Non-circular sparse array based direct positioning method using weighted norm of motion monostatic
By designing a non-circular sparse array and a weighted l0-norm optimization algorithm, the problem of single-station positioning under non-circular signal conditions was solved, the array degrees of freedom and virtual aperture were expanded, and the positioning accuracy and stability were improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2023-05-24
- Publication Date
- 2026-05-29
AI Technical Summary
Under non-circular signal conditions, how can we improve the array degrees of freedom and virtual array aperture in a motion monostation positioning method based on a designed sparse linear array to enhance positioning accuracy and resolution and solve the positioning problem of underdetermined targets?
A direct positioning method based on the weighted l0 norm of a single station moving in motion using a non-circular sparse array is designed. By establishing a signal receiving model and a virtual array model, a sparse linear array with high degree of freedom and low mutual coupling characteristics is designed, and the target is located by combining the weighted l0 norm optimization algorithm.
It significantly improves array degrees of freedom and virtual aperture, enhances positioning accuracy and stability, enables high-resolution positioning of multiple targets, and improves positioning performance.
Smart Images
Figure CN116755030B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of signal processing and relates to a direct localization method for a single station of motion. Specifically, it relates to a method for direct target localization based on a designed sparse array and using a weighted l0 norm. Background Technology
[0002] Passive positioning of motion platforms based on array antennas has received widespread attention in recent years, with applications in fields such as communication, underwater acoustic positioning, and radiation source tracking. Two-step positioning is one of the most commonly used techniques in passive positioning, but this method is a suboptimal solution because it ignores the internal errors generated in the first step, which limits its further development and results in lower positioning accuracy under low signal-to-noise ratio conditions.
[0003] Currently, most positioning algorithms still use uniform linear arrays for their antenna arrays. However, traditional uniform linear arrays are only suitable for over-determined estimations when the number of targets is less than the number of array elements. Furthermore, small element spacing can lead to severe mutual coupling effects. To locate multiple targets, the general approach is to use more antenna elements, but this increases hardware costs and complexity.
[0004] Compared to the traditional two-step positioning method using a uniform linear array, the motion monostation direct positioning method based on a sparse array exhibits superior performance. The introduction of a sparse array allows for higher degrees of freedom and a larger array aperture. Considering non-circular signal scenarios, a sparse array suitable for non-circular structures can be designed, achieving more continuous degrees of freedom while reducing array coupling effects. Subsequently, considering the designed sparse linear array, designing a direct positioning method with high-precision positioning performance becomes a worthy research question. Summary of the Invention
[0005] The technical problem to be solved by this invention is:
[0006] To address the problem of locating underdetermined targets using a motion-based monostation weighted l0-norm direct positioning method based on a designed sparse linear array under non-circular signal conditions, this invention simultaneously achieves array degree of freedom and virtual array aperture expansion, thereby improving positioning accuracy and resolution.
[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:
[0008] A direct localization method for motion monostations based on non-circular sparse array design using weighted norm is characterized by the following steps:
[0009] Step 1: Establish the signal reception model and the virtual array model;
[0010] Step 2: Based on the non-circular characteristics, design a sparse linear array with high degree of freedom and low mutual coupling.
[0011] Step 3: Based on the signal receiving model established in Step 1, derive the motion single-station direct positioning signal model based on non-circular signals;
[0012] Step 4: Combining the sparse linear array from Step 2, design a weighted l0 norm direct positioning method based on a moving monostation.
[0013] A further technical solution of the present invention: The process of establishing the signal receiving model in step 1 is as follows:
[0014] Suppose there are M narrowband and uncorrelated non-circular signals incident on a mobile station in space, and the coordinates of the observation point are defined as follows: Where L i =[x i y i ] T ,i∈{1,...,M};The signal received by the k-th snapshot at the l-th observation position is represented as:
[0015] y l (k)=A l (L)s l (k)+n l (k)
[0016] Among them, s l (k) is the signal envelope, n l (k) represents the Gaussian white noise vector, A l (L)=[a l (L1),a l (L2),...,a l (L M [)] is the array manifold; in order to obtain the virtual array model, the received signal y l The covariance matrix of (k) can be expressed as:
[0017]
[0018] in, It is the signal covariance matrix, g l,i This represents the energy of the i-th source at the l-th observation point; in practice, the covariance matrix can only be formed using a finite number of snapshots, specifically written as:
[0019]
[0020] After straightening the covariance matrix, the column vector is obtained:
[0021]
[0022] Column vector Each element in the array corresponds to a virtual array element position. After removing redundant terms, a complete virtual array structure can be obtained. In non-circular scenarios, the set of virtual array elements can also be called the sum and difference set, which is the basis for designing sparse arrays.
[0023] A further technical solution of the present invention: Step 2, specifically the sparse linear array, is as follows:
[0024] The spacing between array elements is an integer multiple of half the wavelength. Assume the number of elements is Q = M + N + p, where M, N, and p are all positive integers. This array consists of three subarrays, arranged as follows:
[0025]
[0026]
[0027]
[0028] Where i1∈[0,M], i2∈[1,N-1] and i3∈[0,p-1]; therefore, the element positions of the entire array are represented as
[0029] L = L1∪L2∪L3.
[0030] A further technical solution of the present invention: Step 3 is as follows:
[0031] Considering the characteristics of non-circular signals, the signal envelope can also be expressed as s l (k)=Ψs l,0 (k); where, It is a non-circular phase;
[0032] The array received signal model is rewritten as: y l (k)=A l (L)Ψs l,0 (k)+n l (k)
[0033] Signal model received by extended array:
[0034]
[0035] in, The above formula can be further simplified to:
[0036] Z l (k)=A l (L,Ψ)s l (k)+N l (k)
[0037] in,
[0038]
[0039] A further technical solution of the present invention: Step 4 is as follows:
[0040] Straightening the expanded received signal covariance matrix yields the column vector:
[0041]
[0042] in It is the straightened noise vector, while A l (L,Ψ) is the array manifold obtained based on the sparse linear array model designed in step 2; a selection matrix F is defined to remove redundant elements, denoted as...
[0043]
[0044] in e i For one (2M) 2 A column vector of ×1, except at P i The position is 1, and all other elements are 0; The value of is the number of virtual array elements; obviously, the F matrix is only related to the structure of the array. Using the above formula, a new extended array manifold is obtained based on the designed sparse array.
[0045] Based on the sparse reconstruction algorithm, an overcomplete guide vector dictionary A is constructed. l (Θ), specifically represented as:
[0046]
[0047] in This indicates the number of grid points, and the subscript l indicates the l-th observation point;
[0048] Clearly, different overcomplete dictionaries are required for different observation points; therefore, the received signal at the l-th observation point is represented as...
[0049]
[0050] in It is a sparse column vector, where each element is 1 only at its actual position and 0 at all other positions. The goal is to solve for... The non-zero values in the data are used to obtain the position of the actual target;
[0051] Considering that the observation station is a moving station, the received data from each observation point are jointly estimated, as follows:
[0052]
[0053] Where O is a zero matrix;
[0054] Since the target's location is fixed, its corresponding index also remains unchanged; therefore, the definition is... Let represent the joint sparse vector; then the localization problem can be expressed as:
[0055]
[0056] Where A(Θ) is an overcomplete dictionary that combines all observation stations;
[0057] The goal of the solution is Λ s , and ||Λ s The value of ||0 is equivalent to the number of non-zero elements in the column vector, so it can also be written as:
[0058]
[0059] in
[0060]
[0061] However, the sparse optimization problem described above is a non-convex problem. To solve this type of problem, we consider using a similar, continuous weighted l0-norm method. Based on the signal model, assuming the noise is Gaussian noise, the fourth-order cumulant of the received signal can be written as:
[0062]
[0063] Where K is the number of signals; construct an N 2 ×N 2 The fourth-order cumulant matrix R 4x The corresponding element value is R 4x [(m-1)N+p,(n-1)N+q]=C 4x (m,n,p,q); for a fourth-order cumulant matrix R 4x Eigenvalue decomposition is performed to obtain the noise subspace U. n Therefore, the weighting coefficient is defined as:
[0064]
[0065] in, It is a column vector, and the i-th element is equivalent to The 2-norm of the i-th row is then used; subsequently, the multi-target direct localization problem is further solved by using weighted coefficients and minimizing the l0-norm.
[0066] A performance verification method for a motion monostation weighted norm direct localization method based on a non-circular sparse array design, characterized in that:
[0067] Assuming the noise follows a Gaussian distribution, and that the number of signals is known and has the same power; the signal-to-noise ratio (SNR) can be defined as follows:
[0068]
[0069] in, This represents the power of the signal, while This represents the power of the noise;
[0070] The root mean square error (RMSE) is used to reflect the performance of the method, specifically expressed as follows:
[0071]
[0072] Where V is the Monte Carlo simulation and M is the number of target information sources.
[0073] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.
[0074] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.
[0075] The beneficial effects of this invention are as follows:
[0076] This invention provides a direct positioning method for a single moving station based on the weighted norm of a non-circular sparse array. Considering the case of non-circular signals, it utilizes a designed high-degree-of-freedom sparse array to perform direct positioning of a single moving station using the weighted l0 norm. First, this invention designs a sparse array structure suitable for non-circular conditions, significantly improving the array's degrees of freedom and virtual aperture. Then, it designs a direct positioning method based on the weighted l0 norm, which can accurately locate the positions of multiple targets with high resolution, while also improving positioning performance and stability. Attached Figure Description
[0077] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.
[0078] Figure 1 This is a schematic diagram illustrating the principle of the method of the present invention;
[0079] Figure 2A schematic diagram of the motion single-station signal receiving model of this invention;
[0080] Figure 3 This is a schematic diagram of the sparse array structure designed for this invention;
[0081] Figure 4 A schematic diagram of the virtual array elements generated by the sparse array designed in this invention;
[0082] Figure 5 This is a schematic diagram of the motion trajectory of a single station in this invention;
[0083] Figure 6 This is a scatter plot illustrating the positioning performance of the algorithm proposed in this invention;
[0084] Figure 7 This is a schematic diagram illustrating the relationship between the root mean square error of the positioning distance estimation and the signal-to-noise ratio in this invention. Detailed Implementation
[0085] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0086] This embodiment provides a direct positioning method based on a moving monostation using the weighted norm of a non-circular sparse array design. First, a sparse linear array with high degrees of freedom and low mutual coupling effect suitable for non-circular structures is designed. Then, using this array configuration, a direct positioning method based on a moving monostation using the weighted 10-norm is designed. This significantly improves the array's degrees of freedom and virtual aperture, and under multi-target underdetermined conditions, it can significantly increase the number of targets that can be located and the estimation performance of the positioning.
[0087] like Figure 1 As shown, the specific steps include:
[0088] Step 1: Establish the signal reception model and the virtual array model. Figure 2 The receiving model of the motion observation station is given. It is assumed that M narrowband and uncorrelated non-circular signals are incident on a mobile station in space, and there are L observation points. The coordinates of the observation points are defined as follows: Where L i =[x i y i ] T ,i∈{1,...,M}. In this invention, (·) * ,(·) T and(·) HLet represent conjugate, transpose, and conjugate transpose, respectively. At the l-th observation position, the signal received by the k-th snapshot at the l-th observation position can be expressed as:
[0089] y l (k)=A l (L)s l (k)+n l (k)
[0090] Among them, s l (k) is the signal envelope, n l (k) represents the Gaussian white noise vector, A l (L)=[a l (L1),a l (L2),...,a l (L M ] is an array manifold, and the i-th guiding vector can be represented as:
[0091]
[0092] Where, x n This represents the position of the nth element in the sparse array relative to the reference element, and p(l,L) i ) represents a waveform vector, which can be written as:
[0093]
[0094] To obtain the virtual array model, the received signal y l The covariance matrix of (k) can be expressed as:
[0095]
[0096] in, It is the signal covariance matrix, g l,i This represents the energy of the i-th source at the l-th observation point. In practice, the covariance matrix can only be formed using a finite number of snapshots, and can be specifically written as:
[0097]
[0098] After straightening the covariance matrix, the column vector can be obtained:
[0099]
[0100] Column vector Each element in the array corresponds to a virtual array element position. After removing redundant terms, a complete virtual array structure can be obtained. In non-circular scenarios, the set of virtual array elements can also be called the sum and difference set, which is the basis for designing high-degree-of-freedom sparse arrays.
[0101] Step 2: Based on the non-circular property, design a sparse linear array with high degree of freedom and low mutual coupling. This is based on the column vectors obtained in Step 1. The design aims to increase the array's degrees of freedom and virtual array aperture by creating an extended nested array (ENA) structure with greater flexibility. The element spacing in the array is an integer multiple of half the wavelength, and the number of elements is assumed to be Q = M + N + p, where M, N, and p are all positive integers. This array consists of three subarrays, as shown in the specific structure below. Figure 3 As shown, the positions of the array elements can be represented as:
[0102] L={l0,...,l M ,l M+1 ,...,l M+N-1 ,l M+N ,…,l M+N+p-1}
[0103] The specific positions of the elements in the three subarrays can be represented as follows:
[0104]
[0105]
[0106]
[0107] Where i1∈[0,M], i2∈[1,N-1], and i3∈[0,p-1]. Therefore, the positions of the array elements can be represented as:
[0108] L = L1∪L2∪L3.
[0109] Calculations show that this array can obtain 4p(M+N+1)+4N(M+1)-7 independent virtual array elements. To obtain the maximum array degrees of freedom with the same number of array elements, the values of M, N, and p need to be discussed. The maximum number of virtual array elements can be obtained when M = (Q-2) / 3; N = (Q+1) / 3; and p = QMN. Since M, N, and p may not be integers in this case, specific values need to be discussed separately, as shown in Table 1.
[0110] Table 1 shows the maximum array degrees of freedom that can be obtained with different numbers of array elements.
[0111]
[0112]
[0113] To understand this more intuitively, in Figure 4An example with 13 array elements is given, showing the structure of the virtual array formed by the non-negative half-axis. Due to symmetry, the negative half-axis is identical, so only this part needs to be depicted. A uniform linear array is shown in the diagram as a simple comparison, demonstrating that the designed array can achieve more degrees of freedom.
[0114] Step 3: Using the signal receiving model established in Step 1, derive the motion single-station direct positioning signal model based on non-circular signals. Considering that the received signal is a non-circular signal, the signal envelope can be specifically represented as:
[0115]
[0116] in, Represents a real signal, ψ m Let m = 1, 2, ..., M represent the phase of the m-th signal. Therefore, the array receiving signal model can be rewritten as:
[0117] y l (k)=A l (L)Ψs l,0 (k)+n l (k)
[0118] Furthermore, the signal model received by the array can be further extended, as follows:
[0119]
[0120] in, The above formula can be simplified to:
[0121] Z l (k)=A l (L,Ψ)s l (k)+N l (k)
[0122] in,
[0123]
[0124]
[0125] Step 4: Using the above signal model and sparse linear array, design a weighted l0-norm direct positioning method based on a moving monostation. Straightening the extended received signal covariance matrix yields the column vector:
[0126]
[0127] in It is the straightened noise vector, while A l(L,Ψ) is the array manifold obtained based on the sparse linear array model designed in step 2. However, The presence of many duplicate and redundant terms increases the computational complexity. Therefore, a selection matrix F is defined to remove redundant elements, which can be represented as:
[0128]
[0129] in e i For one (2M) 2 A column vector of ×1, except at P i The position is 1, and all other elements are 0. The value of is the number of virtual array elements. Clearly, the F matrix depends only on the array structure. Using the above equation, a new extended array manifold can be obtained based on the designed sparse array:
[0130]
[0131] Among them, the selection matrix Used to remove redundant elements, e i For one (2M) 2 A column vector of ×1, except at P i The position is 1, and all other elements are 0. The value of is the number of virtual array elements. Clearly, the F matrix depends only on the structure of the array.
[0132] Subsequently, based on the sparse reconstruction algorithm, an overcomplete guide vector dictionary A can be constructed. l (Θ), specifically represented as:
[0133]
[0134] in This indicates the number of grid points, and the subscript l indicates the l-th observation point.
[0135] Clearly, different overcomplete dictionaries are required for different observation points. Therefore, the received signal at the l-th observation point can be expressed as:
[0136]
[0137] in It is a sparse column vector, where each element is 1 only at its actual position and 0 at all other positions. Our goal is to solve for... The non-zero values in the data are used to obtain the position of the actual target.
[0138] Considering that the observation station is a moving station, the received data from each observation point are jointly estimated, as follows:
[0139]
[0140] Where O is a zero matrix.
[0141] Since the target's location is fixed and its corresponding index is also constant, it is possible to define... Let represent the joint sparse vector. Then the localization problem can be represented as:
[0142]
[0143] Where A(Θ) is an overcomplete dictionary that combines all observation stations.
[0144] The goal of the solution is Λ s , and ||Λ s The value of ||0 is equivalent to the number of non-zero elements in the column vector, so it can also be written as:
[0145]
[0146] in
[0147]
[0148] However, the sparse optimization problem described above is a non-convex problem. To solve this type of problem, we consider using a similar, continuous, weighted l0-norm method. The weighting coefficients can accelerate the convergence speed. Based on the signal model, assuming the noise is Gaussian, the fourth-order cumulant of the received signal can be written as:
[0149]
[0150] Where K is the number of signals. Therefore, we can construct an N 2 ×N 2 The fourth-order cumulant matrix R 4x The corresponding element value is R 4x [(m-1)N+p,(n-1)N+q]=C 4x (m,n,p,q). For a fourth-order cumulant matrix R 4x Eigenvalue decomposition is performed to obtain the noise subspace U. n Therefore, the weighting coefficients can be defined as:
[0151]
[0152] in, It is a column vector, and the i-th element is equivalent to The 2-norm of the i-th row is then used. Subsequently, weighted coefficients are employed, combined with minimizing the l0-norm, to further solve the multi-target direct localization problem.
[0153] Step 5: Verify the performance of the motion monostation weighted norm direct positioning method based on non-circular sparse array proposed in this invention.
[0154] Figure 5 The trajectory of a single station is given, in kilometers. Five observation points were selected, located at (-15,15), (0,15), (15,15), (15,30), and (15,45). It is assumed that there are two targets in space. Figure 5 The numbers are represented by pentagrams, which are (5,26) and (-5,36) respectively.
[0155] exist Figure 6 The stability simulation of the proposed algorithm is presented. To observe the degree of dispersion of the algorithm, 100 repeated experiments were conducted. As can be seen from the figure, the scatter plot shows a dense distribution that closely approximates the actual locations. Therefore, the algorithm exhibits high accuracy and stability.
[0156] The performance of the proposed motion monostation weighted norm direct localization method based on a non-circular sparse array is verified. The algorithm's performance is characterized by the concentration of the localization results and the root mean square error of the localization distance estimation. In the simulation, we assume that the noise follows a Gaussian distribution, and that the number of signals is known and has the same power. The signal-to-noise ratio of the signals can be defined as:
[0157]
[0158] in, This represents the power of the signal, while This represents the power of the noise.
[0159] The root mean square error (RMSE) can better reflect the performance of an algorithm, specifically expressed as follows:
[0160]
[0161] Where V is the Monte Carlo simulation and M is the number of target information sources.
[0162] Figure 7A schematic diagram illustrating the relationship between the root mean square error (RMSE) of the positioning distance estimation and the signal-to-noise ratio (SNR) is presented. This is compared with several algorithms, including Subspace Direct Positioning (SDF) based on a uniform linear array, Subspace Direct Positioning (NC-SDF) based on non-circular signals, Doppler Extended Coprime Array Direct Positioning (NDMCA-DPD), and the algorithm proposed in this invention. It can be seen that the proposed algorithm based on the sparse array designed in this invention has the best positioning performance, and the performance of direct positioning improves with increasing SNR.
[0163] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.
Claims
1. A direct localization method for a single station based on the weighted norm of a non-circular sparse array design, characterized in that... The steps are as follows: Step 1: Establish the signal reception model and the virtual array model; Step 2: Based on the non-circular characteristics, design a sparse linear array with high degree of freedom and low mutual coupling. Step 3: Based on the signal receiving model established in Step 1, derive the motion single-station direct positioning signal model based on non-circular signals; Step 4: Combining the sparse linear array from Step 2, design a weighted array based on moving monostations. Norm-based direct location method.
2. The motion monostation weighted norm direct positioning method based on non-circular sparse array design according to claim 1, characterized in that: The process of establishing the signal receiving model described in step 1 is as follows: Assuming there is M A narrowband and uncorrelated non-circular signal is incident on a mobile station, and the coordinates of the observation point are defined as follows: ,in ; in the l The observation location, the first k The signal received by each snapshot is represented as follows: in, It is the signal envelope. This represents the Gaussian white noise vector. It is an array manifold; in order to obtain a virtual array model, the received signal The covariance matrix can be expressed as: in, It is the signal covariance matrix. Representing the i The information source is in the first... l The energy of each observation point; in practice, the covariance matrix can only be formed using a finite number of snapshots, specifically written as: The column vector is obtained after straightening the covariance matrix: Column vector Each element in the array corresponds to a virtual array element position. After removing redundant terms, a complete virtual array structure can be obtained. In non-circular scenarios, the set of virtual array elements can also be called the sum and difference set, which is the basis for designing sparse arrays.
3. The motion monostation weighted norm direct positioning method based on non-circular sparse array design according to claim 2, characterized in that: Step 2, specifically the sparse linear array described above, is as follows: The spacing between array elements is an integer multiple of half the wavelength. Assume the number of array elements is... Q = M+N+p ,in M, N, p All values are positive integers; this formation consists of three sub-formations, and the specific arrangement of the sub-formations is as follows: in ; Therefore, the positions of the elements in the entire array are represented as follows: 。 4. The motion monostation weighted norm direct positioning method based on non-circular sparse array design according to claim 3, characterized in that: Step 3 is as follows: Considering the characteristics of non-circular signals, the signal envelope can also be expressed as: ;in, , It is a non-circular phase; The array receiving signal model is rewritten as follows: Signal model received by extended array: in, The above formula can be further simplified to: in, 。 5. The motion monostation weighted norm direct positioning method based on non-circular sparse array design according to claim 4, characterized in that: Step 4 is as follows: Straightening the expanded received signal covariance matrix yields the column vector: in , It is the straightened noise vector, and It is the array manifold obtained based on the sparse linear array model designed in step 2; a selection matrix is defined. To remove redundant elements, represented as in , For one The column vector, except in The position is 1, and all other elements are 0; The value of is the number of virtual array elements; obviously The matrix depends only on the structure of the array. Using the above formula, a new extended array manifold can be obtained based on the designed sparse array. ; Based on the sparse reconstruction algorithm, an overcomplete guide vector dictionary is constructed. Specifically, it is expressed as: in , Indicates the number of grid points, subscript l Then it represents the first l One observation point; Clearly, different overcomplete dictionaries are needed for different observation points; therefore, the first... l The received signal at each observation point is represented as follows: in It is a sparse column vector, where each element is 1 only at its actual position and 0 at all other positions. The goal is to solve for... The non-zero values in the data are used to obtain the position of the actual target; Considering that the observation station is a moving station, the received data from each observation point are jointly estimated, as follows: in It is a zero matrix; Since the target's location is fixed, its corresponding index also remains unchanged; therefore, the definition is... Let represent the joint sparse vector; then the localization problem can be expressed as: in It is a comprehensive dictionary that combines all observation stations; The goal of solving ,and The value of is equivalent to the number of non-zero elements in the column vector, so it can also be written as: in However, the sparse optimization problem described above is a non-convex problem. To solve this type of problem, we can consider using similar, continuous weighted averages. Norm method; based on the signal model, assuming the noise is Gaussian noise, the fourth-order cumulant of the received signal is written as: in K It is the number of signals; construct a The fourth-order cumulant matrix The corresponding element value is For a fourth-order cumulant matrix Eigenvalue decomposition is performed to obtain the noise subspace. Therefore, the weighting coefficient is defined as: in, It is a column vector, the first i Each element is equivalent to The Middle i The 2-norm of the row; then, using weighted coefficients, combined with minimization Norms are used to further solve the multi-objective direct localization problem.
6. A performance verification method for the motion monostation weighted norm direct positioning method based on non-circular sparse array design as described in claim 1, characterized in that: Assuming the noise follows a Gaussian distribution, and that the number of signals is known and has the same power; the signal-to-noise ratio (SNR) can be defined as follows: in, This represents the power of the signal, while This represents the power of the noise; The root mean square error (RMSE) is used to reflect the performance of the method, specifically expressed as follows: in, V It is the number of Monte Carlo tours. M It represents the number of target information sources.
7. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1 or 6.
8. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions that, when executed, are used to implement the method of claim 1 or 6.