GNSS passive radar positioning method based on whale optimization algorithm

Abstract

The invention discloses a GNSS passive radar positioning method based on a whale optimization algorithm, and relates to the technical field of passive radar target positioning. Comprising the following steps: S1, generating a distance-Doppler frequency-frequency modulation cube; s2, initializing a whale population; s3, population individual fitness value calculation; s4, carrying out iterative calculation; and S5, target coordinate output. According to the method, the problem of weak target echoes is solved, target positioning is realized, and meanwhile, relatively high calculation efficiency can be kept.

Description

Technical Field

[0001] The present invention relates to the technical field of passive radar target positioning, and more particularly to a GNSS passive radar positioning method based on a whale optimization algorithm. Background Art

[0002] GNSS satellites can be used as a novel non-cooperative external emitter for bistatic passive radar target detection. Because GNSS utilizes code / frequency division multiple access (CDMA) technology, a single receiver can simultaneously receive and distinguish signals transmitted from multiple satellites. Consequently, multiple bistatic geometries can be constructed using multiple GNSS satellites, receivers, and targets. Existing target detection applications can output multiple sets of bistatic range values ​​for these geometries, which can then be used to determine target positions.

[0003] Existing bistatic passive radar positioning methods based on least squares require that the target detection application accurately detect the target and effectively extract the target's bistatic range value. However, the GNSS echo energy reflected by the target is often very weak, making it difficult to guarantee that the target detection application can accurately detect the target in every bistatic geometry configuration.

[0004] Therefore, it is an urgent problem for those skilled in the art to propose a GNSS passive radar positioning method based on the whale optimization algorithm to solve the difficulties existing in the existing technology. Summary of the Invention

[0005] In view of this, the present invention provides a GNSS passive radar positioning method based on the whale optimization algorithm. This method can give full play to the many advantages of GNSS satellite signal sources. On the basis of the existing target detection method based on long-term accumulation, it further accumulates the target echo energy in the spatial domain, thereby overcoming the problem of weak target echo and achieving target positioning. At the same time, it can also maintain a high computational efficiency.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A GNSS passive radar positioning method based on a whale optimization algorithm comprises the following steps:

[0008] S1. Generate distance-Doppler frequency-frequency modulation cube: select NS GNSS satellites as signal sources, and at observation time T obv The internal receiver collects the direct waves and NS target echoes transmitted by NS satellites, performs signal purification processing on the NS direct waves, and performs range compression, range migration correction, Doppler frequency migration correction, single-frame coherent accumulation, and multi-frame incoherent accumulation operations on the NS target echoes. Finally, NS range-Doppler-frequency modulation cubes are generated at the reference time T0.

[0009] S2. Whale population initialization: set the number of whale populations Np and the maximum number of iterations G max , set the whale population individuals as three-dimensional vectors containing frequency modulation component, X-axis velocity component and Y-axis velocity component, and randomly initialize the whale population individuals according to the target motion constraint conditions;

[0010] S3. Calculation of individual fitness values ​​of populations: Calculation of individual fitness values ​​of whale populations;

[0011] S4, iterative calculation: If the termination condition is met, go to S5; otherwise, perform iterative update on each individual vector of the g-th generation population according to the shrinking and surrounding operation, random search operation, and spiral update operation of the whale optimization algorithm. After the iterative update, perform the out-of-bounds detection operation to generate the g+1-th generation population individual vector. Finally, return to S3;

[0012] S5. Target coordinate output: Output the individual with the maximum fitness value in the current population. The coordinates of the maximum peak on the multi-base local map corresponding to the individual with the maximum fitness value are the target coordinates.

[0013] Optionally, the expression for generating NS range-Doppler-frequency modulation cubes in S1 is:

[0014]

[0015] Among them, n∈[1,NS] represents the nth cube, r∈[0,T p ×c] represents the distance unit, T p represents the GNSS signal ranging code time period, c represents the speed of light, represents the Doppler frequency unit, γ * ∈[γ min ,γ max ] represents each frequency modulation parameter value being searched, γ min and γ max They represent the lower and upper bounds of the frequency modulation search interval, and require the sampling step size of the frequency modulation search interval to be Indicates the total number of frames, T f represents the duration of a single frame, cf(·) represents the cross-correlation function envelope, represents the bistatic distance of the nth target echo at the reference time T0, represents the Doppler frequency of the nth target echo at the reference time T0, and RD represents the range-Doppler-frequency cube.

[0016] Optionally, the expression for setting the whale population individuals in S2 to be a three-dimensional vector containing a frequency modulation component, an X-axis velocity component, and a Y-axis velocity component is:

[0017]

[0018] Among them, k∈[1,Np] represents the kth individual in the population, g∈[1,G max ] represents the g-th iteration, γ k,g 、 and They represent the frequency modulation component, X-axis velocity component and Y-axis velocity component respectively, and T represents vector transposition.

[0019] Optionally, in S2, based on the target motion constraints, the expression for randomly initializing the whale population individuals is:

[0020]

[0021] Among them, rnd represents a random number from 0 to 1, and Respectively represent the lower and upper bounds of the X-axis velocity component, and Represent the lower and upper bounds of the Y-axis velocity component, γ min and γ max They represent the lower and upper bounds of the frequency modulation search interval respectively.

[0022] Optionally, the specific content of calculating the fitness value of the individual whale population in S3 is:

[0023] S31, generate NS distance-Doppler graphs: calculate the frequency modulation component of the individual vector of the current population in the frequency modulation search interval [γ min ,γ max ], find the NS range-Doppler slices corresponding to the current population individual from the generated NS range-Doppler-frequency cubes according to the sampling point index value idx, that is, the NS range-Doppler graphs;

[0024] S32, projection calculation: Based on the known positions and velocities of NS satellites, the receiver position, and the X-axis and Y-axis velocity components of the current population individual vector, the amplitude values ​​on the NS range-Doppler maps are projected into the local coordinate system through projection calculation processing to obtain NS local maps;

[0025] S33, amplitude normalization and non-coherent accumulation: performing normalization and non-coherent accumulation on the amplitude values ​​on the NS local maps to obtain a multi-base local map;

[0026] S34, fitness value calculation and target coordinate recording: The peak signal-to-noise ratio of the multi-base local map is used as the fitness value of the current population individual, and the coordinates of the maximum peak on the multi-base local map are recorded as the target coordinates corresponding to the current population individual.

[0027] Optionally, in S31, the frequency modulation component of the individual vector of the current population is calculated in the frequency modulation search interval [γ min ,γ max The expression of the sampling point index value in ] is:

[0028]

[0029] Among them, round(·) represents the rounding function, γ k,g represents the frequency modulation component, and Δγ represents the sampling step.

[0030] Optionally, the specific content of the projection calculation in S32 is:

[0031] S321. Establishing a local coordinate system: Using the receiver position as a reference point, establish a local coordinate system, i.e., a Cartesian coordinate system, on the monitored sea surface. Grid the coordinate plane and record the position vector of any grid P as P = [x p ,y p ,0] T ;

[0032] S322. Calculation of the bistatic distance value for each grid: It is known that the position vector of the nth satellite at the reference time t0 is and the position vector of the receiver is P r =[x r ,y r ,z r ] T , calculate the bistatic distance value of any grid, the expression is:

[0033]

[0034] Where ||·|| represents the Euclidean norm. Repeat the above process to calculate the bistatic distance value of each grid.

[0035] S323. Calculation of the Doppler frequency value of each grid: It is known that the velocity vector of the nth satellite at the reference time T0 is The X-axis and Y-axis velocity components of the current population individual vector are used as the velocity vector of the grid, expressed as Calculate the Doppler frequency value of the grid, the expression is:

[0036]

[0037] Among them, λ nrepresents the carrier center wavelength of the nth satellite, and the above process is repeated to calculate the Doppler frequency value of each grid;

[0038] S324, local map generation: For any grid P on the nth local map, the nth range-Doppler map position [R n (x p ,y p ),F n (x p ,y p )] is assigned to the current grid, and the expression is:

[0039]

[0040] Repeat the above process to assign amplitude values ​​to each grid to generate the nth local map;

[0041] S325. Generate NS local maps: Repeat S322-S324 to generate NS local maps.

[0042] Optionally, in S33, the amplitude values ​​on the NS local maps are normalized and non-coherently accumulated to obtain the expression of the multi-base local map:

[0043]

[0044] Where norm(·) represents the normalization function, I n Represents the nth local map.

[0045] Optionally, in S34, the expression for taking the peak signal-to-noise ratio of the multi-base local map as the fitness value of the current population individual is:

[0046]

[0047] Among them, A max (·) means taking the maximum amplitude value on the multi-base local map, Indicates taking the average amplitude value on the multi-base local map.

[0048] Optionally, the specific content of the iterative calculation in S4 is:

[0049] S41, termination condition judgment: If the termination condition is met, go to S5, otherwise go to S42;

[0050] S42. Calculation of parameters a, p, A, and C: For the k-th individual vector of the g-th generation population, calculate the parameters a, p, A, and C. The expressions are:

[0051]

[0052] Among them, rnd represents a random number from 0 to 1, Gmax Indicates the maximum number of iterations;

[0053] S43. Shrinkage and bracketing operation: If p < 0.5 and |A| < 1, perform the shrinkage and bracketing operation on the k-th individual vector of the g-th generation population to generate the k-th individual vector of the g+1-th generation population. The expression is:

[0054] X k,g+1 =X best,g -A×|C×X best,g -X k,g | (11)

[0055] Among them, X best,g represents the optimal population individual vector of the g-th generation, that is, the individual with the largest fitness value;

[0056] S44. Random search operation: If p < 0.5 and |A| ≥ 1, a random search operation is performed on the k-th individual vector of the g-th generation population to generate the k-th individual vector of the g+1-th generation population. The expression is:

[0057] X k,g+1 =X rand,g -A×|C×X rand,g -X k,g | (12)

[0058] Among them, X rand,g represents any individual vector of the population in the gth generation;

[0059] S45. Spiral update operation: If p≥0.5, perform a spiral update operation on the k-th individual vector of the g-th generation population to generate the k-th individual vector of the g+1-th generation population. The expression is:

[0060] X k,g+1 =|X best,g -X k,g |×exp(l)×cos(2πl)+X best,g (13)

[0061] Where l represents a random number between -1 and 1, and exp(·) represents a power function with the natural constant e as the base;

[0062] S46, cross-border detection: check X k,g+1 Whether the frequency modulation component in exceeds [γ min ,γ max ] range, whether the X-axis velocity component exceeds And whether the Y-axis velocity component exceeds If it exceeds the range, regenerate X according to formula (3) k,g+1 .

[0063] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a GNSS passive radar positioning method based on the whale optimization algorithm, which has the following beneficial effects:

[0064] 1) The present invention can detect weak echoes from moving targets and simultaneously locate the targets by leveraging the advantages of numerous GNSS satellite signal sources;

[0065] 2) Compared with the existing methods, the positioning accuracy of the present invention is similar, but the calculation efficiency of the method of the present invention is higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0067] Figure 1 A flowchart of a GNSS passive radar positioning method based on a whale optimization algorithm provided by the present invention;

[0068] Figure 2 A schematic diagram of the geometric configuration of multiple bases for target detection provided by the present invention;

[0069] Figure 3 Schematic diagram of the fitness value calculation process provided by the present invention;

[0070] Figure 4 A schematic top view of the simulation experiment scene provided by the present invention;

[0071] Figure 5 Iterative curve diagram of the optimal individual fitness value of each generation provided by the present invention;

[0072] Figure 6 Iterative curve diagram of the optimal individual modulation frequency component of each generation provided by the present invention;

[0073] Figure 7 Iterative curve diagram of the optimal individual X-axis velocity component of each generation provided by the present invention;

[0074] Figure 8 Iterative curve diagram of the optimal individual Y-axis velocity component of each generation provided by the present invention;

[0075] Figure 9 The multi-base local map provided by the present invention;

[0076] Figure 10 A comparison chart of multiple groups of positioning results provided by the present invention. DETAILED DESCRIPTION

[0077] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0078] The following will be combined Figure 1 The step flow chart and specific embodiments shown in the figure further explain in detail the GNSS passive radar positioning method based on the whale optimization algorithm provided by the present invention.

[0079] The present invention discloses a GNSS passive radar positioning method based on a whale optimization algorithm, comprising the following steps:

[0080] S1. Generate distance-Doppler frequency-frequency modulation cube: select NS GNSS satellites as signal sources, and at observation time T obv The internal receiver collects the direct waves and NS target echoes transmitted by NS satellites, performs signal purification processing on the NS direct waves, and performs range compression, range migration correction, Doppler frequency migration correction, single-frame coherent accumulation, and multi-frame incoherent accumulation operations on the NS target echoes. Finally, NS range-Doppler-frequency modulation cubes are generated at the reference time T0.

[0081] For details, see Figure 2 As shown, the receiver fixed on the sea surface is at the observation time T obv The direct waves emitted by NS GNSS satellites and NS target echoes are collected simultaneously.

[0082] S2. Whale population initialization: set the number of whale populations Np and the maximum number of iterations G max , set the whale population individuals as three-dimensional vectors containing frequency modulation component, X-axis velocity component and Y-axis velocity component, and randomly initialize the whale population individuals according to the target motion constraint conditions;

[0083] S3. Calculation of individual fitness values ​​of populations: Calculation of individual fitness values ​​of whale populations;

[0084] S4, iterative calculation: If the termination condition is met, go to S5; otherwise, perform iterative update on each individual vector of the g-th generation population according to the shrinking and surrounding operation, random search operation, and spiral update operation of the whale optimization algorithm. After the iterative update, perform the out-of-bounds detection operation to generate the g+1-th generation population individual vector. Finally, return to S3;

[0085] S5. Target coordinate output: Output the individual with the maximum fitness value in the current population. The coordinates of the maximum peak on the multi-base local map corresponding to the individual with the maximum fitness value are the target coordinates.

[0086] Furthermore, the expression for generating NS range-Doppler-frequency modulation cubes in S1 is:

[0087]

[0088] Among them, n∈[1,NS] represents the nth cube, r∈[0,T p ×c] represents the distance unit, T p represents the GNSS signal ranging code time period, c represents the speed of light, represents the Doppler frequency unit, γ * ∈[γ min ,γ max ] represents each frequency modulation parameter value being searched, γ min and γ max They represent the lower and upper bounds of the frequency modulation search interval, and require the sampling step size of the frequency modulation search interval to be Indicates the total number of frames, T f represents the duration of a single frame, cf(·) represents the cross-correlation function envelope, represents the bistatic distance of the nth target echo at the reference time T0, represents the Doppler frequency of the nth target echo at the reference time T0, and RD represents the range-Doppler-frequency cube.

[0089] Furthermore, in S2, the expression for setting the whale population individuals as a three-dimensional vector containing the frequency modulation component, the X-axis velocity component, and the Y-axis velocity component is:

[0090]

[0091] Among them, k∈[1,Np] represents the kth individual in the population, g∈[1,G max ] represents the g-th iteration, γ k,g 、 and They represent the frequency modulation component, X-axis velocity component and Y-axis velocity component respectively, and T represents vector transposition.

[0092] Furthermore, in S2, based on the target motion constraints, the expression for randomly initializing the whale population individuals is:

[0093]

[0094] Among them, rnd represents a random number from 0 to 1, and Respectively represent the lower and upper bounds of the X-axis velocity component, and Represent the lower and upper bounds of the Y-axis velocity component, γ min and γ max They represent the lower and upper bounds of the frequency modulation search interval respectively.

[0095] For further information, see Figure 3 As shown in Figure 2, the specific content of calculating the fitness value of the individual whale population in S3 is:

[0096] S31, generate NS distance-Doppler graphs: calculate the frequency modulation component of the individual vector of the current population in the frequency modulation search interval [γ min ,γ max ], find the NS range-Doppler slices corresponding to the current population individual from the generated NS range-Doppler-frequency cubes according to the sampling point index value idx, that is, the NS range-Doppler graphs;

[0097] Specifically, NS range-Doppler maps are expressed as

[0098] S32, projection calculation: Based on the known positions and velocities of NS satellites, the receiver position, and the X-axis and Y-axis velocity components of the current population individual vector, the amplitude values ​​on the NS range-Doppler maps are projected into the local coordinate system through projection calculation processing to obtain NS local maps;

[0099] S33, amplitude normalization and non-coherent accumulation: performing normalization and non-coherent accumulation on the amplitude values ​​on the NS local maps to obtain a multi-base local map;

[0100] S34, fitness value calculation and target coordinate recording: The peak signal-to-noise ratio of the multi-base local map is used as the fitness value of the current population individual, and the coordinates of the maximum peak on the multi-base local map are recorded as the target coordinates corresponding to the current population individual.

[0101] Furthermore, in S31, the frequency modulation component of the individual vector of the current population is calculated in the frequency modulation search interval [γ min ,γ max The expression of the sampling point index value in ] is:

[0102]

[0103] Among them, round(·) represents the rounding function, γ k,g represents the frequency modulation component, and Δγ represents the sampling step.

[0104] Furthermore, the specific content of the projection calculation in S32 is:

[0105] S321. Establishing a local coordinate system: Using the receiver position as a reference point, establish a local coordinate system, i.e., a Cartesian coordinate system, on the monitored sea surface. Grid the coordinate plane and record the position vector of any grid P as P = [x p ,y p ,0] T ;

[0106] S322. Calculation of the bistatic distance value for each grid: It is known that the position vector of the nth satellite at the reference time T0 is and the position vector of the receiver is P r =[x r ,y r ,z r ] T , calculate the bistatic distance value of any grid, the expression is:

[0107]

[0108] Where ||·|| represents the Euclidean norm. Repeat the above process to calculate the bistatic distance value of each grid.

[0109] S323. Calculation of the Doppler frequency value of each grid: It is known that the velocity vector of the nth satellite at the reference time T0 is The X-axis and Y-axis velocity components of the current population individual vector are used as the velocity vector of the grid, expressed as Calculate the Doppler frequency value of the grid, the expression is:

[0110]

[0111] Among them, λ n represents the carrier center wavelength of the nth satellite, and the above process is repeated to calculate the Doppler frequency value of each grid;

[0112] S324, local map generation: For any grid P on the nth local map, the nth range-Doppler map position [R n (x p ,y p ),F n (x p ,y p )] is assigned to the current grid, and the expression is:

[0113]

[0114] Repeat the above process to assign amplitude values ​​to each grid to generate the nth local map;

[0115] S325. Generate NS local maps: Repeat S322-S324 to generate NS local maps.

[0116] Furthermore, in S33, the amplitude values ​​on the NS local maps are normalized and non-coherently accumulated to obtain the expression of the multi-base local map:

[0117]

[0118] Where norm(·) represents the normalization function, I n Represents the nth local map.

[0119] Furthermore, in S34, the peak signal-to-noise ratio (PSNR) of the multi-base local map is used as the fitness value of the current population individual:

[0120]

[0121] Among them, A max (·) means taking the maximum amplitude value on the multi-base local map, Indicates taking the average amplitude value on the multi-base local map.

[0122] Furthermore, the specific content of the iterative calculation in S4 is:

[0123] S41, termination condition judgment: If the termination condition is met, go to S5, otherwise go to S42;

[0124] Specifically, one termination condition is g≥G max Or the difference between the maximum fitness values ​​of individuals in any two adjacent generations of the population in several consecutive iterations is less than a certain threshold.

[0125] S42. Calculation of parameters a, p, A, and C: For the k-th individual vector of the g-th generation population, calculate the parameters a, p, A, and C. The expressions are:

[0126]

[0127] Among them, rnd represents a random number from 0 to 1, G max Indicates the maximum number of iterations;

[0128] S43. Shrinkage and bracketing operation: If p < 0.5 and |A| < 1, perform the shrinkage and bracketing operation on the k-th individual vector of the g-th generation population to generate the k-th individual vector of the g+1-th generation population. The expression is:

[0129] X k,g+1 =X best,g -A×|C×X best,g -Xk,g | (11)

[0130] Among them, X best,g represents the optimal population individual vector of the g-th generation, that is, the individual with the largest fitness value;

[0131] S44. Random search operation: If p < 0.5 and |A| ≥ 1, a random search operation is performed on the k-th individual vector of the g-th generation population to generate the k-th individual vector of the g+1-th generation population. The expression is:

[0132] X k,g+1 =X rand,g -A×|C×X rand,g -X k,g | (12)

[0133] Among them, X rand,g represents any individual vector of the population in the gth generation;

[0134] S45. Spiral update operation: If p≥0.5, perform a spiral update operation on the k-th individual vector of the g-th generation population to generate the k-th individual vector of the g+1-th generation population. The expression is:

[0135] X k,g+1 =|X best,g -X k,g |×exp(l)×cos(2πl)+X best,g (13)

[0136] Where l represents a random number between -1 and 1, and exp(·) represents a power function with the natural constant e as the base;

[0137] S46, cross-border detection: check X k,g+1 Whether the frequency modulation component in exceeds [γ min ,γ max ] range, whether the X-axis velocity component exceeds And whether the Y-axis velocity component exceeds If it exceeds the range, regenerate X according to formula (3) k,g+1 .

[0138] In a specific embodiment, the method proposed in the present invention is verified by simulation experiments. Figure 4 See Figure 5-Figure 8 As shown in the figure, the curves composed of the fitness value, frequency modulation component, X-axis and Y-axis velocity components of the best individual in each generation of the whale algorithm are displayed. It can be seen that in the early stages of the iteration, all curves change dramatically. As the number of iterations increases, all curves eventually converge, that is, a focused multi-base local map is successfully generated. Figure 9As shown in the figure, the target peak can be clearly seen on the generated multi-base local map, which is different from the background noise. Threshold detection can be performed on the multi-base local map to extract the location data of the target peak. Figure 10 As shown, the positioning results of the mobile target at 5 different positions are calculated respectively using the method of the present invention and the method in the prior art (see: NASSO I, SANTI FA centralized ship localization strategy for passive multistatic radar based on navigation satellites [J]. IEEE Geoscience and Remote Sensing Letters, 2022, 19: 1-5). It can be seen that the positioning results of the two methods are very close to the true position of the target. The root mean square errors of the positioning of the method of the present invention and the method in the prior art are 9.42m and 7.14m, respectively. However, the calculation time of the method of the present invention is only 102.46s, while the calculation time of the method in the prior art is 408.07s. Therefore, the positioning accuracy of the method of the present invention is close to that of the method in the prior art, but the calculation efficiency of the method of the present invention has a significant advantage.

[0139] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0140] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A GNSS passive radar positioning method based on a whale optimization algorithm, characterized in that: The following steps are involved: S1. Generate distance-Doppler frequency-frequency modulation cube: select NS GNSS satellites as signal sources, and at observation time T obv The internal receiver collects the direct waves and NS target echoes transmitted by NS satellites, performs signal purification processing on the NS direct waves, and performs range compression, range migration correction, Doppler frequency migration correction, single-frame coherent accumulation, and multi-frame incoherent accumulation operations on the NS target echoes. Finally, NS range-Doppler-frequency modulation cubes are generated at the reference time T0. S2. Whale population initialization: set the number of whale populations Np and the maximum number of iterations G max , set the whale population individuals as three-dimensional vectors containing frequency modulation component, X-axis velocity component and Y-axis velocity component, and randomly initialize the whale population individuals according to the target motion constraint conditions; S3. Calculation of individual fitness values ​​of populations: Calculation of individual fitness values ​​of whale populations; S4, iterative calculation: If the termination condition is met, go to S5; otherwise, perform iterative update on each individual vector of the g-th generation population according to the shrinking and surrounding operation, random search operation, and spiral update operation of the whale optimization algorithm. After the iterative update, perform the out-of-bounds detection operation to generate the g+1-th generation population individual vector. Finally, return to S3; S5. Target coordinate output: Output the individual with the maximum fitness value in the current population. The coordinates of the maximum peak on the multi-base local map corresponding to the individual with the maximum fitness value are the target coordinates.

2. The GNSS passive radar positioning method based on the whale optimization algorithm according to claim 1, characterized in that: The expression for generating NS range-Doppler-frequency cubes in S1 is: Among them, n∈[1,NS represents the nth cube, r∈[0,T p ×c] represents the distance unit, T p represents the GNSS signal ranging code time period, c represents the speed of light, represents the Doppler frequency unit, γ * ∈[γ min ,γ max ] represents each frequency modulation parameter value being searched, γ min and γ max They represent the lower and upper bounds of the frequency modulation search interval, and require that the sampling step length Δγ of the frequency modulation search interval is ≤ Indicates the total number of frames, T f represents the duration of a single frame, cf(·) represents the cross-correlation function envelope, represents the bistatic distance of the nth target echo at the reference time T0, represents the Doppler frequency of the nth target echo at the reference time T0, and RD represents the range-Doppler-frequency cube.

3. The GNSS passive radar positioning method based on the whale optimization algorithm according to claim 1 is characterized in that: In S2, the expression for setting the whale population individuals as a three-dimensional vector containing the frequency modulation component, the X-axis velocity component, and the Y-axis velocity component is: Among them, k∈[1,Np represents the kth individual in the population, g∈[1,G max ] represents the g-th iteration, γ k,g 、 and They represent the frequency modulation component, X-axis velocity component and Y-axis velocity component respectively, and T represents vector transposition.

4. The GNSS passive radar positioning method based on the whale optimization algorithm according to claim 1 or 3, characterized in that: In S2, based on the target motion constraints, the expression for randomly initializing the whale population individuals is: Among them, rnd represents a random number from 0 to 1, and Respectively represent the lower and upper bounds of the X-axis velocity component, and Represent the lower and upper bounds of the Y-axis velocity component, γ min and γ max They represent the lower and upper bounds of the frequency modulation search interval respectively.

5. The GNSS passive radar positioning method based on the whale optimization algorithm according to claim 1, characterized in that: The specific content of calculating the individual fitness value of the whale population in S3 is: S31, generate NS distance-Doppler graphs: calculate the frequency modulation component of the individual vector of the current population in the frequency modulation search interval [γ min ,γ max ], find the NS range-Doppler slices corresponding to the current population individual from the generated NS range-Doppler-frequency cubes according to the sampling point index value idx, that is, the NS range-Doppler graphs; S32, projection calculation: Based on the known positions and velocities of NS satellites, the receiver position, and the X-axis and Y-axis velocity components of the current population individual vector, the amplitude values ​​on the NS range-Doppler maps are projected into the local coordinate system through projection calculation processing to obtain NS local maps; S33, amplitude normalization and non-coherent accumulation: performing normalization and non-coherent accumulation on the amplitude values ​​on the NS local maps to obtain a multi-base local map; S34, fitness value calculation and target coordinate recording: The peak signal-to-noise ratio of the multi-base local map is used as the fitness value of the current population individual, and the coordinates of the maximum peak on the multi-base local map are recorded as the target coordinates corresponding to the current population individual.

6. The GNSS passive radar positioning method based on the whale optimization algorithm according to claim 5, characterized in that: In S31, the frequency modulation component of the individual vector of the current population is calculated in the frequency modulation search interval [γ min ,γ max The expression of the sampling point index value in ] is: Among them, round(·) represents the rounding function, γ k,g represents the frequency modulation component, and Δγ represents the sampling step.

7. The GNSS passive radar positioning method based on the whale optimization algorithm according to claim 5, characterized in that: The specific content of the projection calculation in S32 is: S321. Establishing a local coordinate system: Using the receiver position as a reference point, establish a local coordinate system, i.e., a Cartesian coordinate system, on the monitored sea surface. Grid the coordinate plane and record the position vector of any grid P as P = [x p ,y p ,0] T ; S322. Calculation of the bistatic distance value for each grid: It is known that the position vector of the nth satellite at the reference time T0 is and the position vector of the receiver is P r =[x r ,y r ,z r ] T , calculate the bistatic distance value of any grid, the expression is: Where ||·|| represents the Euclidean norm. Repeat the above process to calculate the bistatic distance value of each grid. S323. Calculation of the Doppler frequency value of each grid: It is known that the velocity vector of the nth satellite at the reference time T0 is The X-axis and Y-axis velocity components of the current population individual vector are used as the velocity vector of the grid, expressed as Calculate the Doppler frequency value of the grid, the expression is: Among them, λ n represents the carrier center wavelength of the nth satellite, and the above process is repeated to calculate the Doppler frequency value of each grid; S324, local map generation: For any grid P on the nth local map, the nth range-Doppler map position [R n (x p ,y p ),F n (x p ,y p )] is assigned to the current grid, and the expression is: Repeat the above process to assign amplitude values ​​to each grid to generate the nth local map; S325. Generate NS local maps: Repeat S322-S324 to generate NS local maps.

8. The GNSS passive radar positioning method based on the whale optimization algorithm according to claim 1, characterized in that: In S33, the amplitude values ​​on the NS local maps are normalized and non-coherently accumulated, and the expression of the multi-base local map is obtained as follows: Where norm(·) represents the normalization function, I n Represents the nth local map.

9. The GNSS passive radar positioning method based on the whale optimization algorithm according to claim 1, characterized in that: In S34, the peak signal-to-noise ratio of the multi-base local map is used as the fitness value of the current population individual: Among them, A max (·) means taking the maximum amplitude value on the multi-base local map, Indicates taking the average amplitude value on the multi-base local map.

10. The GNSS passive radar positioning method based on the whale optimization algorithm according to claim 1, characterized in that: The specific content of the iterative calculation in S4 is: S41, termination condition judgment: If the termination condition is met, go to S5, otherwise go to S42; S42. Calculation of parameters a, p, A, and C: For the k-th individual vector of the g-th generation population, calculate the parameters a, p, A, and C. The expressions are: Among them, rnd represents a random number from 0 to 1, G max Indicates the maximum number of iterations; S43. Shrinkage and bracketing operation: If p < 0.5 and |A| < 1, perform the shrinkage and bracketing operation on the k-th individual vector of the g-th generation population to generate the k-th individual vector of the g+1-th generation population. The expression is: X k,g+1 =X best,g -A×|C×X best,g -X k,g | (11) Among them, X best,g represents the optimal population individual vector of the g-th generation, that is, the individual with the largest fitness value; S44. Random search operation: If p < 0.5 and |A| ≥ 1, a random search operation is performed on the k-th individual vector of the g-th generation population to generate the k-th individual vector of the g+1-th generation population. The expression is: X k,g+1 =X rand,g -A×|C×X rand,g -X k,g | (12) Among them, X rand,g represents any individual vector of the population in the gth generation; S45. Spiral update operation: If p≥0.5, perform a spiral update operation on the k-th individual vector of the g-th generation population to generate the k-th individual vector of the g+1-th generation population. The expression is: X k,g+1 =|X best,g -X k,g |×exp(l)×cos(2πl)+X best,g (13) Where l represents a random number between -1 and 1, and exp(·) represents a power function with the natural constant e as the base; S46, cross-border detection: check X k,g+1 Whether the frequency modulation component in exceeds [γ min ,γ max ] range, whether the X-axis velocity component exceeds And whether the Y-axis velocity component exceeds If it exceeds the range, regenerate X according to formula (3) k,g+1 .

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