Robust dynamic direction of arrival tracking method and system based on quantum flower leopard search mechanism, and storage medium

Abstract

The invention discloses a robust dynamic direction-of-arrival tracking method and system based on a quantum flower leopard search mechanism and a storage medium, relates to the field of array signal processing, and aims to solve the problem that the existing method cannot solve the problems of poor robustness and huge calculation amount of dynamic direction-of-arrival tracking under impact noise. Comprising the following steps: 1, constructing an expansion fractional low-order covariance according to received data in an impact noise environment; 2, initializing a quantum flower leopard algorithm; 3, determining a global optimal quantum flower leopard position based on a fitness function; 4, updating the position of the quantum flower leopard; 5, updating a local optimal quantum position and a global optimal quantum position; repeating the steps 4-5 until the maximum number of iterations is reached; 6, obtaining new snapshot sampling data, and updating and expanding the fractional low-order covariance matrix and the search space; and 7, repeatedly executing the steps 2-6 until the maximum number of snapshots is reached, outputting a global optimal position, and obtaining a dynamic direction-of-arrival tracking result.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and more specifically, to a robust dynamic direction-of-arrival tracking method, system, and storage medium based on a quantum leopard search mechanism. Background Art

[0002] Direction finding, also known as spatial spectrum estimation or Direction of Arrival (DOA) estimation, is an important research area in array signal processing, with wide applications in passive detection, radar, sonar, and communications. After decades of development, the DOA estimation theory based on the Gaussian model assumption has gradually become more complete and mature. However, in practical applications, many random signals and noises are not Gaussian distributed, such as atmospheric lightning noise, instantaneous spikes in speech signals on communication lines, marine environmental noise, and various anthropogenic noises. These signals contain significant spikes and can be described by SaS processes with different characteristic exponents. Traditional methods based on second- and fourth-order statistics cannot yield satisfactory results. Finding a DOA estimation algorithm that can improve the direction finding performance of fractional low-order moment-based algorithms in the context of impulsive noise, while also expanding the array aperture and enabling coherent direction finding of dynamic targets from coherent sources, is a challenge in engineering applications. Effective solutions to these problems are essential to further improve the quality and efficiency of radar and wireless communication system design, and to make direction finding technology more practical.

[0003] A review of existing technical literature revealed that Diao Ming et al., in their paper "A Novel DOA Tracking Method Based on Particle Swarm Optimization Algorithm" published in *Systems Engineering and Electronics Technology* (2009, Vol. 29, No. 12, pp. 2046-2049), used the particle swarm optimization algorithm and the maximum likelihood algorithm for dynamic DOA estimation of multiple moving targets. While performing well under Gaussian noise conditions, the method's performance deteriorated significantly under impact noise conditions, leading to failure. Zhao Dayong et al., in their paper "Dynamic DOA Tracking under Impact Noise Background" published in *Journal of Shandong University* (2010, Vol. 40, No. 1, pp. 133-138), proposed the particle swarm optimization algorithm and the maximum likelihood method with fractional low-order moments to solve the dynamic DOA estimation problem under weak impact noise conditions. The dynamic update using fractional low-order moments can achieve dynamic DOA estimation to a certain extent, but the algorithm fails when the number of sources exceeds the number of array elements. Furthermore, the particle swarm optimization algorithm and the maximum likelihood method with fractional low-order moments fail under strong impact noise conditions with an eigenvalue less than 1.

[0004] Existing literature indicates that the robustness problem of dynamic tracking remains unsolved in harsh noise environments such as impact noise. A major drawback of using the maximum likelihood algorithm for angle estimation is the complex and time-consuming search process, resulting in a huge computational burden. Dynamic tracking in impact noise environments is a challenge, especially for multi-source dynamic tracking with a greater number of array elements. Therefore, DOA estimation algorithms for Gaussian noise environments cannot be directly ported. Robust dynamic DOA estimation under impact noise should first establish a high-performance optimization equation for robust dynamic tracking. Classical intelligent computing methods in impact noise environments struggle to overcome the constraint of the trade-off between convergence speed and convergence performance. Under current computational conditions, it is difficult to find the optimal solution within a limited time. Therefore, new intelligent algorithms are needed to solve the robust dynamic tracking problem in impact noise environments, especially under impact noise conditions. Summary of the Invention

[0005] The technical problem to be solved by this invention is:

[0006] Existing methods cannot solve the problems of poor robustness and huge computational load in dynamic direction-of-arrival tracking under impact noise.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] This invention provides a robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism, comprising the following steps:

[0009] Step 1: Determine the antenna positions based on the number of antennas and direction finding requirements, and construct the spread fractional low-order covariance based on the received data under impulse noise conditions;

[0010] Step 2: Initialize the quantum leopard algorithm to determine the initial state of all leopards in the leopard pack;

[0011] Step 3: Construct a fitness function based on the constructed extended fractional low-order covariance and array manifold matrix to determine the current globally optimal quantum leopard position;

[0012] Step 4: Update the quantum position of the quantum leopard according to the quantum search mode or quantum tracking mode;

[0013] Step 5: Update the local optimal quantum position and the global optimal quantum position; determine if the maximum number of iterations has been reached. If yes, record the global optimal quantum position and its location, and proceed to Step 6; otherwise, let t = t + 1, and return to Step 4 to continue the loop.

[0014] Step 6: Obtain new snapshot sampling data, update and expand the low-order covariance matrix of the scores and the search space;

[0015] Step 7: Determine if the maximum number of snapshots has been reached. If not, let k = k + 1, the number of iterations t = 0, and return to Step 2 to continue estimating the direction of the dynamic target at the next moment; otherwise, based on a series of globally optimal quantum positions obtained from the snapshot sampling data, map the obtained globally optimal position to obtain the dynamic direction of arrival tracking result.

[0016] Furthermore, step one includes the following steps:

[0017] Far-field signal at θ n N narrowband point sources, n = 1, 2, ..., N, are incident with plane waves at a given location. The incident waves are projected onto a non-uniform special linear array composed of M isotropic elements, the elements being placed to satisfy the following condition: the distance d between the nth element and the first element... n d1 = 0 <d2<…<d M Their values ​​are all integer multiples of half the wavelength, and satisfy the following conditions: It is complete, that is, Ω={-d M , ..., 0, ..., d M};

[0018] The received data from the k-th snapshot under impact noise conditions is as follows:

[0019]

[0020] In the formula, x(k) = [x1(k), x2(k), ..., x M (k)] T For an M×1 dimensional array snapshot data vector; s(k)=[s1(k),s2(k),··; s N (k)] T Let θ be an N×1 dimensional signal vector, where θ = (θ1, θ2, ..., θ3) N Let A(θ) be the source azimuth vector, and let A(θ) = [a(θ1) a(θ2) … a(θ)]. N [)] is the signal steering vector matrix, where the nth steering vector n = 1, 2, ..., N, It is an M×1 dimensional noise vector;

[0021] The infinite norm normalized signal of the kth sampled data is: in Let be a constant, and let its fractional lower-order covariance be C(k), where the th is a constant. Vidi Column elements are In the formula, * is the conjugate operator, and p is the fractional low-order covariance parameter;

[0022] The non-uniform linear array is virtualized into a uniform linear array with more elements, and the maximum correlation delay of the array is M.a Then the number of virtual uniform linear array elements is [M+1, M]. a +1]; Let ε be the minimum spacing between array elements, then the array element coordinate vector is d = [d1, d2, ..., d1]. M ] = ε[n1, ..., n M ],n1,…,n M If all values ​​are integers, then the M×M dimensional fractional lower-order covariance C(k) of the k-th sampling is:

[0023]

[0024] make m = 1, 2, ..., M a E() is the mean function; the k-th sampling virtual uniform linear array (M) a +1)×(M a +1) The lower-order covariance C(k) of the extended fractional dimension is:

[0025]

[0026] The array manifold matrix of the original array, which is then virtualized into a uniform linear array, is B(θ) = [b(θ1), b(θ2), ..., b(θ)]. N ]], its nth guiding vector is n = 1, 2, ..., N; M is virtualized based on a non-uniform linear array. a If +1>M array elements, then the number of measurable sources is equal to M. a .

[0027] Furthermore, step two includes the following steps:

[0028] Initialize the number of leopards in the quantum leopard pack. The quantum leopard's search space dimension N and maximum number of iterations;

[0029] Define the quantum position of the i-th leopard as y i (t)=[y i1 (t), y i2 (t), ..., y iN [t], i = 1, 2, ..., 0≤y in (t)≤1 represents the nth-dimensional qubit of the quantum position of the i-th leopard, where n=1,2,…,N; mapping the quantum position of the i-th leopard to the defined interval, the leopard's position is... The mapping relationship is as follows: h n (k) and b n (k) represents the upper and lower limits of the nth-dimensional angle search interval during the kth sampling data processing, and the speed corresponding to the i-th leopard is vi. (t)=[v i1 (t), v i2 (t), ..., v iN (t)], This represents the nth dimension velocity of the i-th leopard. The upper bound of the velocity is defined; the quantum position is randomly initialized in the quantum field [0, 1], and the velocity is defined as follows: Random initialization; determine the upper and lower bounds of the search interval.

[0030] Furthermore, the method for setting the maximum number of iterations in step two is as follows:

[0031]

[0032] in Here is the floor function, and T is the floor function.

[0033] Furthermore, step three includes the following steps:

[0034] Location of the i-th leopard The fitness value of the extended fractional low-order covariance maximum likelihood equation is:

[0035]

[0036] In the formula, the orthogonal projection matrix The superscript H represents the transpose of the conjugate, and trO denotes the trace operation of a matrix; the local optimal quantum position of the i-th leopard is p. i (t)=[p i1 (t), p i2 (t), ..., p iN (t)],p in (t) represents the nth-dimensional optimal qubit experienced by the i-th leopard up to the t-th iteration; the global optimal qubits of all leopards are g(t) = [g1(t), g2(t), ..., g...]. N [(t)], where g n (t) represents the nth dimension of the optimal qubit experienced by all leopards up to the t-th iteration.

[0037] Furthermore, step four includes the following steps:

[0038] For the i-th leopard, generate a uniformly random number between [0, 1]. According to probability P s Choose either quantum tracking mode or quantum search mode to update the quantum leopard's quantum position:

[0039] like Choosing the quantum tracking mode to update based on group behavior, the nth dimension velocity of the i-th leopard is updated as follows:

[0040] v in (t+1)=c1r1[g n (t)-y in (t)]+c2r2[p in (t)-y in (t)]+v in (t)

[0041] Where r1 and r2 are uniform random numbers between [0, 1], and c1 and c2 are weighting constants;

[0042] The new quantum position y for the i-th leopard i (t+1), where,

[0043]

[0044] abs() is the absolute value function for qubits;

[0045] The quantum position y of the i-th leopard i (t+1) is mapped to the defined interval. Calculate the fitness value;

[0046] like The i-th leopard uses quantum search mode to copy its current position to S. MP A copy is placed in the memory pool. Each individual copy in the memory pool evolves, and the i-th leopard evolves... The quantum rotation angle of the nth dimension of each copy is:

[0047]

[0048] r3 and r4 are both uniformly random numbers between [0, 1], p kn Let (t) be the nth dimension of the randomly selected t-th local optimal quantum position of the leopard with index k. Then:

[0049]

[0050] Calculate the fitness values ​​of all candidate solutions after evolution in the memory pool, and select the candidate solution with the highest fitness value from the memory pool as the current quantum position y of the leopard. i (t+1) updates the quantum position of the leopard.

[0051] Furthermore, step five includes the following steps:

[0052] For the i-th leopard, if Let g(t+1) = y i (t+1), g(t) = y i(t+1); otherwise, g(t+1) = g(t), where The position is obtained by mapping the globally optimal quantum position found up to generation t;

[0053] like p i (t+1)=y i (t+1); otherwise, p i (t+1)=p i (t);

[0054] Determine if the maximum number of iterations has been reached. If so, record the optimal position and proceed to step six; otherwise, set t = t + 1 and return to step four to continue the loop.

[0055] Furthermore, step six includes the following steps:

[0056] Obtain new snapshot sampling data x(k+1), and construct the (M)th sampling virtual linear array. a +1)×(M a +1) Dimensional Extended Fractional Low-Order Covariance Matrix Update the lower-order covariance of the currently sampled synthetic expanded fraction. Line number List: in The expanded fractional lower-order covariance of the newly added (k+1)th sample data The Line number List, M a +1, M a +1; Update the search space after k+1 sampling to... β is the convergence factor, and the constant r is the search radius of the search space in the locked state. This is the estimated value for the nth direction at the kth sampling. Let n be the center value of the nth direction in the kth sampling search space, and its update formula is: Where δ represents the genetic factor.

[0057] The present invention also provides a robust dynamic direction-of-arrival tracking system based on the quantum leopard search mechanism. The system has a program module corresponding to the steps of any of the above-described technical solutions, and executes the steps of the robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism described above when running.

[0058] The present invention also provides a computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps in the robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism described in any of the above technical solutions.

[0059] Compared with the prior art, the beneficial effects of the present invention are:

[0060] This invention provides a robust dynamic direction-of-arrival tracking method, system, and storage medium based on a quantum leopard search mechanism. By employing a special non-uniform linear array structure, the target is locked within a varying search range. Simultaneously, an extended fractional low-order covariance matrix is ​​constructed to suppress impact noise. A quantum leopard search mechanism is designed to search for the optimal angle value of the extended weighted signal maximum likelihood equation within the search space. By gradually reducing the search range and utilizing an intelligent search mechanism, the computational load of the search method is effectively reduced. Specifically, it offers the following advantages:

[0061] (1) This invention is suitable for impact noise environments, as well as Gaussian noise and strong impact noise environments, and can improve the dynamic direction of arrival angle estimation performance of uniform linear arrays with the same number of array elements.

[0062] (2) The present invention effectively solves the problem of array expansion for direction finding in impact noise environment, and can also perform effective tracking when the number of antennas is less than the number of array elements.

[0063] (3) The present invention can meet the requirements of measuring more signal sources or obtaining better decoherence capability by adjusting the antenna position according to the specific application environment. When the position is limited, it can avoid some points where the antenna cannot be placed and achieve better results.

[0064] (4) The present invention uses the designed quantum leopard swarm search method to quickly and accurately solve the extended fractional low-order covariance maximum likelihood equation.

[0065] Simulation experiments show that the multi-moving target tracking method under impact noise environment of the present invention can guarantee the real-time performance of the designed method, and has the ability to expand the array and good tracking accuracy. It also has good performance in harsh noise environments such as strong impact noise. Attached Figure Description

[0066] Figure 1 This is a flowchart of the dynamic tracking method of the quantum leopard search mechanism in an embodiment of the present invention;

[0067] Figure 2 This is a diagram showing the angle tracking results of using the particle swarm optimization algorithm and the fractional low-order moment maximum likelihood algorithm for three independent information sources when the feature index α = 1.25 in this embodiment of the invention.

[0068] Figure 3 This is a diagram showing the angle tracking of the proposed quantum leopard dynamic tracking method for three independent information sources when the feature index α = 1.25 in an embodiment of the present invention.

[0069] Figure 4 This is a diagram showing the angle tracking results for four information sources when the feature index α = 1.65 in this embodiment of the invention, using the particle swarm optimization algorithm and the fractional low-order moment maximum likelihood algorithm.

[0070] Figure 5 This is a diagram showing the angle tracking of the proposed quantum leopard dynamic tracking method for four information sources when the feature index α = 1.65 in an embodiment of the present invention.

[0071] Figure 6 The figure shows the dynamic tracking of five independent information sources by the proposed quantum leopard dynamic tracking method when the feature index α = 1.85 in the embodiment of the present invention.

[0072] Figure 7 The figure shows the dynamic tracking of six independent information sources by the proposed quantum leopard dynamic tracking method when the feature index α = 1.855 in the embodiment of the present invention.

[0073] Figure 8 This diagram illustrates the dynamic tracking of two independent information sources using the particle swarm optimization algorithm and the fractional low-order moment maximum likelihood algorithm when the feature index α = 0.75 in this embodiment of the invention.

[0074] Figure 9 This diagram illustrates the dynamic tracking of two independent information sources by the proposed quantum leopard dynamic tracking method when the feature index α = 0.75 in this embodiment of the invention. Detailed Implementation

[0075] To enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are merely some, not all, of the embodiments or examples of the present invention. All other embodiments or examples obtained by those skilled in the art based on the embodiments or examples of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0076] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0077] Specific Implementation Plan 1: Combining Figure 1 As shown, this invention provides a robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism, comprising the following steps:

[0078] Step 1: Determine the antenna positions based on the number of antennas and direction finding requirements, and construct the spread fractional low-order covariance based on the received data under impulse noise conditions;

[0079] Step 2: Initialize the quantum leopard algorithm to determine the initial state of all leopards in the leopard pack;

[0080] Step 3: Construct a fitness function based on the constructed extended fractional low-order covariance and array manifold matrix to determine the current globally optimal quantum leopard position;

[0081] Step 4: Update the quantum position of the quantum leopard according to the quantum search mode or quantum tracking mode;

[0082] Step 5: Update the local optimal quantum position and the global optimal quantum position found up to generation t; determine if the maximum number of iterations has been reached. If so, record the global optimal quantum position and its location, and proceed to step 6; otherwise, let t = t + 1, return to step 4 and continue the loop.

[0083] Step 6: Obtain new snapshot sampling data, update and expand the low-order covariance matrix of the scores and the search space;

[0084] Step 7: Determine if the maximum number of snapshots has been reached. If not, let k = k + 1, the number of iterations t = 0, and return to Step 2 to continue estimating the direction of the dynamic target at the next moment. Otherwise, based on a series of globally optimal quantum positions obtained from the snapshot sampling data, map the obtained globally optimal position, i.e., the direction value of the tracked dynamic target, and output the dynamic tracking result.

[0085] Specific Implementation Plan Two: Step One includes the following steps:

[0086] Far-field signal at θ n N narrowband point sources, n = 1, 2, ..., N, are incident with plane waves at a given location. The incident waves are projected onto a non-uniform special linear array composed of M isotropic elements, the elements being placed to satisfy the following condition: the distance d between the nth element and the first element... n d1 = 0 <d2<…<d M Their values ​​are all integer multiples of half the wavelength, and satisfy the following conditions: It is complete, that is, Ω={-d M , ..., 0, ..., d M};

[0087] The received data model for the k-th snapshot under impulsive noise conditions is as follows:

[0088]

[0089] In the formula, x(k) = [x1(k), x2(k), ..., x M (k)] T For an M×1 dimensional array snapshot data vector; s(k)=[s1(k),s2(k),··; s N (k)] T Let θ be an N×1 dimensional signal vector, where θ = (θ1, θ2, ..., θ3) N Let A(θ) be the source azimuth vector, and let A(θ) = [a(θ1) a(θ2) … a(θ)]. N [)] is the signal steering vector matrix, where the nth steering vector n = 1, 2, ..., N, It is an M×1 dimensional noise vector;

[0090] The infinite norm normalized signal of the kth sampled data is: in Let be a constant, and let its fractional lower-order covariance be C(k), where the th is a constant. Vidi Column elements are In the formula, * is the conjugate operator, and p is the fractional low-order covariance parameter;

[0091] Based on the characteristics of special linear arrays, the non-uniform linear array is virtualized into a uniform linear array with more array elements, and the maximum correlation delay of the array is M. a Then the number of virtual uniform linear array elements is [M+1, M]. a +1]; Let ε be the minimum spacing between array elements, then the array element coordinate vector is d = [d1, d2, ..., d1]. M ] = ε[n1, ..., n M ],n1,…,n M All are integers. To better represent the relationship between the received fractional low-order covariance and the extended fractional low-order covariance of the virtual uniform linear array, the M×M dimensional fractional low-order covariance C(k) of the k-th sampling is:

[0092]

[0093] If let m = 1, 2, ..., M a E() is the mean function; the k-th sampling virtual uniform linear array (M) a +1)×(M a +1) Dimensional Extended Fractional Lower-Order Covariance for:

[0094]

[0095] The array manifold matrix of the original array, which is then virtualized into a uniform linear array, is B(θ) = [b(θ1), b(θ2), ..., b(θ)].N ]], its nth guiding vector is n = 1, 2, ..., N; M is virtualized based on a non-uniform linear array. a If +1>M array elements, then the number of measurable sources is M. a The first quick-sampling sample (M) a +1)×(M a +1) Dimensional composite extended fractional lower-order covariance Equal to its expanded fractional lower-order covariance

[0096] Specific implementation plan three: Step two includes the following steps:

[0097] Initialize the number of leopards in the quantum leopard pack. The quantum leopard's search space dimension N and maximum number of iterations;

[0098] Define the quantum position of the i-th leopard as y i (t)=[y i1 (t), y i2 (t), ..., y iN [t], i = 1, 2, ..., 0≤y in (t)≤1 represents the nth-dimensional qubit of the quantum position of the i-th leopard, where n = 1, 2, ..., N; t represents the iteration number of the quantum leopard swarm search mechanism, initially set to t = 0. Mapping the quantum position of the i-th leopard to the defined interval, the leopard's position is... The mapping relationship is as follows: h n (k) and b n (k) represents the upper and lower limits of the nth-dimensional angle search interval during the kth sampling data processing, and v represents the speed of the i-th leopard. i (t)=[v i1 (t), v i2 (t), ..., v iN (t)], This represents the nth dimension velocity of the i-th leopard. The initial position is defined as an upper bound for the velocity; to ensure that the initial position has a certain degree of dispersion and uniformity, the quantum position is defined as being randomly initialized in the quantum field [0, 1], and the velocity is defined as... Random initialization; determine the upper and lower bounds of the search interval. Its initial value is a search space vector with N angles.

[0099] Specific Implementation Plan Four: The method for setting the maximum number of iterations mentioned in Step Two is as follows:

[0100]

[0101] in Here is the floor function, and T is the floor function.

[0102] Specific implementation plan five: Step three includes the following steps:

[0103] Location of the i-th leopard The fitness value of the extended fractional low-order covariance maximum likelihood equation is:

[0104]

[0105] In the formula, the orthogonal projection matrix The superscript H represents the transpose of the conjugate, and tr() represents the trace operation of the matrix; the larger the fitness value, the better the quantum position and the more accurate the estimated angle. According to The fitness value is used to evaluate the quality of a leopard's position and its corresponding quantum position; a higher fitness value indicates a better position. The local optimal quantum position of the i-th leopard is p. i (t)=[p i1 (t), p i2 (t), ..., p iN (t)],p in g(t) represents the nth-dimensional optimal quantum bit experienced by the i-th leopard up to the t-th iteration; the global optimal quantum position of all leopards, i.e., the quantum position with the largest fitness value, is denoted as g(t) = [g1(t), g2(t), ..., g...]. N [(t)], where g n (t) represents the nth dimension of the optimal qubit experienced by all leopards up to the t-th iteration.

[0106] Specific implementation plan six: Step four includes the following steps:

[0107] For the i-th leopard, generate a uniformly random number between [0, 1]. According to probability P s Choose either quantum tracking mode or quantum search mode to update the quantum leopard's quantum position:

[0108] like Choosing the quantum tracking mode to update based on group behavior, the nth dimension velocity of the i-th leopard is updated as follows:

[0109] v in (t+1)=c1r1[g n (t)-y in (t)]+c2r2[p in (t)-y in (t)]+v in (t)

[0110] Where r1 and r2 are uniform random numbers between [0, 1], and c1 and c2 are weighting constants;

[0111] For v in (t+1), if it exceeds the boundary value, restrict it to the boundary, that is, if but like but

[0112] The new quantum position y for the i-th leopard i (t+1)=[y i1 (t+1), y i2 (t+1), ..., y iN [(t+1)], where,

[0113]

[0114] abs() is the absolute value function for qubits;

[0115] The quantum position y of the i-th leopard i (t+1) is mapped to the defined interval. Calculate the fitness value; the fitness function is:

[0116] like The i-th leopard uses quantum search mode to copy its current position to S. MP A copy is placed in a memory pool, the size of which is S. MP Evolution is performed on each individual copy in the memory pool, and the i-th leopard... The quantum rotation angle of the nth dimension of each copy is:

[0117]

[0118] r3 and r4 are both uniformly random numbers between [0, 1], p kn (t) represents the nth dimension of the local optimal quantum position of a randomly selected leopard labeled k in generation t, where...

[0119]

[0120] Replace the original value with the updated value, calculate the fitness value of all candidate solutions in the memory pool after evolution, select the candidate solution with the highest fitness value from the memory pool as the current quantum position of the leopard, and update the quantum position of the leopard as follows:

[0121] y i (t+1)=[y i1 (t+1), y i2 (t+1), ..., y iN (t+1)].

[0122] Specific implementation plan seven: Step five includes the following steps:

[0123] For the i-th leopard, if Let g(t+1) = y i (t+1), g(t) = y i (t+1); otherwise, g(t+1) = g(t), where The position is obtained by mapping the globally optimal quantum position found up to generation t;

[0124] For the i-th leopard, p i (t+1)=y i (t+1); otherwise, p i (t+1)=p i (t);

[0125] Determine if the maximum number of iterations has been reached. If so, record the optimal position and proceed to step six; otherwise, set t = t + 1 and return to step four to continue the loop.

[0126] Specific implementation plan eight: Step six includes the following steps

[0127] Obtain new snapshot sampling data x(k+1) = [x1(k+1), x2(k+1), ..., x M (k+1)] T The infinite norm normalized signal is but It is the fractional low-order covariance increment matrix of the newly added (k+1)th sample; if let Constructing the (k+1)th sampling virtual linear array (M) a +1)×(M a +1) Dimensional Extended Fractional Low-Order Covariance Matrix Expressed as

[0128] Update the lower-order covariance of the currently sampled synthetic expanded fraction. Line number List: in The expanded fractional lower-order covariance of the newly added (k+1)th sample data The Line number List, The search space after k+1 sampling is updated as follows: β is the convergence factor, which determines the convergence rate of the search space; the constant r is the search radius of the search space in the locked state. This is the estimated value for the nth direction at the kth sampling. Let n be the center value of the nth direction in the kth sampling search space, and its update formula is: Where δ represents the genetic factor.

[0129] The robust dynamic direction-of-arrival tracking method (algorithm) based on the quantum leopard search mechanism proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.

[0130] Based on the method proposed in this invention, a robust dynamic direction-of-arrival tracking system based on the quantum leopard search mechanism is developed using a programming language. This system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism described above when running.

[0131] The developed system (software) computer program is stored on a computer-readable storage medium. This computer program is configured to implement the steps of the robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism when invoked by a processor. In other words, the invention is materialized on a carrier, becoming a computer program product.

[0132] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0133] The computational programs (also referred to as programs, software, software applications, or code) of this invention include machine instructions of a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0134] The beneficial effects of the present invention will be described below with reference to specific embodiments.

[0135] Example 1

[0136] The specific parameter settings in the simulation experiment are as follows:

[0137] Using 5 array elements, the array elements are placed at positions 0.5λ [0 1 3 6 9], but the array elements placed by this method expand to a virtual array element number M. a +1 equals 10. The quantum leopard dynamic tracking method of this invention has an initial search space within its domain and expands the fractional low-order covariance. The updated formula sets μ = 0.95, the convergence factor in the method is β = 0.995, the genetic factor is δ = 0.8, the radius of convergence is r = 3, c1 = c2 = 0.78, and S... MP =3, P s =0.5. The dynamic tracking method used for comparison in the experimental simulation was dynamic DOA estimation based on particle swarm optimization and fractional low-order moment maximum likelihood algorithm (PSO-FLOM) ("Dynamic DOA Tracking under Impact Noise Background" published by Zhao Dayong et al. in the Journal of Shandong University (2010, Vol.40, No.1, pp.133-138)). In the experiment, an equidistant uniform linear array with an element spacing of 0.5 times the wavelength was used, the number of elements M=5, and the fractional low-order covariance parameter p=1.8. In order to examine the convergence speed and performance of the two dynamic tracking methods, the search interval was set to [-90°, 90°]. The population size (number of individuals) of both the quantum leopard dynamic tracking method and the particle swarm optimization algorithm was set to 30. The maximum number of iterations was set in the same way, taking an integer multiple of the difference of the first dimension search boundary region of the snapshot, with a multiple value of T=4. Assuming the generalized signal-to-noise ratio is 15dB under impact noise conditions, and all signal sources in the simulation are set to equal power, if the initial value of the nth signal source is θ n (0), the maximum number of samples is K, the current number of samples is k, then the motion trajectory of the dynamic target's angle is n = 1, 2, ..., N, where N is the number of information sources.

[0138] from Figure 2 , Figure 3 , Figure 4 and Figure 5 It can be seen that the quantum leopard dynamic DOA tracking method proposed in this invention has better tracking accuracy for independent sources under impulsive noise background than existing dynamic DOA estimation methods based on particle swarm optimization and fractional low-order moment maximum likelihood algorithms, and has better convergence accuracy. Figure 6 and Figure 7It can be seen that the quantum leopard swarm dynamic tracking method proposed in this invention can perform relatively accurate dynamic tracking of multiple targets when the number of information sources is greater than or equal to the number of array elements. The dynamic DOA method based on particle swarm optimization and fractional low-order moment maximum likelihood algorithm fails because dynamic DOA tracking based on these algorithms is only applicable when the number of array elements is greater than the number of information sources. Figure 8 and Figure 9 It can be seen that the quantum leopard swarm dynamic tracking method proposed in this invention can perform relatively accurate dynamic tracking of two targets under strong impact noise with a feature exponent of less than 1. However, the dynamic DOA method based on particle swarm optimization and fractional low-order moment maximum likelihood algorithm fails. This is because the dynamic DOA tracking based on particle swarm optimization and fractional low-order moment maximum likelihood algorithm is only applicable to the case where the feature exponent is greater than 1.

[0139] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism, characterized in that, Includes the following steps: Step 1: Determine the antenna positions based on the number of antennas and direction finding requirements, and construct the spread fractional low-order covariance based on the received data under impulse noise conditions; Step 2: Initialize the quantum leopard algorithm to determine the initial state of all leopards in the leopard pack; Step 3: Construct a fitness function based on the constructed extended fractional low-order covariance and array manifold matrix to determine the current globally optimal quantum leopard position; Step 4: Update the quantum position of the quantum leopard according to the quantum search mode or quantum tracking mode; Step 5: Update the local optimal quantum position and the global optimal quantum position; determine if the maximum number of iterations has been reached. If yes, record the global optimal quantum position and its location, and proceed to Step 6; otherwise, let t = 1, return to Step 4 and continue the loop. Step 6: Obtain new snapshot sampling data, update and expand the low-order covariance matrix of the scores and the search space; Step 7: Determine if the maximum number of snapshots has been reached. If not, let k = k + 1, the number of iterations t = 0, and return to Step 2 to continue estimating the direction of the dynamic target at the next moment; otherwise, based on a series of globally optimal quantum positions obtained from the snapshot sampling data, map the obtained globally optimal position to obtain the dynamic direction of arrival tracking result.

2. The robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism according to claim 1, characterized in that, Step one includes the following steps: Far-field signal at θ n N narrowband point sources, n = 1, 2, ..., N, are incident with plane waves at a given location. The incident waves are projected onto a non-uniform special linear array composed of M isotropic elements, the elements being placed to satisfy the following condition: the distance d between the nth element and the first element... n For d1 = 0 < d2 < ... < d M Their values ​​are all integer multiples of half the wavelength, and satisfy the following conditions: It is complete, that is, Ω={-d M , ..., 0, ..., d M ); The received data from the k-th snapshot under impact noise conditions is as follows: In the formula, x(k) = [x1(k), x2(k), ..., x M (k)] T For an M×1 dimensional array snapshot data vector; s(k)=[s1(k), s2(k), ··; s N (k)] T Let θ be an N×1 dimensional signal vector, where θ = (θ1, θ2, ..., θ3) N Let A(θ) be the source azimuth vector, and let A(θ) = [a(θ1) a(θ2) … a(θ)]. N [)] is the signal steering vector matrix, where the nth steering vector n = 1, 2, ..., N, It is an M×1 dimensional noise vector; The infinite norm normalized signal of the kth sampled data is: in Let be a constant, and let its fractional lower-order covariance be C(k), where the th is a constant. Vidi Column elements are In the formula, * is the conjugate operator, and p is the fractional low-order covariance parameter; The non-uniform linear array is virtualized into a uniform linear array with more elements, and the maximum correlation delay of the array is M. a Then the number of virtual uniform linear array elements is [M+1, M]. a +1]; Let ε be the minimum spacing between array elements, then the array element coordinate vector is d = [d1, d2, ..., d1]. M ] = ε[n1, ..., n M ],n1,…,n M If all values ​​are integers, then the M×M dimensional fractional lower-order covariance C(k) of the k-th sampling is: make m = 1, 2, ..., M a E() is the mean function; the k-th sampling virtual uniform linear array (M) a +1)×(M a +1) Dimensional Extended Fractional Lower-Order Covariance for: The array manifold matrix of the original array, which is then virtualized into a uniform linear array, is B(θ) = [b(θ1), b(θ2), ..., b(θ)]. N ]], its nth guiding vector is n = 1, 2, ..., N; M is virtualized based on a non-uniform linear array. a If +1>M array elements, then the number of measurable sources is equal to M. a .

3. The robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism according to claim 2, characterized in that, Step two includes the following steps: Initialize the number of leopards in the quantum leopard pack. The quantum leopard's search space dimension N and maximum number of iterations; Define the quantum position of the i-th leopard as y i (t)=[y i1 (t), y i2 (t), ..., v iN (t)], 0≤y in (t)≤1 represents the nth-dimensional qubit of the i-th leopard quantum position, where n=1,2,…,N; Map the quantum position of the i-th leopard to the defined interval, where the leopard's position is... The mapping relationship is as follows: h n (k) and b n (k) represents the upper and lower limits of the nth-dimensional angle search interval during the kth sampling data processing, and v represents the speed of the i-th leopard. i (t)=[v i1 (t), v i2 (t), ..., v iN (t)], This represents the nth dimension velocity of the i-th leopard. The upper bound of the velocity is defined; the quantum position is randomly initialized in the quantum field [0, 1], and the velocity is defined as follows: Random initialization; determine the upper and lower bounds of the search interval.

4. The robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism according to claim 3, characterized in that, The method for setting the maximum number of iterations in step two is as follows: in Here is the floor function, and T is the floor function.

5. The robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism according to claim 4, characterized in that, Step three includes the following steps: Location of the i-th leopard The fitness value of the extended fractional low-order covariance maximum likelihood equation is: In the formula, the orthogonal projection matrix The superscript H represents the transpose of the conjugate, and tr() denotes the trace operation of a matrix; the local optimal quantum position of the i-th leopard is p. i (t)=[p i1 (t), p i2 (t), ..., p iN (t)],p in (t) represents the nth-dimensional optimal qubit experienced by the i-th leopard up to the t-th iteration; the global optimal qubits of all leopards are g(t) = [g1(t), g2(t), ..., g...]. N [(t)], where g n (t) represents the nth dimension of the optimal qubit experienced by all leopards up to the t-th iteration.

6. The robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism according to claim 5, characterized in that, Step four includes the following steps: For the i-th leopard, generate a uniformly random number between [0, 1]. According to probability P s Choose either quantum tracking mode or quantum search mode to update the quantum leopard's quantum position: like Choosing the quantum tracking mode to update based on group behavior, the nth dimension velocity of the i-th leopard is updated as follows: v in (t+1)=c1r1[g n (t)-y in (t)]+c2r2[p in (t)-y in (t)]+v in (t) Where r1 and r2 are uniform random numbers between [0, 1], and c1 and c2 are weighting constants; The new quantum position y for the i-th leopard i (t+1), where, abs() is the absolute value function for qubits; The quantum position y of the i-th leopard i (t+1) is mapped to the defined interval. Calculate the fitness value; like The i-th leopard uses quantum search mode to copy its current position to S. MP A copy is placed in the memory pool. Each individual copy in the memory pool evolves, and the i-th leopard evolves... The quantum rotation angle of the nth dimension of each copy is: r3 and r4 are both uniformly random numbers between [0, 1], p kn Let (t) be the nth dimension of the randomly selected t-th local optimal quantum position of the leopard with index k. Then: Calculate the fitness values ​​of all candidate solutions after evolution in the memory pool, and select the candidate solution with the highest fitness value from the memory pool as the current quantum position y of the leopard. i (t+1) updates the quantum position of the leopard.

7. The robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism according to claim 6, characterized in that, Step five includes the following steps: For the i-th leopard, if Let g(t+1) = y i (t+1), g(t) = y i (t+1); otherwise, g(t+1) = g(t), where The position is obtained by mapping the globally optimal quantum position found up to generation t; like p i (t+1)=y i (t+1); otherwise, p i (t+1)=p i (t); Determine if the maximum number of iterations has been reached. If so, record the optimal position and proceed to step six; otherwise, set t = t + 1 and return to step four to continue the loop.

8. The robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism according to claim 7, characterized in that, Step six includes the following steps: Obtain new snapshot sampling data x(k+1), and construct the (M)th sampling virtual linear array. a +1)×(M a +1) Dimensional Extended Fractional Low-Order Covariance Matrix Update the lower-order covariance of the currently sampled synthetic expanded fraction. Line number List: in The expanded fractional lower-order covariance of the newly added (k+1)th sample data The Line number List, The search space after k+1 sampling is updated as follows: β is the convergence factor, and the constant r is the search radius of the search space in the locked state. This is the estimated value for the nth direction at the kth sampling. Let n be the center value of the nth direction in the kth sampling search space, and its update formula is: Where δ represents the genetic factor.

9. A robust dynamic direction-of-arrival tracking system based on the quantum leopard search mechanism, characterized in that, The system has a program module corresponding to the steps of the method described in any one of claims 1 to 8, and executes the steps in the robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism described above when it is run.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the robust dynamic direction-of-arrival tracking method based on the quantum leopard search mechanism as described in any one of claims 1 to 8.

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