Joint design method based on space-time nested sampling of equal time domain parameters

Abstract

The present application discloses a joint design method based on space-time nested sampling of equal time domain parameters, the method comprising: obtaining a differential set of nested parameters of array element receiving signals; processing the differential set in virtual time domain and space domain to obtain an equivalent received signal for estimation; wherein, the equivalent received signal includes an estimation of parameters DOA and Doppler frequency, solving the optimal nested parameters under the DOA and Doppler frequency estimation and obtaining the optimal time domain and space domain nested parameters. The present application constructs a virtual space domain array and time domain sequence based on a nested structure to obtain a larger aperture than the original nested array or sequence, thereby increasing the degree of freedom and improving the resolution. At the same time, the constructed virtual array is a uniform linear array in the space domain, which avoids spatial aliasing of the spectrum.

Description

Technical Field

[0001] The present application relates to the field of signal processing, and in particular to a joint design method based on space-time nested sampling of equal time domain parameters. Background Art

[0002] In modern society, as application requirements become increasingly complex, many problems require the joint estimation of multiple parameters.

[0003] There are usually two methods for the joint estimation of Direction Of Arrival (DOA) and frequency: the dimension estimation method is simple to implement, but the parameter matching requires the algorithm to have high robustness. If the matching is wrong, it may cause a large error; the automatic parameter matching method is more complicated to implement than the former, and for uniform linear arrays, the automatic parameter matching method needs to increase the number of array elements to improve the resolution, which requires more physical resources.

[0004] Therefore, in order to solve the problem of limited radar system resources, how to jointly estimate DOA and frequency is the key to achieving multi-parameter joint estimation. Summary of the invention

[0005] The present application provides a joint design method based on space-time nested sampling of equal time domain parameters to solve the joint estimation problem of DOA and frequency.

[0006] In order to achieve the above objectives, the technical solutions adopted in this application include the following aspects.

[0007] In a first aspect, the present application provides a joint design method based on space-time nested sampling of equal time domain parameters, the method comprising:

[0008] Obtaining a differential set of nested parameters of an array element receiving signal;

[0009] Estimate the equivalent received signal obtained by differential set processing in virtual time domain and space domain;

[0010] The equivalent received signal includes the estimation of parameters DOA and Doppler frequency, and the optimal nesting parameters under the DOA and Doppler frequency estimation are solved and the optimal time domain and space domain nesting parameters are obtained.

[0011] Optionally, the acquiring a differential set of nested parameters of an array element receiving signal specifically includes:

[0012] Obtain radar system array element information and its original array element receiving signal and time domain sampling point information;

[0013] A nested array of array elements is constructed, and the original array element receiving signal is nested and sampled to obtain a differential set of time domain and space domain nesting parameters.

[0014] Optionally, the estimating an equivalent received signal obtained by performing differential set processing in a virtual time domain and a spatial domain specifically includes:

[0015] By using the original array element receiving signal and the differential set of nested parameters, a virtual time domain steering vector and a virtual space domain steering vector are obtained to obtain an equivalent receiving signal;

[0016] The equivalent received signal is estimated, where for a sampling sequence of specific time sample points, the received signal of a single array element is represented by DOA and Doppler frequency.

[0017] Optionally, the equivalent received signal includes estimating parameters DOA and Doppler frequency, solving the optimal nesting parameters under the DOA and Doppler frequency estimation and obtaining the optimal time domain and space domain nesting parameters, specifically including:

[0018] The optimal solution of spatial and temporal nested parameters for estimating DOA and Doppler frequency based on spatial array elements and temporal sampling point information is obtained, and the optimal solution of spatial and temporal nested parameters is solved to obtain a joint estimate of DOA and Doppler frequency.

[0019] Optionally, it further includes nesting the array elements in the spatial domain to obtain a nested array consisting of uniform sub-arrays;

[0020] The received signal at each array element is sampled at the same time point in the time domain, and a nested array is constructed for the array elements in the spatial domain.

[0021] Optionally, the acquiring a differential set of nested parameters of an array element receiving signal specifically includes:

[0022] Based on the autocorrelation matrix of the array element receiving signal of the normalized DOA and Doppler frequency, a differential set of time domain and space domain nesting parameters is calculated, where the differential set is a set after removing repeated elements, and the repeated elements are sample values ​​of the same virtual array element and the same time domain sampling point.

[0023] In a second aspect, the present application provides a joint design system based on space-time nested sampling of equal time domain parameters, the system comprising: a processor and a memory;

[0024] The memory stores computer-executable instructions;

[0025] When the processor executes the computer-executable instructions stored in the memory, the method as described in any one of the first aspects is implemented.

[0026] In a third aspect, the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are executed by a processor, they are used to implement the method as described in any one of the first aspects.

[0027] In a fourth aspect, the present application provides a joint design device based on space-time nested sampling of equal time domain parameters, the device comprising:

[0028] An acquisition module, used to acquire a differential set of nested parameters of a signal received by an array element;

[0029] An estimation module, used for estimating an equivalent received signal obtained by differential set processing in virtual time domain and space domain;

[0030] The equivalent received signal includes the estimation of parameters DOA and Doppler frequency, and the optimal nesting parameters under the DOA and Doppler frequency estimation are solved and the optimal time domain and space domain nesting parameters are obtained.

[0031] According to a fifth aspect, a computer program product comprises a computer program, wherein when the computer program is executed by a processor, the method according to any one of the first aspects is implemented.

[0032] In summary, due to the adoption of the above technical solution, the present application has at least the following beneficial effects:

[0033] Through the solution of the present application, a virtual spatial array and time domain sequence can be constructed based on a nested structure under the allowed number of array elements and sampling points, and a larger aperture than the original nested array or sequence can be obtained, thereby increasing the degree of freedom and improving the resolution. At the same time, the constructed virtual array is a uniform linear array in the spatial domain, avoiding spatial aliasing of the spectrum. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of a joint design method based on space-time nested sampling of equal time domain parameters provided according to an exemplary embodiment of the present application;

[0035] Figure 2 It is a structural diagram of space-time nested sampling (STNI) of equal time domain parameters in a joint design method based on space-time nested sampling of equal time domain parameters provided according to an exemplary embodiment of the present application;

[0036] Figure 3 is a comparison diagram of Doppler frequency estimation resolution under STUI, STCI and STNI sampling structures provided according to an exemplary embodiment of the present application;

[0037] Figure 4 is a comparison diagram of DOA estimation resolution under STUI, STCI and STNI sampling structures provided according to an exemplary embodiment of the present application;

[0038] Figure 5 is a DOA estimation performance curve diagram under STUI, STCI and STNI sampling structures provided according to an exemplary embodiment of the present application;

[0039] Figure 6 It is a Doppler frequency estimation performance curve diagram under the STUI, STCI and STNI sampling structures provided according to the exemplary embodiments of the present application. DETAILED DESCRIPTION

[0040] The present application is further described in detail below in conjunction with the accompanying drawings and embodiments to make the purpose, technical solutions and advantages of the present application more clearly understood. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0041] In modern society, with the increasing complexity of application requirements, many problems require the joint estimation of multiple parameters. For the joint estimation of direction of arrival (DOA) and frequency, there are usually two methods: the first is the dimension estimation method, which uses the frequency measurement system and the direction finding system to estimate the frequency and angle respectively, and then selects the matching algorithm to match the two estimation results. This method is simple to implement, but the parameter matching requires the algorithm to have high robustness. If the matching is wrong, it may cause a large error (see reference: J. Lin, W. Fang, Y. Wang and J. Chen, "FSF MUSIC for Joint DOA and Frequency Estimation and Its Performance Analysis," IEEE Transactions on Signal Processing, vol. 54, no. 12, pp. 4529-4542, Dec. 2006.); the other is the parameter automatic matching method, which no longer needs to match the two parameters. Compared with the former method, it has better robustness, but the implementation is more complicated (see reference: HNP Wisudawan, D. Dony Ariananda and R. Hidayat, "Joint DoA and Frequency Band Estimation Based on MUSIC for Unknown Number of Sources," in Proceedings of 2020 23rd International Symposium on Wireless Personal Multimedia Communications, Oct. 2020, pp. 1-6.). At the same time, in the DOA estimation problem, a uniform linear array is used to limit the distance between adjacent array elements within the array to no more than half the wavelength of the signal, thereby avoiding spatial aliasing of the spectrum. However, when the number of array elements is given, the array aperture of the uniform linear array is small, resulting in low DOA estimation resolution. For a uniform linear array, if you want to improve the resolution, you need to increase the number of array elements, which requires more physical resources.

[0042] One of the purposes of the embodiments of the present application is at least to solve the problem of joint estimation of DOA and Doppler frequency, especially when the number of array elements and the number of time-domain samples of a radar system are limited, and is applicable to the joint processing of sparse arrays and sparse sampling.

[0043] The embodiment of the present application is based on a space-time nested sampling structure and proposes a joint design method based on space-time nested sampling with equal time domain parameters.

[0044] Methods include:

[0045] Figure 1 is a flow chart of a joint design method based on space-time nested sampling of equal time domain parameters provided according to an exemplary embodiment of the present application, such as Figure 1 shown.

[0046] S101, obtaining a differential set of nested parameters of an array element receiving signal;

[0047] S102, estimating an equivalent received signal obtained by differential set processing in virtual time domain and space domain;

[0048] The equivalent received signal includes the estimation of parameters DOA and Doppler frequency, and the optimal nesting parameters under the DOA and Doppler frequency estimation are solved and the optimal time domain and space domain nesting parameters are obtained.

[0049] Optionally, step S101, obtaining a differential set of nested parameters of an array element receiving signal, specifically includes:

[0050] Obtain radar system array element information and its original array element receiving signal and time domain sampling point information;

[0051] A nested array of array elements is constructed, and the original array element receiving signal is nested and sampled to obtain a differential set of time domain and space domain nesting parameters.

[0052] Optionally, step S102, estimating an equivalent received signal obtained by differential set processing in a virtual time domain and a spatial domain, specifically includes:

[0053] By using the original array element receiving signal and the differential set of nested parameters, a virtual time domain steering vector and a virtual space domain steering vector are obtained to obtain an equivalent receiving signal;

[0054] The equivalent received signal is estimated, where for a sampling sequence of specific time sample points, the received signal of a single array element is represented by DOA and Doppler frequency.

[0055] Optionally, the equivalent received signal includes an estimation of parameters DOA and Doppler frequency, solving optimal nesting parameters under the DOA and Doppler frequency estimation and obtaining optimal time domain and space domain nesting parameters, specifically including:

[0056] The optimal solution of spatial and temporal nested parameters for estimating DOA and Doppler frequency based on spatial array elements and temporal sampling point information is obtained, and the optimal solution of spatial and temporal nested parameters is solved to obtain a joint estimate of DOA and Doppler frequency.

[0057] Optionally, it further includes nesting the array elements in the spatial domain to obtain a nested array consisting of uniform sub-arrays;

[0058] The received signal at each array element is sampled at the same time point in the time domain, and a nested array is constructed for the array elements in the spatial domain.

[0059] Optionally, obtaining a differential set of nested parameters of an array element receiving signal specifically includes:

[0060] Based on the autocorrelation matrix of the array element receiving signal of the normalized DOA and Doppler frequency, the differential set of time domain and space domain nesting parameters is calculated. The differential set is a set after removing repeated elements, and the repeated elements are sample values ​​of the same virtual array element and the same time domain sampling point.

[0061] In a feasible implementation, the present application may include the following steps:

[0062] Step 1: Construct a nested array consisting of L elements. Two uniform subarrays and Composition, among which, d represents the interval between adjacent array elements.

[0063] Step 2: Perform the same nested sampling on the received signals of L array elements in the time domain. Assuming the total number of sampling points is R, the number of sampling points at each array element is R1 = R / L. Similar to the spatial domain nested array structure, the time domain nested sampling sequence is in, M2+N2=R1, T represents the time interval.

[0064] Step 3: Based on the autocorrelation matrix of the received signal x, obtain the differential set of time domain and spatial domain nesting parameters. The autocorrelation matrix of the received signal x is

[0065]

[0066] in, and represents the normalized DOA and Doppler frequency, represents the space-time steering vector, represents the time-domain steering vector, represents the spatial domain steering vector. Therefore, the difference sets of temporal and spatial domain nesting parameters are

[0067]

[0068] and

[0069]

[0070] Among them, u′1, u′2 and u1, u2 are sets and The elements in .

[0071] Step 4: Construct virtual time domain and space domain steering vectors to obtain an equivalent received signal model. xx Carrying redundant information, extracting differential sets and The virtual time domain and space domain steering vectors are constructed as follows:

[0072]

[0073] and

[0074]

[0075] in, and represents the set after the duplicate elements are removed from the differential set. Therefore, the equivalent received signal model can be expressed as

[0076]

[0077] in, represents the virtual space-time steering vector, e1∈C 2K+1 represents a vector whose elements are all 0 except the (K+1)th element which is 1, e2∈C 2K'+1 It represents a vector whose elements are all 0 except the (K'+1)th element which is 1.

[0078] Step 5: Use spatial smoothing technology to estimate the autocorrelation matrix of the equivalent received signal Z. Construct a spatial smoothing window with a size of (K+1)×(K'+1). When the window is moved by p and q in the spatial and temporal dimensions respectively, p=0,1,…,K, q=0,1,…,K', the output signal corresponding to the equivalent received signal Z can be expressed as

[0079]

[0080] Among them, e 1,p is a vector consisting of the elements of rows K+1-p to 2K+1-p of e1, e 2,p It is a vector consisting of the elements of the K'+1-pth to 2K'+1-pth rows of e2. Average the (K+1)(K'+1) sliding results to obtain the estimated autocorrelation matrix

[0081]

[0082] Among them, z p,q =vec(Z p,q ).

[0083] Step 6: Estimate the normalized and Doppler frequency The Multiple Signal Classification (MUSIC) spectrum is

[0084]

[0085] According to the peak value of the MUSIC spectrum, we can get the estimated and Among them, E ω To decompose R ss The noise subspace obtained.

[0086] Step 7: When the number of available array elements L in the spatial domain and the number of sampling points R in the time domain are limited, the optimization problem for selecting spatial nesting parameters is:

[0087]

[0088] The optimization problem for selecting time domain nesting parameters is:

[0089]

[0090] The above optimization problem can be solved using the arithmetic-geometric mean inequality.

[0091] In another feasible implementation manner, the present application may include the following steps:

[0092] Bold capital letters represent matrices, bold lowercase letters represent vectors, (·) T represents transpose, (·) H represents the conjugate transpose, represents the Kronecker product, vec(·) represents vectorizing the matrix, and I represents the identity matrix.

[0093] Consider a nested array consisting of L elements Assume that B independent far-field narrowband sources are transmitted at radial velocities v b From the angle θ b The Doppler frequency of the source incident on the nested array is f b =v b / λ, b=1,…,B, then the received signal of the lth array element can be expressed as

[0094]

[0095] in, Represents the amplitude of the signal source, satisfying represents Gaussian white noise.

[0096] The received signal of each array element is sampled at R1 time points, and the sampling sequence is expressed as Then the received signal of the lth array element can be expressed as

[0097]

[0098] in, and represents the normalized DOA and Doppler frequency, which are defined as

[0099]

[0100] The received signals of L array elements are stacked up to obtain the received signal vector:

[0101]

[0102] in,

[0103] The autocorrelation matrix of the received signal x can be calculated as follows

[0104]

[0105] and but

[0106]

[0107] in, Therefore, the difference sets of time domain and space domain nesting parameters are expressed as and m r -m r' and n l -n l' They are and There are repeated elements inside. From this, we can see that There are many sample values ​​from the same virtual array element and the same time domain sampling point in R xx Elements that carry a lot of identical information are called redundant information.

[0108] Remove the difference set and The repeated elements in get the set and Thus, the virtual time domain and space domain steering vector can be constructed as

[0109]

[0110] and

[0111]

[0112] Let K = N1(M1+1)-1, K' = N2(M2+1)-1, the equivalent received signal model can be expressed as

[0113]

[0114] Among them, Z∈C (2K+1)×(2K'+1) , represents the virtual space-time steering vector, e1∈C 2K+1 represents a vector whose elements are all 0 except the (K+1)th element which is 1, e2∈C 2K'+1 It represents a vector whose elements are all 0 except the (K'+1)th element which is 1.

[0115] Next, the autocorrelation matrix of the received signal Z is estimated using spatial smoothing technology. Divide into K+1 sub-arrays, each sub-array contains K+1 array elements. Similarly, the time domain virtual sampling sequence It is divided into K'+1 subsequences, each of which contains K'+1 samples. Then the window size of the spatial smoothing technique is (K+1)×(K'+1). When the window is at the initial position, the output signal corresponding to Z can be expressed as

[0116]

[0117] in, When the window is shifted by p and q in two dimensions, p=0,1,…,K,q=0,1,…,K', the output signal corresponding to Z is expressed as

[0118]

[0119] Among them, e 1,p is a vector consisting of the elements of rows K+1-p to 2K+1-p of e1, e 2,p is a vector consisting of the elements of the K'+1-pth to 2K'+1-pth rows of e2. According to the definition of the spatial smoothing matrix, averaging (K+1)(K'+1) sliding results, the estimated autocorrelation matrix can be obtained as

[0120]

[0121] Among them, z p,q =vec(Z p,q ).

[0122] Decomposition R ss , respectively get the signal subspace E s and the noise subspace Eω , then the MUSIC spectrum can be obtained as

[0123]

[0124] By observing the peak of the MUSIC spectrum, we can estimate and

[0125] Finally, the problem of limited number of available array elements L in the spatial domain and limited number of sampling points R in the temporal domain is solved. The optimization problem of spatial nesting parameter selection is established as

[0126]

[0127] Among them, 2M1(N1+1)-1 is the difference set Contains the number of elements, i.e., the empty virtual array Similarly, the optimization problem of selecting time-domain nesting parameters is established and solved

[0128]

[0129] Among them, 2M2+N2-1 is the difference set The number of elements contained, that is, the time domain virtual sequence The two optimization problems can be solved using the arithmetic-geometric mean inequality.

[0130] In summary, in another feasible implementation of the embodiment provided in the present application, a physical array element position is represented as A nested array whose difference set Can be defined as

[0131]

[0132] Difference Set It is composed of Subtract any two elements in the set to get the value of In the DOA estimation problem, the second-order statistics of the received signal will have a difference set. This set includes physical array points and virtual array points, so it is generally It is called a differential synthesis array. By sorting and removing duplicate elements inside, you can get a set without duplicate elements. The values ​​of the elements in this set are continuous and range from {-(N1(M1+1)-1),...,0,...,N1(M1+1)-1}d, containing a total of 2N1(M1+1)-1 elements.

[0133] for Element m r -m r' The difference set of time domain nested parameters There are repeated elements in the set, and many new virtual sample points appear. n l -n l' is the difference set of spatial nesting parameters There are also repeated elements in the set, and many new virtual array element positions appear. Therefore, There are many sample values ​​from the same virtual array element and the same sample point in R xx There are many elements that carry the same information, which is redundant information.

[0134] Redundant information will not play any extra role in the subsequent estimation work, but will increase the complexity of calculation, so it is necessary to extract non-redundant information from the existing model. and The non-overlapping elements in the ,can construct virtual spatial and temporal steering vectors and Thus, an equivalent received signal model Z can be obtained. The equivalent received signal Z can be regarded as a virtual spatial domain and time domain steering vector and The corresponding virtual array and virtual time series receive the signal. The virtual array and virtual time series have a larger aperture, higher degrees of freedom, and higher resolution than the original nested array and nested sampling sequence, which can improve the estimation performance.

[0135] Figure 2 is a flow chart of a joint design method based on space-time nested sampling of equal time domain parameters provided according to an exemplary embodiment of the present application, such as Figure 2As shown in the figure, two examples are given to verify the theoretical results and illustrate the benefits of the space-time nested sampling structure (STNI) based on equal time domain parameters in terms of estimation resolution and overall estimation performance. In these two examples, it is assumed that the number of spatial array elements L = 6, the number of time domain sampling points R = 54, and the nested sparse parameters are M1 = M2 = 3, N1 = N2 = 5. Consider the other two sampling structures for comparison with the STNI structure. The first is the space-time uniform sampling structure (STUI) based on equal time domain parameters, and the second is the space-time coprime sampling structure (STCI) based on equal time domain parameters. Example 1 Consider comparing the resolution under the three sampling structures, and the signal-to-noise ratio SNR = 0dB. First, consider the Doppler frequencies of the two sources are 175Hz and 295Hz, and the DOA is 30°, and the Doppler frequency estimation under the three sampling structures of STUI, STCI, and STNI. In the time domain, 105Hz~305Hz is discretized into 120 uniform grid points with an interval of 1.6667Hz. Secondly, consider the DOA of two sources of 30° and 36°, and the Doppler frequency is 200Hz, and the DOA estimation under three sampling structures of STUI, STCI, and STNI. In the spatial domain, the observation angle range of 0°~60° is discretized into 121 uniform grid points with an interval of 0.5°. Example 2 Consider the relationship between the RMSE of the verification estimated variable and the SNR. Assume that the DOA of the two sources is [θ1,θ2]=[-10°,10°], and the Doppler frequency is [f1,f2]=[200Hz,300Hz].

[0136] For example 1, Figure 3 is a comparison diagram of Doppler frequency estimation resolution under STUI, STCI and STNI sampling structures provided according to an exemplary embodiment of the present application; Figure 4 is a comparison diagram of DOA estimation resolution under STUI, STCI and STNI sampling structures provided according to an exemplary embodiment of the present application; Figure 3 and Figure 4 As shown, we can see that STUI sampling, STCI sampling, and STNI sampling can all effectively identify two signal sources, but STNI sampling has the highest peak height, followed by STCI sampling, and STUI sampling is the worst, indicating that STNI sampling has the highest resolution, followed by STCI and STUI sampling, indicating that the aperture of the virtual spatial array and time domain sequence generated by STNI sampling is larger than that of the other two sampling methods. For Example 2, Figure 5 is a DOA estimation performance curve diagram under STUI, STCI and STNI sampling structures provided according to an exemplary embodiment of the present application; Figure 6 is a Doppler frequency estimation performance curve diagram under the STUI, STCI and STNI sampling structures provided by the exemplary embodiment of the present application. Figure 5 and Figure 6 It can be found that STNI sampling is better than STCI and STUI sampling because STNI sampling has higher degrees of freedom than STCI and STUI sampling. As the signal-to-noise ratio increases, STCI sampling gradually approaches STNI sampling, and when the signal-to-noise ratio is 5, STCI sampling achieves the same estimation performance as STNI sampling.

[0137] Through the technical solution provided in the embodiment of the present application, a virtual spatial array and time domain sequence can be constructed based on a nested structure under the allowed number of array elements and sampling points, thereby obtaining a larger aperture than the original nested array or sequence, thereby increasing the degree of freedom and improving the resolution. At the same time, the constructed virtual array is a uniform linear array in the spatial domain, avoiding spatial aliasing of the spectrum.

[0138] Those skilled in the art can understand that: all or part of the steps of implementing the above-mentioned method embodiment can be completed by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps of the above-mentioned method embodiment; and the aforementioned storage medium includes: mobile storage devices, read-only memories (ROM), disks or optical disks, etc. Various media that can store program codes.

[0139] When the above-mentioned integrated unit of the present application is implemented in the form of a software functional unit and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the embodiment of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the methods described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as mobile storage devices, ROMs, magnetic disks, or optical disks.

[0140] The above is only a detailed description of the specific implementation methods of the present application, rather than a limitation of the present application. Various substitutions, modifications and improvements made by technicians in the relevant technical field without departing from the principle and scope of the present application should be included in the protection scope of the present application.

Claims

1. A joint design method based on space-time nested sampling of equal time domain parameters, characterized in that: include: Obtaining a differential set of nested parameters of an array element receiving signal; The equivalent received signal is estimated by processing the difference set in the virtual time domain and space domain, specifically including: obtaining a virtual time domain steering vector and a virtual space domain steering vector through the difference set of the original array element received signal and the nested parameters to obtain the equivalent received signal; estimating the equivalent received signal, wherein for a sampling sequence of a specific time sample point, the received signal of a single array element is represented by DOA and Doppler frequency; Among them, the equivalent received signal includes the estimation of parameters DOA and Doppler frequency, solving the optimal nesting parameters under the DOA and Doppler frequency estimation and obtaining the optimal time domain and spatial domain nesting parameters, including: obtaining the optimal solution of spatial domain and time domain nesting parameters for estimating DOA and Doppler frequency based on spatial domain array elements and time domain sampling point information, and solving the optimal solution of spatial domain and time domain nesting parameters to obtain a joint estimation of DOA and Doppler frequency.

2. The method according to claim 1, characterized in that The step of obtaining a differential set of nested parameters of an array element receiving signal specifically includes: Obtain radar system array element information and its original array element receiving signal and time domain sampling point information; A nested array of array elements is constructed, and the original array element receiving signal is nested and sampled to obtain a differential set of time domain and space domain nesting parameters.

3. The method according to claim 1, characterized in that It also includes nesting array elements in the spatial domain to obtain a nested array consisting of uniform sub-arrays; The received signal at each array element is sampled at the same time point in the time domain, and a nested array is constructed for the array elements in the spatial domain.

4. The method according to claim 3, characterized in that The step of obtaining a differential set of nested parameters of an array element receiving signal specifically includes: Based on the autocorrelation matrix of the array element receiving signal of the normalized DOA and Doppler frequency, a differential set of time domain and space domain nesting parameters is calculated, where the differential set is a set after removing repeated elements, and the repeated elements are sample values ​​of the same virtual array element and the same time domain sampling point.

5. A joint design system based on space-time nested sampling of equal time domain parameters, characterized in that: including a processor and a memory; The memory stores computer-executable instructions; When the processor executes the computer-executable instructions stored in the memory, the method according to any one of claims 1 to 4 is implemented.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, which are used to implement the method according to any one of claims 1 to 4 when executed by a processor.

7. A joint design device based on space-time nested sampling of equal time domain parameters, characterized in that: The module for implementing the method according to any one of claims 1 to 4 is as follows: An acquisition module, used to acquire a differential set of nested parameters of a signal received by an array element; An estimation module, used for estimating an equivalent received signal obtained by differential set processing in virtual time domain and space domain; The equivalent received signal includes the estimation of parameters DOA and Doppler frequency, and the optimal nesting parameters under the DOA and Doppler frequency estimation are solved and the optimal time domain and space domain nesting parameters are obtained.

8. A computer program product, characterized in that The invention comprises a computer program, which implements the method according to any one of claims 1 to 4 when being executed by a processor.

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