Bayesian doa estimation method and device based on weighted atomic norm with feedback information assistance

Abstract

The application discloses a feedback information auxiliary Bayesian DOA estimation method and device based on a weighted atomic norm, and the method comprises the following steps: acquiring output information of a target tracker of a fusion center, and calculating a predicted direction of arrival (DOA) of each target according to the output information; constructing a prior interval of a DOA estimation value of each target according to the predicted DOA; and calculating the DOA estimation value of each target by using the prior interval and an atomic norm algorithm. The application converts the prior knowledge, i.e. the prior interval of the DOA estimation value of each target, into a semi-positive constraint, and then uses a meshless sparse method of atomic norm minimization to perform DOA estimation. The application combines array observation data and prior information, can obtain a high-resolution DOA estimation value, and reduces the calculation cost.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a feedback-assisted Bayesian DOA estimation method and apparatus based on weighted atomic norm. Background Technology

[0002] Direction of Arrival (DOA) estimation has wide applications in radar, sonar, wireless communication, and the Internet of Things (IoT). Existing high-resolution DOA estimation methods are mainly based on array observation data and can be divided into subspace methods, maximum likelihood methods, and sparse methods. Traditional subspace algorithms, such as MUSIC and ESPRIT, are based on eigenvalue decomposition or single-value decomposition. Although they have computational advantages, their estimation performance degrades when the impact signal is coherent or highly correlated. To address this, those skilled in the art have proposed preprocessing techniques such as front-to-back averaging or spatial smoothing for coherent signals, but this comes at the cost of sacrificing the effective aperture of the array. Maximum likelihood methods exhibit good performance, especially in cases of low signal-to-noise ratios; however, they require multidimensional grid search or iterative gradient search for DOA estimation, resulting in high computational complexity.

[0003] In recent years, a sparse DOA estimation method has emerged for high-resolution DOA estimation, demonstrating good performance in DOA estimation under adverse conditions such as insufficient array observations and coherent impulse signals. Specifically, by discretizing the region of interest into a grid, a sparse signal recovery problem can be constructed from DOA estimation. However, in practice, grid mismatch exists. Although increasing the grid density can improve estimation accuracy and alleviate the mismatch problem, it also increases computational cost and may lead to numerical problems due to the high correlation between adjacent columns in the dictionary matrix.

[0004] In numerous practical applications, prior information about the target's direction of arrival (DOA) can be obtained. For example, in networked radar or sensor network applications, the target's DOA, range, and Doppler information are sent to the tracker at the fusion center, and the tracker can also provide feedback on the predicted target position. This predicted target position information can be used to construct prior information about the target's DOA. However, classical estimation methods struggle to utilize this prior knowledge because, in these application scenarios, the target's DOA is no longer a definite value but should be assumed to be a random variable satisfying a prior distribution. Bayesian high-resolution estimation methods are introduced into array signal processing in such contexts. Existing Bayesian DOA estimation methods are based on the traditional Bayesian estimation framework, which mainly includes MAP (Maximum A Posteriori) estimators and MMSE (Minimum Mean Square Error) estimators. The former can be seen as an extension of the ML estimator, incorporating prior knowledge. Therefore, implementing MAP still requires multidimensional grid search or iterative gradient search. The latter involves multidimensional integrals, whose closed-form expressions are difficult to derive, and are typically solved using Monte Carlo methods. However, both the MAP and MMSE methods are computationally intensive. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a feedback-assisted Bayesian DOA estimation method and apparatus based on weighted atomic norm. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] In a first aspect, the present invention provides a feedback-assisted Bayesian DOA estimation method based on weighted atomic norm, comprising:

[0007] Obtain the output information of the target tracker in the fusion center, and calculate the predicted direction of arrival (DOA) of each target based on the output information;

[0008] Based on the predicted DOA, construct the prior interval for the DOA estimate of each target;

[0009] Using the prior interval and atomic norm algorithm, the DOA estimate of each target is calculated.

[0010] In one embodiment of the present invention, the output information includes the predicted location of each target and the covariance matrix of the predicted location;

[0011] The steps of acquiring the output information of the target tracker at the fusion center and calculating the predicted direction of arrival (DOA) of each target based on the output information include:

[0012] Calculate the predicted DOA for each target based on its predicted location:

[0013]

[0014] Among them, [t kx , t ky ] T This represents the predicted location of the k-th target;

[0015] Based on the predicted DOA of each target, calculate the average of the estimated DOA values ​​for the k-th target. k = 1, 2, ..., K, where K represents the target quantity;

[0016] Based on the covariance matrix of the predicted location, calculate the variance of the DOA estimate of the k-th target.

[0017] In one embodiment of the present invention, the predicted DOA of the k-th target conforms to the mean value. variance is Gaussian distribution;

[0018] The steps for constructing the prior interval for the DOA estimate of each objective based on the predicted DOA include:

[0019] make Where, θ k Let σ represent the estimated DOA of the k-th objective. k γ represents the standard deviation of the predicted DOA for the k-th target, n is the preset coefficient that determines the range of the prior interval, and γ n Indicates the confidence level. express The probability of;

[0020] The prior interval for the DOA estimate of the k-th target is determined as follows:

[0021] In one embodiment of the present invention, n = 3, γ n =0.997, the prior interval for the DOA estimate of the k-th target is:

[0022] In one embodiment of the present invention, the DOA estimate of each target is calculated using the prior interval and atomic norm algorithm according to the following formula:

[0023]

[0024]

[0025] T g (u)≥0;

[0026] ||YZ|| F ≤p;

[0027]

[0028] In the formula, X represents the free variable to be estimated, Z represents the noiseless received signal to be estimated, and T(u) is the Toeplitz matrix to be optimized, with the matrix element vector u = [u1, u2, ..., u...]. N Y represents the received signal matrix, λ is a preset constant, p and q are auxiliary variables to be estimated, tr represents the trace of the matrix, and ||·|| F Let F be the F-norm, N be the snapshot number, and H be the conjugate transpose, a semidefinite matrix. Where u1, u2, ..., u N Let ω1, ω0, and ω be the matrix elements in T(u). -1 These are the weighting coefficients.

[0029] In one embodiment of the present invention, ω0=-2cos(π(θ L -θ H )), θ L θ H Let represent the two endpoints of the prior interval for the DOA estimate of the k-th target.

[0030] In one embodiment of the present invention, when the prior intervals of the DOA estimates of each target are different, the DOA estimates of each target are calculated using the prior intervals and the atomic norm algorithm according to the following formula:

[0031]

[0032]

[0033]

[0034] T gl (ul)≥0, l=1, 2,…,L r ;

[0035] ||YZ|| F ≤p;

[0036]

[0037] In the formula, L r The matrix element vector u represents the number of prior intervals for the DOA estimates of each target. l =[u l1 ul2 , ..., u lN ].

[0038] Secondly, the present invention provides a feedback-assisted Bayesian DOA estimation device based on weighted atomic norm, comprising:

[0039] The acquisition module is used to acquire the output information of the target tracker in the fusion center and calculate the predicted direction of arrival (DOA) of each target based on the output information.

[0040] The building module is used to construct the prior interval of the DOA estimate for each target based on the predicted DOA;

[0041] The calculation module is used to calculate the DOA estimate of each target using the prior interval and atomic norm algorithm.

[0042] Thirdly, the present invention provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0043] Memory, used to store computer programs;

[0044] When a processor executes a program stored in memory, it implements the steps of the method described in the first aspect.

[0045] Fourthly, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the method described in the first aspect.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] This invention provides a feedback-assisted Bayesian DOA estimation method and apparatus based on weighted atomic norm. This method transforms prior knowledge—the prior interval of each target DOA estimate—into a positive semidefinite constraint, and then uses a meshless sparse method that minimizes the atomic norm to perform DOA estimation. This invention combines array observation data and prior information, enabling the acquisition of high-resolution DOA estimates while reducing computational costs.

[0048] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0049] Figure 1 This is a flowchart of a feedback information-assisted Bayesian DOA estimation method based on weighted atomic norm provided in an embodiment of the present invention;

[0050] Figure 2This is a schematic diagram of the prior region of the DOA estimates of two targets provided in an embodiment of the present invention;

[0051] Figure 3 This is a comparison chart of DOA estimation results provided in an embodiment of the present invention;

[0052] Figure 4 This is another comparison chart of DOA estimation results provided by an embodiment of the present invention;

[0053] Figure 5 This is another comparison chart of DOA estimation results provided by an embodiment of the present invention;

[0054] Figure 6 This is a comparison chart of DOA estimation performance under different signal-to-noise ratios provided in the embodiments of the present invention;

[0055] Figure 7 This is a schematic diagram of a Bayesian DOA estimation method based on weighted atomic norm assisted by feedback information provided in an embodiment of the present invention;

[0056] Figure 8 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0058] Figure 1 This is a flowchart of a Bayesian DOA estimation method based on weighted atomic norm assisted by feedback information provided in an embodiment of the present invention. Figure 1 As shown, this embodiment of the invention provides a feedback-assisted Bayesian DOA estimation method based on weighted atomic norm, comprising:

[0059] S1. Obtain the output information of the target tracker at the fusion center, and calculate the predicted direction of arrival (DOA) of each target based on the output information;

[0060] S2. Based on the predicted DOA, construct the prior interval for the DOA estimate of each target.

[0061] S3. Using the prior interval and atomic norm algorithm, calculate the DOA estimate of each target.

[0062] In this embodiment, the output information includes the predicted location of each target and the covariance matrix of the predicted location;

[0063] Step S1, which involves acquiring the output information of the target tracker at the fusion center and calculating the predicted direction of arrival (DOA) for each target based on the output information, includes:

[0064] S101. Based on the predicted locations of each target, calculate the predicted DOA for each target:

[0065]

[0066] Among them, [t kx , t ky ] T This represents the predicted location of the k-th target;

[0067] S102. Based on the predicted DOA of each target, calculate the average of the estimated DOA values ​​for the k-th target. k = 1, 2, ..., K, where K represents the target quantity;

[0068] S103. Based on the covariance matrix of the predicted location, calculate the variance of the DOA estimate of the k-th target.

[0069] This embodiment only considers a two-dimensional positioning scenario. Specifically, the output information of the tracker at the fusion center includes the predicted positions of each target and the covariance matrix of the predicted positions, where the predicted position of the k-th target is t. k =[t kx , t ky ] T Its covariance matrix is ​​Q tk If the sensor array is located at the origin, then the DOA of the k-th target relative to the array is:

[0070]

[0071] Where, ρ k ∈[0, 2π), the predicted direction of arrival ρ of the k-th target k The mean is variance is The Gaussian distribution.

[0072] Optionally, step S2 above, which involves constructing the prior interval for the DOA estimate of each target based on the predicted DOA, includes:

[0073] S201, Order Where, θ k Let σ represent the estimated DOA of the k-th objective. k γ represents the standard deviation of the predicted DOA of the k-th target, n is a preset coefficient that determines the range of the confidence interval (i.e., the prior interval in this embodiment), and γ n Indicates the confidence level. express The probability of;

[0074] S202. Determine the prior interval for the DOA estimate of the k-th target as follows:

[0075] Figure 2 This is a schematic diagram of the prior region for two-target DOA estimates provided in an embodiment of the present invention. In this embodiment, for the prior distribution of p(θ) in the DOA estimation, the prior region can be constructed using the confidence interval of the Gaussian distribution, i.e.:

[0076]

[0077] For example, if n = 3 and γ3 = 0.997, then the prior interval for the DOA estimate of the k-th target is: like Figure 2 As shown, the final prior region is the union of the prior regions of the two target DOA estimates, and should be within the range of (-90°, 90°).

[0078] Taking a uniform linear array containing M omnidirectional sensors as an example, there are K targets with angles θ1, θ2, ..., θ3 respectively. K The signal is incident on the array sensor, where k = 1, 2, ..., K, and the signal radiated by the k-th source is s. k (t), and s k Let y(t) be a narrowband signal. Let y(t) = [y1(t), y2(t), ..., y... M (t)] T ,s(t)=[s1(t),s2(t),…,s K (t)] T Therefore, after demodulation, the signal received by the array sensor at time t can be expressed as:

[0079]

[0080] In the formula, n(t) represents additive noise, n(t) = [n1(t), n2(t), ..., n M (t)] T .

[0081] Furthermore, equation (1) can be written as:

[0082] Y = AS + N (2)

[0083] in, Guiding vector matrix N represents the number of snapshots.

[0084] It should be understood that the atomic norm method is a meshless sparse method for DOA estimation. To perform DOA search in a continuous space, DOA estimation can be viewed as operating in the presence of noise and ||N|| FFind the noise-free data Z = AS when η < η. The set of values ​​for the unknown noise-free data Z can be represented as follows:

[0085]

[0086] The atomic norm method searches for the DOA in a gridded space rather than a directional domain. The set of all possible orientation vectors is defined as:

[0087]

[0088] Therefore, the noiseless received signal Z to be estimated can be written as A linear combination of K atoms. The l0 norm of Z is defined as:

[0089]

[0090] The goal of the atomic norm method is to find a solution in Z using the atomic norm l0:

[0091]

[0092] In fact, calculation The solution is equivalent to finding the rank minimization problem. However, the rank minimization problem is not easy to solve because it is a non-convex NP-hard problem. Therefore, this embodiment uses ||Z|| A，0 Convex relaxation norm:

[0093]

[0094] The above formula is called the atomic norm. By using the atomic norm... The minimization problem (6) can be transformed into the following SDP problem:

[0095]

[0096]

[0097] After solving the above SDP problem, the Toeplitz matrix estimate obtained by Vandermonde (VD) decomposition is used for meshless DOA estimation.

[0098] Optionally, in step S3, the DOA estimate of each target is calculated using the prior interval and atomic norm algorithm according to the following formula:

[0099]

[0100]

[0101] T g(u)≥0;

[0102] ||YZ|| F ≤p;

[0103]

[0104] In the formula, X represents the free variable to be estimated, Z represents the noiseless received signal to be estimated, and T(u) is the Toeplitz matrix to be optimized, with the matrix element vector u = [u1, u2, ..., u...]. N Y represents the received signal matrix, λ is a preset constant, p and q are auxiliary variables to be estimated, tr represents the trace of the matrix, and ||·|| F Let F be the F-norm, N be the snapshot number, and H be the conjugate transpose, a semidefinite matrix. Where u1, u2, ..., u N Let ω1, ω0, and ω be the matrix elements in T(u). -1 These are the weighting coefficients.

[0105] In this embodiment, the DOA estimates of all targets are in the same prior region. When, the set of atoms in equation (4) It can be modified to:

[0106]

[0107] Replace the entire possible region (-π / 2, π / 2) in the direction of incoming waves with the prior region Θ = [θ]. L θ H The corresponding atomic norm minimization problem becomes:

[0108]

[0109] Transform this problem into an SDP problem:

[0110]

[0111]

[0112] ||YZ|| F ≤η (11c)

[0113] T g (u)≥0 (11d)

[0114] in,

[0115]

[0116] Among them, T g(u) is a semidefinite matrix constructed from the prior region. That is, constraint (11d) requires Z (or the equivalent T(u)) to be derived from the prior region. The atomic composition of T. g The expression for (u) is given by equation (12), where ω j j = -1, 0, 1 are weighting coefficients, and are related to the prior region [θ]. L θ H The relationship is:

[0117]

[0118] ω0=-2cos(π(θ L -θ H (13b)

[0119] θ L θ H Let represent the two endpoints of the prior interval for the DOA estimate of the k-th target.

[0120] To linearize the objective function, another convex problem can be constructed from equation (11a) by introducing auxiliary p and q:

[0121]

[0122]

[0123] T g (u)≥0 (14c)

[0124] ||YZ|| F ≤p (14d)

[0125]

[0126] The optimization problem in equation (14a) is in the form of SDP, where (14d) is the SOCP constraint.

[0127] Furthermore, when the prior intervals for the DOA estimates of different targets are different, the DOA estimates of each target are calculated using the prior interval and atomic norm algorithm according to the following formula:

[0128]

[0129]

[0130]

[0131] T gl (u l )≥0, l=1,2,…,L r ;

[0132] ||YZ|| F ≤p;

[0133]

[0134] In the formula, L r The matrix element vector u represents the number of prior intervals for the DOA estimates of each objective. l =[u l1 u l2 , ..., u lN ].

[0135] Specifically, in practical applications, the target's DOA estimate may also be located in L. r Non-intersecting regions Therefore, this embodiment can construct a series of regions Θ similar to the prior region Θ. l Relevant constraints.

[0136] T(u l )≥0,T gl (ul)≥0, l=1, 2,…,L r (15)

[0137] Where T is the Toeplitz matrix, expressed as: T gl (u l ) is T(u) in equations (11a), (12), and (14a) l ) and Θ k The DOA is estimated from the given components. The SDP when the prior regions are independent can be expressed as:

[0138]

[0139]

[0140]

[0141] T gl (u l )≥0, l=1,2,…,L r (16d)

[0142] ||YZ|| F ≤p (19e)

[0143]

[0144] It should be noted that when the target's DOA estimate is located in L... r Disjoint prior intervals Θ l At that time, T(u)l This indicates that a matrix similar to T(u) can be constructed within the l-th prior interval, where the matrix element vector is u. l =[u l1 u l2 , ..., u lN Similar to equation (11b), the Toeplitz matrix in the positive semidefinite constraint of equation (16b) can be represented by T, through... express.

[0145] Furthermore, using Vandermonde (VD) decomposition, the Toeplitz matrix estimate is obtained and used for meshless DOA estimation.

[0146] The following simulation experiment further illustrates the feedback-assisted Bayesian DOA estimation method based on weighted atomic norm provided by this invention.

[0147] Specifically, a uniform linear array of 8 elements is used, with the element spacing being half a wavelength, i.e. There are two targets, both with a signal carrier frequency of f = 3 × 10⁻⁶. 8 Hz, carrier wavelength Based on the predicted positions of the targets, the predicted DOAs of the two targets are calculated as ρ1 = 10° and ρ2 = -5°, respectively, and the variances of the predicted DOAs of the two targets are σ1 = 2° and σ2 = 1°, respectively. Combining the 3σ criterion, the prior intervals of the two targets are Θ1 = [4°, 16°] and Θ2 = [-8°, -2°].

[0148] Figure 3 This is a comparison chart of DOA estimation results provided by an embodiment of the present invention. Figure 3 With a snapshot count of 100 and a signal-to-noise ratio of 20dB, the echo signals from the two targets are incoherent. Figure 3 As can be seen, both the MUSIC algorithm and the prior information-assisted atomic norm minimization method proposed in this invention can accurately estimate the directions of arrival of the two signals.

[0149] Figure 4 This is another comparison chart of DOA estimation results provided by an embodiment of the present invention. The experiment was conducted again after setting the two signals as coherent signals, as shown below. Figure 4 As shown, the MUSIC method exhibits three high spectral peaks, failing to distinguish the direction of arrival of the target signal. This method has failed. However, the method provided by this invention can still accurately estimate the direction of arrival of the two targets even in the case of coherent signals, indicating that this invention still has a very high resolution capability when facing coherent signals.

[0150] Figure 5This is another comparison chart of DOA estimation results provided by an embodiment of the present invention. Optionally, after setting the two signals as coherent signals, the signal-to-noise ratio is further set to -10dB. Figure 5 As can be seen, the spectral function image of MUSIC can no longer accurately distinguish the direction of arrival of the target. Although the method provided by this invention has certain errors under low signal-to-noise ratio conditions, it can still estimate the direction of arrival of the two targets, indicating that the above method still has excellent performance under low signal-to-noise ratio conditions.

[0151] Figure 6 This is a comparison chart of DOA estimation performance under different signal-to-noise ratios provided in the embodiments of the present invention. Figure 6 As shown, the performance metric is measured by the mean square error (RMSE) of the estimate, and BCRLB (Bayesian Cramer-Rao Lower Bound) represents the Bayesian Cramer-Rao lower bound for the corresponding direction-of-arrival estimate, serving as a reference standard for estimation performance. Figure 6 As shown, the DOA estimation result of the MUSIC algorithm is far from BCRLB. Both the method of this invention and the ANM method can achieve BCRLB when the signal-to-noise ratio is greater than -5dB, but the method of this invention has a lower mean square error when the signal-to-noise ratio is less than -5dB. Therefore, the DOA estimation method provided by this invention has superior performance under low signal-to-noise ratio conditions.

[0152] Figure 7 This is a schematic diagram of a feedback information-assisted Bayesian DOA estimation device based on weighted atomic norm provided in an embodiment of the present invention. Figure 7 As shown, this embodiment of the invention provides a feedback-assisted Bayesian DOA estimation device based on weighted atomic norm, comprising:

[0153] The acquisition module 710 is used to acquire the output information of the target tracker in the fusion center and calculate the predicted direction of arrival (DOA) of each target based on the output information.

[0154] Module 720 is used to construct the prior interval of the DOA estimate for each target based on the predicted DOA.

[0155] The calculation module 730 is used to calculate the DOA estimate of each target using the prior interval and atomic norm algorithm.

[0156] As can be seen from the above embodiments, the beneficial effects of the present invention are as follows:

[0157] This invention provides a feedback-assisted Bayesian DOA estimation method and apparatus based on weighted atomic norm. This method transforms prior knowledge—the prior interval of each target DOA estimate—into a positive semidefinite constraint, and then uses a meshless sparse method that minimizes the atomic norm to perform DOA estimation. This invention combines array observation data and prior information, enabling the acquisition of high-resolution DOA estimates while reducing computational costs.

[0158] This invention also provides an electronic device, such as... Figure 8 As shown, it includes a processor 801, a communication interface 802, a memory 803, and a communication bus 804. The processor 801, communication interface 802, and memory 803 communicate with each other via the communication bus 804.

[0159] Memory 803 is used to store computer programs;

[0160] When processor 801 executes a program stored in memory 803, it performs the following steps:

[0161] Obtain the output information of the target tracker in the fusion center, and calculate the predicted direction of arrival (DOA) of each target based on the output information;

[0162] Based on the predicted DOA, construct the prior interval for the DOA estimate of each target;

[0163] Using the prior interval and atomic norm algorithm, the DOA estimate of each target is calculated.

[0164] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.

[0165] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0166] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0167] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0168] The method provided in this invention can be applied to electronic devices. Specifically, the electronic device can be a desktop computer, a portable computer, a smart mobile terminal, a server, etc. No limitation is made herein; any electronic device that can implement this invention falls within the protection scope of this invention.

[0169] For the embodiments of the device / electronic device / storage medium, since they are basically similar to the method embodiments, the description is relatively simple, and relevant parts can be referred to in the description of the method embodiments.

[0170] It should be noted that the device, electronic device, and storage medium in the embodiments of the present invention are respectively devices, electronic devices, and storage media that apply the above-mentioned feedback information to assist the Bayesian DOA estimation method based on weighted atomic norm. Therefore, all embodiments of the above-mentioned feedback information-assisted Bayesian DOA estimation method based on weighted atomic norm are applicable to the device, electronic device, and storage medium, and can achieve the same or similar beneficial effects.

[0171] The terminal device provided by the embodiments of the present invention can display proper nouns and / or fixed phrases for users to select, thereby reducing user input time and improving user experience.

[0172] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0173] The use of terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples" indicates that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0174] Although this application has been described herein in conjunction with various embodiments, other variations of the disclosed embodiments can be understood and implemented by those skilled in the art in carrying out the claimed application by reviewing the accompanying drawings, the disclosure, and the appended claims.

[0175] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A Bayesian DOA estimation method based on weighted atomic norm and assisted by feedback information, characterized in that, include: Obtain the output information of the target tracker in the fusion center, and calculate the predicted direction of arrival (DOA) of each target based on the output information; Based on the predicted DOA, construct the prior interval for the DOA estimate of each target; Using the prior interval and atomic norm algorithm, the DOA estimate of each target is calculated; Using the prior interval and atomic norm algorithm, the DOA estimate for each objective is calculated according to the following formula: ； ； ； ； ； In the formula, Represents the free variables to be estimated. This represents the noise-free received signal to be estimated. All are Toeplitz matrices to be optimized, and matrix element vectors. , Represents the received signal matrix. As a preset constant, For the auxiliary variable to be estimated, Represents the trace of a matrix. express -norm, For the number of snapshots, Represents the conjugate transpose, a semidefinite matrix. ,in, for Matrix elements in , and These are the weighting coefficients.

2. The feedback-assisted Bayesian DOA estimation method based on weighted atomic norm according to claim 1, characterized in that, The output information includes the predicted location of each target and the covariance matrix of the predicted location; The steps of acquiring the output information of the target tracker at the fusion center and calculating the predicted direction of arrival (DOA) of each target based on the output information include: Calculate the predicted DOA for each target based on its predicted location: ； in, Indicates the first The predicted location of each target; Based on the predicted DOA of each target, calculate the first... The average of the DOA estimates for each target , , Indicates the target quantity; Based on the covariance matrix of the predicted location, calculate the first... The variance of the DOA estimates for each target.

3. The feedback information-assisted Bayesian DOA estimation method based on weighted atomic norm according to claim 2, characterized in that, The first The predicted DOA for each objective conforms to the mean. variance is Gaussian distribution; The steps for constructing the prior interval for the DOA estimate of each objective based on the predicted DOA include: make ,in, Indicates the first The estimated DOA of each target. Indicates the first The standard deviation of the predicted DOA for each target To determine the preset coefficients for the range of the prior interval, Indicates the confidence level. express The probability of; Determine the first The prior intervals for the DOA estimates of each target are: , ].

4. The feedback information-assisted Bayesian DOA estimation method based on weighted atomic norm according to claim 2, characterized in that, , , No. The prior intervals for the DOA estimates of each target are: , ].

5. The feedback-assisted Bayesian DOA estimation method based on weighted atomic norm according to claim 4, characterized in that, , , , They represent the first The two endpoints of the prior interval of the DOA estimate of each target.

6. The feedback-assisted Bayesian DOA estimation method based on weighted atomic norm according to claim 5, characterized in that, When the prior intervals for the DOA estimates of each target are different, the DOA estimates of each target are calculated using the prior intervals and the atomic norm algorithm according to the following formula: ； ； ； ； ； ； In the formula, The matrix element vector represents the number of prior intervals for the DOA estimates of each target. .

7. A feedback-assisted Bayesian DOA estimation device based on weighted atomic norm, characterized in that, include: The acquisition module is used to acquire the output information of the target tracker in the fusion center and calculate the predicted direction of arrival (DOA) of each target based on the output information. The building module is used to construct the prior interval of the DOA estimate for each target based on the predicted DOA; The calculation module is used to calculate the DOA estimate of each target using the prior interval and atomic norm algorithm according to the following formula: ； ； ； ； ； In the formula, Represents the free variables to be estimated. This represents the noise-free received signal to be estimated. All are Toeplitz matrices to be optimized, and matrix element vectors. , Represents the received signal matrix. As a preset constant, For the auxiliary variable to be estimated, Represents the trace of a matrix. express -norm, For the number of snapshots, Represents the conjugate transpose, a semidefinite matrix. ,in, for Matrix elements in , and These are the weighting coefficients.

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

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

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