB lower bound as follows:

[0211] RMSE(u k )≥max(RCRLB(u k ),RSLB(u k ))

[0212] RMSE(v k )≥max(RCRLB(v k ),RSLB(v k ))

[0213] Here, max(·) represents the function that takes the maximum value.

[0214] Specific limitations regarding the calculation device for the theoretical estimation accuracy of multi-target position and velocity can be found in the limitations of the calculation method for the theoretical estimation accuracy of multi-target position and velocity described above, and will not be repeated here. Each module in the aforementioned calculation device for the theoretical estimation accuracy of multi-target position and velocity can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independent of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0215] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 11 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a method for calculating the theoretical estimation accuracy of multi-target position and velocity. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0216] Those skilled in the art will understand that Figure 11 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0217] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps in the above method embodiment.

[0218] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0219] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0220] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0221] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for calculating the accuracy of theoretical estimation of the position and velocity of multiple targets, characterized in that, The method includes: A direct measurement model for estimating the position and velocity parameters of multiple targets is constructed based on the output results of the matched filtering of linear frequency modulated signals in all transmit-receive channels of the distributed MIMO radar; however, the output results of the matched filtering of the linear frequency modulated signals exhibit a time delay-Doppler coupling effect at the peak point. A first FIM matrix model of the unknown parameter vector in the direct method measurement model is constructed. Based on the time delay-Doppler coupling effect at the peak point position of the output result of the linear frequency modulated signal matched filtering, a first intermediate vector is constructed. The unknown parameter vector includes multi-target position and velocity parameter vectors. The first intermediate vector contains parameter vectors characterizing the relationship between the peak point position and time delay and Doppler frequency shift. The time delay and Doppler frequency shift are related to the multi-target position and velocity. Based on the chain rule, the first FIM matrix model is solved using the intermediate vector to determine the root CRLB lower bound for the position and velocity estimation of each target. For the discrete form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect existing at the peak point position in the output result of the matched filtering of the linear frequency modulated signal, a peak point measurement model in the time domain is constructed, and a second intermediate vector is introduced according to the peak point measurement model; the second intermediate vector contains parameter vectors of time delay and Doppler frequency shift; the time delay and Doppler frequency shift are related to the position and velocity of multiple targets; Based on the chain rule, the second FIM matrix model of the multi-target position and velocity parameter vectors is solved by the second intermediate vector to determine the root SLB lower bound of the position and velocity estimation for each target. The root mean square error lower bound of the position and velocity estimation of each target is obtained based on the root CRLB lower bound and the root SLB lower bound, and the theoretical estimation accuracy of the multi-target position and velocity of the direct method measurement model is determined.

2. The method according to claim 1, characterized in that, Constructing the first FIM matrix model of the unknown parameter vector in the direct method measurement model includes: The first FIM matrix model for the unknown parameter vector in the direct method measurement model is constructed as follows: in, For an unknown parameter vector, u k and v k These are the position and velocity parameters of the k-th target, respectively. and Let be the real and imaginary parts of the complex scattering coefficient vector α of the received signal from the distributed MIMO radar, respectively. Let p(r|θ) represent the expectation, and let p(r|θ) represent the joint probability density function of r given θ, where r is the discrete form of the received signal of the distributed MIMO radar.

3. The method according to claim 2, characterized in that, Based on the time-delay-Doppler coupling effect present at the peak point of the output of the matched filter for the linear frequency modulated signal, a first intermediate vector is constructed, including: Based on the time-delay-Doppler coupling effect at the peak point of the output of the matched filter for the linear frequency modulated signal, the first intermediate vector is constructed as follows: in: A parameter vector characterizing the relationship between the peak point location and time delay and Doppler frequency shift. for The element vector, for The element vector, for The element vector, for The element, f mnk τ represents the Doppler frequency shift of the k-th target in the mn-th transmit-receive channel. mnk This represents the time delay of the k-th target under the mn-th transmit-receive channel. To adjust the frequency.

4. The method according to claim 3, characterized in that, Based on the chain rule, the first FIM matrix model is solved using the intermediate vector to determine the root CRLB lower bound for each target position and velocity estimate, including: Based on the chain rule, the first FIM matrix is ​​rewritten according to the intermediate vector as follows: Solving for each term on the right side of the above equation, we get: in, J UL J UR J UR and J LR To express J(ζ) as a block matrix element, M is the number of the distributed MIMO radar transmitters, N is the number of the distributed MIMO radar receivers, K is the total number of targets, and P indicates that the distributed MIMO radar system transmits mutually orthogonal LFM signals consisting of P (P≥1) independent pulses with different characteristics. The CRLB lower bound of the estimated unknown parameter vector is obtained as follows: in, The root CRLB lower bound for the position and velocity estimates of each target is determined as follows: Where q represents the index of an element in the matrix, [B1] q,q This represents the element in the q-th row and q-th column of matrix B1.

5. The method according to claim 4, characterized in that, For the discrete-form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect present at the peak point position in the output of the matched filter of the linear frequency modulated signal, a peak point measurement model in the time domain is constructed, including: For the discrete-form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect at the peak point position of the output of the matched filter of the linear frequency modulated signal, the peak point measurement model in the time domain is constructed as follows: Among them, f s The sampling rate represents how a continuously received signal is sampled as a discrete received signal. This indicates rounding to the nearest integer, where ε is the measurement error, and we can assume that ε follows a distribution. And the probability p(-1 / 2f) s ≤ε≤1 / 2f s Approximately 0.9, we get I MNKP This represents an identity matrix of size MNKP×MNKP.

6. The method according to claim 5, characterized in that, A second intermediate vector is introduced based on the peak point measurement model, including: Based on the peak point measurement model, the second intermediate vector is introduced as follows: g T =[τ T ,f T ] T Where τ represents the vector consisting of the time delays of all targets in all channels, and f represents the vector consisting of the Doppler frequency shifts of all targets in all channels.

7. The method according to claim 6, characterized in that, Based on the chain rule, the second FIM matrix model of the multi-target position and velocity parameter vectors is solved using the second intermediate vector to determine the root SLB lower bound for the position and velocity estimation of each target, including: Based on the chain rule, the second FIM matrix model of the multi-target position and velocity parameter vectors is rewritten according to the second intermediate vector as follows: Solving for each term on the right side of the above equation, we get: Where: D(·) is the coefficient matrix, and F(·) is the coefficient matrix; The root SLB lower bound for the position and velocity estimation of each target is determined as follows: Among them, C CRLB (i T )=[J(θ T )] -1 。 8. The method according to claim 7, characterized in that, The root mean square error lower bound for each target position and velocity estimate is obtained based on the root CRLB lower bound and the root SLB lower bound, including: Based on the root CRLB lower bound and the root SLB lower bound, the root mean square error lower bound for the position and velocity estimation of each target is obtained as follows: RMSE(u k )≥max(RCRLB(u k ),RSLB(u k )) RMSE(v k )≥max(RCRLB(v k ),RSLB(v k )) Here, max(·) represents the function that takes the maximum value.

9. A device for calculating the theoretical estimation accuracy of multi-target position and velocity, characterized in that, The device includes: The parameter estimation module is used to construct a direct measurement model for estimating the position and velocity parameters of multiple targets based on the output results of the matched filtering of the linear frequency modulated signals in all transmit-receive channels of the distributed MIMO radar; the output results of the matched filtering of the linear frequency modulated signals exhibit a time delay-Doppler coupling effect at the peak point position; The first intermediate vector construction module is used to construct the first FIM matrix model of the unknown parameter vector in the direct method measurement model. Based on the time delay-Doppler coupling effect existing at the peak point position of the output result of the linear frequency modulated signal matched filtering, the first intermediate vector is constructed. The unknown parameter vector includes multi-target position and velocity parameter vectors. The first intermediate vector contains parameter vectors characterizing the relationship between the peak point position and the time delay and Doppler frequency shift. The time delay and Doppler frequency shift are related to the multi-target position and velocity. The CRLB determination module is used to solve the first FIM matrix model based on the chain rule through the intermediate vector, and determine the root CRLB lower bound for the position and velocity estimation of each target respectively; The second intermediate vector determination module is used to construct a time-domain peak point measurement model for the discrete form received signal of the distributed MIMO radar, based on the time delay-Doppler coupling effect present at the peak point position of the output result of the matched filtering of the linear frequency modulated signal, and to introduce a second intermediate vector according to the peak point measurement model; the second intermediate vector contains parameter vectors of time delay and Doppler frequency shift; the time delay and Doppler frequency shift are related to the position and velocity of multiple targets; The SLB determination module is used to solve the second FIM matrix model of the multi-target position and velocity parameter vectors based on the chain rule through the second intermediate vector, and determine the root SLB lower bound for the position and velocity estimation of each target respectively. The estimation accuracy determination module is used to obtain the root mean square error lower bound of the position and velocity estimation of each target based on the root CRLB lower bound and the root SLB lower bound, and to determine the theoretical estimation accuracy result of the multi-target position and velocity of the direct method measurement model.

10. The apparatus according to claim 9, characterized in that, The first intermediate vector construction module is also used for: The first FIM matrix model for the unknown parameter vector in the direct method measurement model is constructed as follows: in, Let be a vector of unknown parameters, where u k and v k These are the position and velocity parameters of the k-th target, respectively. and Let be the real and imaginary parts of the complex scattering coefficient vector α of the received signal from the distributed MIMO radar, respectively. Let p(r|θ) represent the expectation, and let p(r|θ) represent the joint probability density function of r given θ, where r is the discrete form of the received signal of the distributed MIMO radar.

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