Mobile sparse array optimization method for low signal-to-noise ratio DOA estimation

Abstract

The invention provides a mobile sparse array optimization method for low signal-to-noise ratio DOA (direction of arrival) estimation, which is suitable for direction of arrival estimation under the condition of low signal-to-noise ratio. According to the method, array receiving signal data models of the sparse array on a horizontal motion platform and a vertical motion platform are respectively established aiming at virtual array element expansion and degree-of-freedom improvement characteristics formed in the motion process of the sparse array, and a corresponding direction of arrival estimation Ziv-Zakai boundary expression is deduced. Compared with a method using a Cramer-Rao boundary as an array configuration optimization performance index, the Ziv-Zakai boundary can more accurately represent a parameter estimation error lower bound in a low signal-to-noise ratio region, and a theoretical performance lower bound is provided for optimization design of horizontal and vertical motion sparse arrays in the low signal-to-noise ratio region. And ZZB is used as a target function for configuration optimization of the mobile sparse array, so that the sparse array with higher DOA estimation precision in a low signal-to-noise ratio scene is designed.

Description

Technical Field

[0001] This application belongs to the field of array signal processing, specifically relating to a method for optimizing moving sparse arrays for low signal-to-noise ratio (DOA) estimation. Background Technology

[0002] Array signal processing technology is widely used in radar, sonar, wireless communication, and navigation and positioning systems. Among these, direction of arrival (DOA) estimation, as a core method for obtaining the spatial location of a target, directly restricts the system's detection performance. Constrained by the Rayleigh criterion, traditional uniform linear arrays have a strict linear constraint between their physical aperture and degrees of freedom, making it difficult to meet the demands of increasingly complex electromagnetic environments under finite element conditions. In recent years, sparse array architectures, represented by coprime arrays and nested arrays, have become the mainstream direction in array configuration design due to their ability to provide a much higher number of degrees of freedom than the physical array elements and to expand the virtual aperture using differential coarrays. In the configuration optimization process of sparse arrays, the core task is to construct a reasonable sensor spatial arrangement to obtain the best parameter estimation performance, and this process is highly dependent on the selected performance evaluation index or optimization objective function.

[0003] For a long time, the Cramér-Rao Bound (CRB) has been widely used in engineering as the main standard for measuring array performance and optimizing configurations due to its simple analytical form and ease of calculation. However, the CRB is essentially a lower bound on error based on the assumption of local unbiasedness, and it can only accurately reflect the actual estimation error through asymptotic approximation under conditions of high signal-to-noise ratio or large snapshot number. In low signal-to-noise ratio or the so-called "prior region," due to anomalous errors caused by nonlinear transformation and sidelobe ambiguity effects, the actual mean square error will rise sharply and deviate significantly from the CRB. The unpredictability of this "threshold effect" constitutes a major drawback of CRB applications. This means that in non-ideal environments such as low signal-to-noise ratio, sparse arrays designed directly based on the CRB maximization or degree-of-freedom maximization criteria often cannot withstand the threshold effect, leading to severe degradation of detection performance in practical applications, and even complete failure of direction estimation.

[0004] To overcome the theoretical shortcomings of CRB failure under low signal-to-noise ratio conditions, existing technologies, such as the Ziv-Zakai lower bound for target nonlinear parameter estimation by Zhang Zongyu of Zhejiang University, have begun to introduce the Ziv-Zakai bound (ZZB) as a global performance evaluation tool. For example, research on the Ziv-Zakai lower bound for target nonlinear parameter estimation has established a relatively complete theoretical framework for ZZB. This framework not only derives the closed-form expression for multi-source DOA estimation but also solves the theoretical derivation difficulties caused by the ambiguity of multi-target ordering by introducing order statistics. Furthermore, it proves that ZZB can accurately predict the system's performance threshold across the entire signal-to-noise ratio range.

[0005] Although ZZB has made some progress in static array theory, it still faces many unresolved theoretical and modeling challenges when applied to moving sparse arrays. Unlike static arrays, the receiving array data model of a moving array is directly modulated by motion parameters (such as velocity and time intervals). This motion not only brings about spatiotemporal changes in phase but may also lead to complex redundant structures or dimensional expansion in the synthetic aperture data. For example, when the array moves horizontally, physical array elements at different times may occupy the same spatial position, resulting in overlapping information in the observation data; while during vertical motion, the original one-dimensional linear array scans in space to form a virtual plane, and its array data model essentially transforms into a two-dimensional estimation problem. Existing ZZB theories based on static models do not cover these special signal structures introduced by motion and cannot be directly used to accurately evaluate the signal-to-noise ratio threshold and global error characteristics of moving sparse arrays during motion synthesis. Summary of the Invention

[0006] Firstly, in view of the shortcomings of the prior art, the purpose of this application is to provide a moving sparse array optimization method for low signal-to-noise ratio (DOA) estimation, which improves the problem that the existing ZZB theory based on static models does not cover these special signal structures introduced by motion, and cannot be directly used to accurately evaluate the signal-to-noise ratio threshold and global error characteristics of moving sparse arrays in the motion synthesis process.

[0007] The objective of this application can be achieved through the following technical solutions: A method for optimizing a moving sparse array for low signal-to-noise ratio (DOA) estimation, the method being executed by a data processing device, comprising: Based on the platform motion mode, the initial array configuration data is subjected to spatiotemporal equivalent transformation to construct a synthetic array data model. The synthetic array data model has an extended aperture structure adapted to the platform motion mode, which includes horizontal motion and vertical motion. Based on the statistical characteristics of the synthetic array data model under horizontal and vertical motion, the prior error bound and Cramer-Rao lower bound of parameter estimation are derived respectively. Among them, dynamic weighting coefficients are generated based on the signal-to-noise ratio, number of information sources, and number of elements of the synthetic array in the current environment. The dynamic weighting coefficients are then used to perform a weighted summation operation on the prior error bound and the Cramer-Rao lower bound to obtain the Ziv-Zakai bound value corresponding to the synthetic array data model. Enumerate and calculate the Ziv-Zakai boundary values ​​of candidate arrays in horizontal and vertical motion, select the array configuration corresponding to the minimum Ziv-Zakai boundary value as the target array configuration and output it.

[0008] Furthermore, when the platform's motion mode is horizontal, the step of constructing the synthetic array data model includes: satisfying the displacement condition. ,in For the signal wavelength, The speed of movement in the platform motion mode. The sampling time interval; Under the displacement conditions, the synthetic array data model generated in the construction step is a reduced-dimensional observation matrix. Its computational logic is defined by the following formula: in, For synthesizing array manifold matrices, For the signal sampling matrix, This is the noise matrix; The set of effective normalized array element positions corresponding to the synthetic array manifold matrix The original array element normalized position set Definition of translation union: .

[0009] Furthermore, the step of constructing the synthetic array data model includes: Based on differential co-array The sub-step of determining degrees of freedom, the differential coarray The set of integer coordinates is defined as: Wherein, the degrees of freedom are The number of consecutive integers in the sequence is determined.

[0010] Furthermore, when the platform's motion mode is vertical, the step of constructing the synthetic array data model includes: satisfying the displacement condition. ,in For the signal wavelength, This refers to the vertical displacement during the platform's motion. Under the displacement condition, the synthetic array data model generated in the construction step is a virtual two-dimensional received signal vector. Its computational logic is defined by the following formula: in, For the initial observation signal, This is the displacement observation signal after phase compensation. For noise vectors, It is the complex envelope vector of the signal; The phase compensation is based on a diagonal matrix, which is the manifold matrix of a virtual two-dimensional array. Its diagonal elements are defined as ,in Indicates the first The angle between the incident path of each signal source and the X-axis.

[0011] Furthermore, the functional relationship used in the weighted summation operation is as follows: in, For the a priori lower bound, This is the lower bound of the Clamer-Loh term; The minimum error probability coefficient, These are the coefficients of the incompletely normalized Gamma function.

[0012] Furthermore, the minimum error probability coefficient The calculation is defined by the following formula: in, For the number of snapshots, For signal-to-noise ratio, The complementary cumulative distribution function of the standard normal distribution; For the number of information sources; for moving sparse arrays, Indicates the number of effective sensors; When the platform's motion mode is horizontal motion... The value is the set of effective array element positions in the synthesized array. number of elements ; When the platform's motion mode is vertical motion... The value is twice the number of physical array elements. .

[0013] Furthermore, the upper limit of the integral of the normalized incomplete Gamma function. The calculation is defined by the following formula: in, This is the Fisher information matrix corresponding to the synthetic array signal receiving matrix under the aforementioned mobile model. For dimension A column vector of all 1s. Secondly, in view of the shortcomings of the prior art, the purpose of this application is to provide a moving sparse array optimization device based on Ziv-Zakai bound under low signal-to-noise ratio conditions, which improves the problem that the existing ZZB theory based on static model does not cover these special signal structures introduced by motion, and cannot be directly used to accurately evaluate the signal-to-noise ratio threshold and global error characteristics of moving sparse array in motion synthesis process.

[0014] The objective of this application can be achieved through the following technical solutions: A device for optimizing a moving sparse array based on Ziv-Zakai bounds under low signal-to-noise ratio conditions includes: The parameter acquisition module is used to acquire a candidate parameter set for the mobile sparse array to be optimized. The candidate parameter set includes the initial arrangement data of the physical array elements and the platform motion mode. The evaluation computation module is used to perform the steps of constructing the synthetic array data model and calculating the Ziv-Zakai boundary value as described in the first aspect; and The configuration decision module is used to execute numerical comparison logic, retrieve the minimum value from multiple Ziv-Zakai boundary values, identify the physical array element arrangement data associated with the minimum value as the target array configuration, and output it.

[0015] Thirdly, in view of the shortcomings of the prior art, the purpose of this application is to provide a computer-readable storage medium that improves the problem that the existing ZZB theory based on static models does not cover these special signal structures introduced by motion, and cannot be directly used to accurately evaluate the signal-to-noise ratio threshold and global error characteristics of moving sparse arrays in the motion synthesis process.

[0016] The objective of this application can be achieved through the following technical solutions: A computer-readable storage medium having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the method as described in the first aspect.

[0017] The beneficial effects of this application are: This invention addresses the shortcomings of the CRB (Constant Boundary Scale) in predicting threshold effects and large error anomalies in low signal-to-noise ratio (SNR) environments. It adopts the Ziv-Zakai bound as a global performance evaluation index. By fusing the prior error bound of parameter estimation with the CRB, and utilizing dynamic weighting coefficients generated from multi-dimensional parameters including SNR, number of sources, and number of effective array elements of the synthesized array, it achieves an accurate characterization of the lower bound of the estimation error across the entire SNR range. Especially in the low SNR region, it can effectively suppress error divergence by utilizing the statistical constraints of prior information, ensuring the robustness of the optimization results in harsh electromagnetic environments. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the positions of the array elements before and after the nested array moves on the horizontal platform; Figure 2 This is a schematic diagram of the sensor positions of the nested array before and after it moves on the vertical platform; Figure 3 This is a comparison of CRB and ZZB results when the SNR of the array changes from -40dB to 20dB under horizontal motion conditions; Figure 4 This is a comparison of CRB and ZZB results when the SNR of the array changes from -40dB to 20dB under vertical motion conditions. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] Example 1: Symbol explanation: Vectors and matrices are represented by bold lowercase letters and bold uppercase letters, respectively. Dimensions are... The identity matrix is ​​denoted as Operator and Let represent the transpose and conjugate transpose, respectively. The expectation operator is denoted as . , Let represent the Hadamard product. The trace of the matrix is ​​denoted as . .gather The set of integer indices representing the positions of physical array elements, while This represents the set of integer indices of the difference coarray (DCA). The complex field is denoted as... The mean is The covariance matrix is The complex Gaussian random vector is represented as The number of information sources is denoted as... The number of quick shots is recorded as , The signal-to-noise ratio (SNR) of the information source is represented by the following: For signal power, This represents noise power.

[0022] A method for optimizing a moving sparse array for low signal-to-noise ratio (DOA) estimation, the method being executed by a data processing device, comprising: Based on the platform motion mode, the initial array configuration data is subjected to spatiotemporal equivalent transformation to construct a synthetic array data model. The synthetic array data model has an extended aperture structure adapted to the platform motion mode, which includes horizontal motion and vertical motion. Based on the statistical characteristics of the synthetic array data model under horizontal and vertical motion, the prior error bound and Cramer-Rao lower bound of parameter estimation are derived respectively. Among them, dynamic weighting coefficients are generated based on the signal-to-noise ratio, number of information sources, and number of elements of the synthetic array in the current environment. The dynamic weighting coefficients are then used to perform a weighted summation operation on the prior error bound and the Cramer-Rao lower bound to obtain the Ziv-Zakai bound value corresponding to the synthetic array data model. Enumerate and calculate the Ziv-Zakai boundary values ​​of candidate arrays in horizontal and vertical motion, select the array configuration corresponding to the minimum Ziv-Zakai boundary value as the target array configuration and output it.

[0023] The method described above is executed by a data processing device, which is existing technology. In some cases, the data processing device executing the optimization method can be a radar system main control computer equipped with a high-performance computing unit, an offline array design workstation, or an embedded digital signal processor (DSP). To initiate the optimization process, the data processing device is configured with a dedicated data input interface and instruction parsing module. When an array design instruction is triggered—this instruction can be a start signal input by the designer through a human-machine interface (such as a GUI terminal), or an automatic configuration request issued by the radar mission scheduling system via a PCIe bus or Ethernet interface—the data processing device first responds to the instruction by initializing the memory space and establishing a communication link with the configuration database or real-time parameter stream. Subsequently, the data processing device obtains the candidate parameter set of the mobile sparse array to be optimized through the communication link. This acquisition process specifically involves parsing and verifying the integrity of the input data stream to ensure the validity of subsequent calculations. The candidate parameter set is encapsulated in the data structure as a configuration package containing two core subsets: one is the initial arrangement data of the physical array elements, which specifically defines the geometric coordinate information of each array element in the sparse array in a static state, such as a set of array element position vectors represented in Cartesian coordinates, which corresponds to the original array element position set described in the claims. Secondly, there are platform motion parameters, which quantitatively describe the motion state of the carrier. Within the internal logic of the data processing device, the processor extracts specific scalar values ​​from these platform motion parameters according to a preset communication protocol. When the motion mode flag is detected as horizontal motion, the processor automatically parses and determines the horizontal motion speed of the carrier. and the system sampling time interval The data is temporarily stored in the cache for subsequent spatiotemporal equivalent transformations; when the motion mode flag is detected as vertical motion, the processor then parses the vertical displacement accordingly. Or it can be used to calculate the velocity vector and time parameters of the displacement.

[0024] This invention relates to constructing a synthetic array data model by performing a spatiotemporal equivalent transformation on the initial array configuration data based on the platform's motion mode. The synthetic array data model has an extended aperture structure adapted to the platform's motion mode. The platform motion mode includes horizontal motion and vertical motion. For example, in this application, the platform motion mode includes horizontal motion and vertical motion. The synthetic array data model is constructed by performing a spatiotemporal equivalent transformation on the initial array configuration data through horizontal motion and by performing a spatiotemporal equivalent transformation on the initial array configuration data through vertical motion.

[0025] Specifically, this application presents array data models for sparse arrays with horizontal and vertical motion, and derives ZZB expressions for DOA estimation under these two motion models.

[0026] A. Array data model of horizontally shifted sparse array Assuming by A sparse array composed of individual elements moves at a constant speed Moving horizontally. Figure 1 Taking a 7-element array with an aperture of 15 as an example, the time interval between the two received signals before and after the array movement is set as... ,in ,and The unit element spacing indicates that the array's positional interval before and after the movement is half a wavelength. Figure 1 The circles in the diagram represent the positions of the array elements before movement, and the squares represent the positions of the array elements after movement. Consider... A series of uncorrelated quasi-stationary narrowband far-field signals from the direction Incident on a by A sparse linear array composed of elements, the positions of the elements are as follows: The position of the array element is defined as follows: , ,in The integer representing the element index. The unit element spacing, This represents the signal wavelength. To simplify the analysis, the position of the first array element is taken as the reference point and set as... On a relatively high-speed platform, assuming the array undergoes a short translational motion, the direction of arrival of the signal source relative to the array remains constant. Therefore, at time... The array observation matrix can be represented as: in, The direction vector matrix (guiding matrix) represents the sparse array. For the corresponding number The steering vector of each signal source is expressed as follows: Signal vector This indicates the result after corresponding Doppler frequency shift modulation. One source signal, among which The sampling interval is... This represents the number of snapshots. Let represent an additive white complex Gaussian noise vector with zero mean and covariance matrix . .

[0027] After the time interval The array's observation signal can then be represented as: in Let the manifold matrix of the array after motion be represented by the following: and , Indicates time The noise vector, and in this paper, it is assumed and They are unrelated.

[0028] For carrier frequency is Narrowband signals, have Therefore, equation (2) can be rewritten as: Because the displacement satisfies Therefore, at time When this happens, the corresponding array steering vector can be expressed as: Referring to the literature, the array signal is defined in equation (4). Apply phase correction factor ,Right now: It represents the received signal vector after phase synchronization, where .

[0029] Combining equations (1) and (6), the synthesized array signal can be obtained as follows: in The array manifold matrix represents the composite array. Indicates a composite array, This represents the synthesized array noise vector.

[0030] Since the positions of array elements may overlap at two observation times, the array observation matrix will also contain duplicate data. Considering that the noise received by the array is usually spatiotemporally uncorrelated white noise, the data and noise received by the overlapping array elements before and after the array motion can be combined. Specifically, by removing the redundant rows in the array manifold matrix on the right side of equation (7) corresponding to the duplicate signals received by the overlapping array elements before and after the motion, a dimension reduction model can be obtained. This model describes the received signal of the synthetic array composed of array elements before and after the array motion, and the number of array elements satisfies Therefore, the receiving array data model of the synthesized array can be represented in matrix form as follows: in, This represents the observation matrix of the synthetic array. The array manifold matrix of the synthesized array, Represents a synthetic array Upper The steering vectors of the signal sources, where the position of the first array element is set to coordinate 0, and ; For the signal sampling matrix, This represents the noise matrix of the synthesized array.

[0031] For synthetic arrays, the degrees of freedom (DOF) will be significantly improved due to the increased number of elements and the greater diversity of element positions. Let... and Let each represent an integer set of the positions of the array elements in the original array and the composite array, respectively. According to the definition of a composite array, we have: set up and Let represent the sets of integer coordinates corresponding to the differential coarrays (DCA) of the original array and the synthesized array, respectively. According to the definition of DCA, we have: This application makes the following assumptions: Assumption 1: All signals They are uncorrelated with each other, and the array noise is uncorrelated in both the time and spatial domains.

[0032] Assumption 2: Each signal has a unique direction of arrival (DOA), that is, when From time to time .

[0033] Assumption 3: Each DOA Follow the interval The uniform distribution on, where and These represent the lower and upper bounds of the DOA range, respectively.

[0034] Therefore, the synthesized array data matrix The theoretical covariance matrix can be expressed as: in, , Indicates the first The power of each signal source, Indicates noise power. for 3D identity matrix.

[0035] The Cramér-Rao lower bound (CRB) can be obtained from the inverse of the Fisher information matrix (FIM). Regarding the angle vector... FIM ) Each element can be represented as: This expression involves both the signal covariance matrix and its derivative. For the number of snapshots, Let CRB represent the theoretical covariance matrix of the synthetic array data. For the DOA estimation of a horizontally moving sparse array, its CRB can be expressed as: in in, Fisher's information matrix, column vector and binary matrix .

[0036] B. Array data model for vertically shifted sparse arrays Similarly, when a sparse array moves vertically with the same array configuration and motion parameters as in the horizontal motion case, Figure 2 This shows the positions of the array elements before and after the movement. The time interval between the two snapshots remains the same. And the displacement in the vertical direction also satisfies This allows the array to form a spatial interval of half a wavelength before and after movement.

[0037] like Figure 2 As shown, Indicates the first Two-dimensional direction of arrival (2D-DOA) of a signal source, where the pitch angle Defined as the first The incident path of each signal source and Angle between axes, azimuth Defined as the incident path in Projection on a plane and The angle between axes. and Representing the incident path and shaft and The angle between axes. and The relationship between them can be given by the literature: For a sparse array with vertical motion, at time... The array observation model can be expressed as: in, This represents the array response vector corresponding to the k-th source. Let v represent the complex envelope of the k-th source, and v represent the platform's velocity. Indicates the incident path and The angle between the axes, For the signal wavelength, The sampling interval is... For the number of snapshots, Let represent an additive white complex Gaussian noise vector with zero mean and covariance matrix . .

[0038] The vertical motion model is mainly reflected in the first The correction of the steering vector of each signal source distinguishes it from the case of horizontal motion. Specifically, its steering vector is constructed as follows: . The complex envelope column vector of each incident signal is represented as: At that moment The array moved a distance perpendicular to its axis. The array's observation data at this time can be represented as: in .because ,so It can be written as: Similar to equation (4), equation (17) can be written as: Apply a phase compensation factor to the array received signal in equation (19). The received signal vector after phase synchronization can be obtained: According to equations (16) and (20), the synthesized array received signals at the two moments can be expressed as: in , Based on the above array data model, its covariance matrix can be expressed as: .right Vectorization yields ,in , Based on the literature, the CRB matrix of the vertical motion sparse array can be derived as follows: in Based on the statistical characteristics of the synthetic array data model under the aforementioned horizontal and vertical motions, the prior error bounds and Cramer-Rao lower bounds for parameter estimation are derived respectively. Specifically: Assuming a uniform prior distribution, the Fisher information matrix (FIM) in the Bayesian Cramér-Rao lower bound (BCRB) does not include information from the parameters. The contribution of prior information means that the CRB only has high accuracy in the high signal-to-noise ratio (asymptotic) region. Therefore, the reliability of the CRB as a performance evaluation benchmark decreases significantly within the apriori performance range. In contrast, the globally compact Ziv-Zakai lower bound (ZZB) provides a more reliable lower bound for the mean square error (MSE) over a wider signal-to-noise ratio range.

[0039] ZZB can be expressed as a weighted sum of the prior performance lower bound (APB) and the critical performance bound (CRB), with the corresponding weights being respectively... and .in, Indicates two hypotheses and The minimum probability of error when making a decision between them. for The known reference value, This represents the offset. Its expression can be written as: in, The complementary cumulative distribution function of the standard normal distribution is defined as follows: . Here is the normalized incomplete Gamma function, where This function reflects the attenuation characteristics of the assumed decision error probability under different signal-to-noise ratios, parameter intervals, and other conditions, and is defined as follows: in This indicates the number of effective sensors in the synthetic array; This is the Fisher information matrix corresponding to the synthetic array signal receiving matrix under the aforementioned mobile model. For dimension A column vector of all 1s. .

[0040] Within the prior performance region, when and At that time, ZZB degenerates into APB: in, The signal-to-noise ratio (SNR) of the information source is represented. and These represent signal power and noise power, respectively. Indicates the angular range of DOA. Within the asymptotic region, when... and At that time, ZZB and CRB are equivalent: Therefore, the ZZB of the DOA estimation based on the horizontally moving sparse array can be expressed as: Among them, and Winning For a sparse array undergoing vertical motion, the positions of the elements before and after displacement do not coincide, therefore there are no redundant elements, and the number of elements in the composite array is twice that of the original array. Thus, the ZZB of a vertically moving sparse array can be derived as follows: Among them, and Winning .

[0041] For this purpose, the Ziv-Zakai boundary values ​​of candidate arrays in horizontal and vertical motion are enumerated and calculated. The array configuration corresponding to the minimum Ziv-Zakai boundary value is selected as the target array configuration and output. In some cases, the array configuration corresponding to the minimum Ziv-Zakai boundary value is manually selected as the target array configuration and output. Alternatively, in other cases, the data processing device first determines the target array configuration based on preset system constraints, such as the total number of grid cells in the physical aperture. and the total number of available physical array elements The next step is to construct a set of candidate parameters to be optimized. This step generates all parameters that satisfy the given conditions by either a traversal algorithm or a random combination generation logic. Individual elements The system generates a candidate codebook containing several possible array manifold structures by combining the distribution patterns of each grid position. Then, in the iterative evaluation phase, for each specific initial physical element arrangement data in the candidate codebook, the system calls the aforementioned synthetic aperture mapping logic, combining preset platform motion parameters (such as horizontal velocity or vertical displacement) to generate its corresponding synthetic array data model. Next, the system substitutes the geometric parameters of this model (such as effective aperture and number of elements) and current environmental parameters (such as signal-to-noise ratio and number of sources) into the aforementioned ZZB weighted calculation formula to quantify the theoretical lower bound of the specific configuration under the current operating conditions. The data processing device maintains a dynamic comparison register in memory to record the minimum ZZB value calculated during the current traversal and its corresponding array index. After traversing all or a preset number of configurations in the candidate parameter set, the ultimate minimum value locked in the comparison register represents the theoretically optimal solution. At this point, the data processing equipment identifies the physical array element arrangement data associated with the minimum value as the target array configuration, and outputs it to the radar control module for hardware configuration through the system interface, or outputs it to the display terminal for designers to confirm.

[0042] To verify the effectiveness and accuracy of the proposed optimization method for moving sparse arrays for low signal-to-noise ratio (DOA) estimation, this embodiment analyzes the constructed synthetic array data model and its ZZB performance bound through the following numerical simulation experiments: Since the calculation of ZZB requires a priori distributions, the simulation assumes that each DOA is in... arrive The sources are uniformly distributed within a certain range. To ensure the distinguishability of the sources, it is assumed that the sources are uncorrelated, and the minimum angular interval between any two DOAs is set to... At the same time, the number of snapshots is fixed at 1. For each SNR value, ZZB uses... The average of the Monte Carlo experiments was used. A traditional 7-element nested array (NA) was used in the experiment, with the element positions as follows: The proposed method is not limited to this specific one-dimensional array structure; the array's motion speed is set to... .

[0043] Figure 3 The results comparing CRB and ZZB are presented when the array's SNR varies from -40dB to 20dB under horizontal motion conditions. In the asymptotic region, ZZB is consistent with CRB, while in the a priori performance region, ZZB degenerates to APB. As the number of sources increases... As the SNR increases, the APB gradually decreases while the CRB gradually increases, thus narrowing the gap between ZZB and CRB in the transition region. However, as the SNR decreases, the CRB still diverges and can no longer reflect the actual estimation error level, thus failing to provide a more reliable performance evaluation metric for sparse array selection.

[0044] Figure 4 The CRB and ZZB of the array under vertical motion conditions were compared, with the number of sources set to... Because vertical motion can synthesize a virtual two-dimensional array, Figure 4 The ZZB corresponding to azimuth and elevation angles, namely ZZB(az) and ZZB(el), are also given, and they exhibit similar trends. When the SNR is below 10dB, ZZB deviates significantly from CRB. This is because CRB fails to account for the large errors that may occur under low SNR conditions, and therefore cannot converge within the prior performance region. Therefore, in summary... Figure 3 and Figure 4 The results lead to the conclusion that, under low SNR conditions, ZZB provides a more reliable performance evaluation metric for the selection of sparse arrays for both horizontal and vertical motion compared to CRB.

[0045] In the description of this specification, the references to terms such as "an embodiment," "example," "specific example," etc., indicate 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 this application. 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.

[0046] The foregoing has shown and described the basic principles, main features, and advantages of this application. Those skilled in the art should understand that this application is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this application. Various changes and modifications can be made to this application without departing from the spirit and scope thereof, and all such changes and modifications fall within the scope of the claims of this application.

Claims

1. A method for optimizing moving sparse arrays for low signal-to-noise ratio (DOA) estimation, characterized in that, The method is executed by a data processing device and includes: Based on the platform motion mode, the initial array configuration data is subjected to spatiotemporal equivalent transformation to construct a synthetic array data model. The synthetic array data model has an extended aperture structure adapted to the platform motion mode, which includes horizontal motion and vertical motion. Based on the statistical characteristics of the synthetic array data model under horizontal and vertical motion, the prior error bound and Cramer-Rao lower bound of parameter estimation are derived respectively. Among them, dynamic weighting coefficients are generated based on the signal-to-noise ratio, number of information sources, and number of elements of the synthetic array in the current environment. The dynamic weighting coefficients are then used to perform a weighted summation operation on the prior error bound and the Cramer-Rao lower bound to obtain the Ziv-Zakai bound value corresponding to the synthetic array data model. Enumerate and calculate the Ziv-Zakai boundary values ​​of candidate arrays in horizontal and vertical motion, select the array configuration corresponding to the minimum Ziv-Zakai boundary value as the target array configuration and output it.

2. The method according to claim 1, characterized in that, When the platform's motion mode is horizontal, the steps for constructing the synthetic array data model include: satisfying the displacement condition. ,in For the signal wavelength, The speed of movement in the platform motion mode. The sampling time interval; Under the displacement conditions, the synthetic array data model generated in the construction step is a reduced-dimensional observation matrix. Its computational logic is defined by the following formula: in, For synthesizing array manifold matrices, For the signal sampling matrix, This is the noise matrix; The set of effective normalized array element positions corresponding to the synthetic array manifold matrix The original array element normalized position set Definition of translation union: 。 3. The method according to claim 2, characterized in that, The steps for constructing the synthetic array data model include: Based on differential co-array The sub-step of determining degrees of freedom, the differential coarray The set of integer coordinates is defined as: Wherein, the degrees of freedom are The number of consecutive integers in the sequence is determined.

4. The method according to claim 1, characterized in that, When the platform's motion mode is vertical, the steps for constructing the synthetic array data model include: satisfying the displacement condition. ,in For the signal wavelength, This refers to the vertical displacement during the platform's motion. Under the displacement condition, the synthetic array data model generated in the construction step is a virtual two-dimensional received signal vector. Its computational logic is defined by the following formula: in, For the initial observation signal, The displacement observation signal after phase compensation. For noise vectors, It is the complex envelope vector of the signal; The phase compensation is based on a diagonal matrix, which is the manifold matrix of a virtual two-dimensional array. Its diagonal elements are defined as ,in Indicates the first The angle between the incident path of each signal source and the X-axis.

5. The method according to claim 1, characterized in that, The functional relationship used in the weighted summation operation is as follows: in, For the a priori lower bound, This is the lower bound of the Clamer-Loh term; The minimum error probability coefficient, These are the coefficients of the incompletely normalized Gamma function.

6. The method according to claim 5, characterized in that, The minimum error probability coefficient The calculation is defined by the following formula: in, For the number of snapshots, For signal-to-noise ratio, The complementary cumulative distribution function of the standard normal distribution; For the number of information sources; for moving sparse arrays, Indicates the number of effective sensors; When the platform's motion mode is horizontal motion... The value is the set of effective array element positions in the synthesized array. number of elements ; When the platform's motion mode is vertical motion... The value is twice the number of physical array elements. .

7. The method according to claim 5, characterized in that, The upper limit of integration of the incompletely normalized Gamma function The calculation is defined by the following formula: in, This is the Fisher information matrix corresponding to the synthetic array signal receiving matrix under the aforementioned mobile model. For dimension A column vector of all 1s This defines the search range for the DOA.

8. A device for optimizing a moving sparse array based on Ziv-Zakai bounds under low signal-to-noise ratio conditions, characterized in that, include: The parameter acquisition module is used to acquire a candidate parameter set for the mobile sparse array to be optimized. The candidate parameter set includes the initial arrangement data of the physical array elements and the platform motion mode. The evaluation calculation module is used to perform the steps of constructing the synthetic array data model and calculating the Ziv-Zakai boundary value as described in any one of claims 1 to 7; and The configuration decision module is used to execute numerical comparison logic, retrieve the minimum value from multiple Ziv-Zakai boundary values, identify the physical array element arrangement data associated with the minimum value as the target array configuration, and output it.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

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