Improved self-adaptive firefly optimization particle filter-based long baseline positioning method

Abstract

The invention discloses a long baseline positioning method based on improved adaptive firefly optimization particle filtering, and belongs to the technical field of underwater target positioning. According to the invention, the problem of low positioning precision of the existing particle filtering method is solved. According to the method, the firefly algorithm is used for replacing a resampling process based on a particle filtering method, and the firefly algorithm is introduced into the particle filtering algorithm, so that low-weight particles move to other particles and new random particles are introduced; the problem of particle depletion caused by loss of sample effectiveness and diversity due to continuous abandoning of particles with low weights by resampling and supplementation through weight copy particles is solved. The firefly brightness calculation formula is improved based on the weight, and the accuracy of the fusion algorithm is improved. And the step length factor is adaptively adjusted in the position updating process, so that the accuracy of a target positioning result is effectively ensured through the combination of various means. The method can be applied to underwater target positioning.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater target positioning, and in particular relates to a long baseline positioning method based on improved adaptive firefly optimized particle filtering. Background Art

[0002] The long baseline (LBL) positioning system is based on acoustic principles and uses the relatively stable propagation of sound waves in water. It is usually used in situations where high-precision underwater positioning is required. It mainly forms a baseline array by placing multiple transducers (element) with known positions on the seabed. When an underwater target carries a transponder or beacon and enters the working area of ​​the baseline array, the surface unit or other control unit sends an inquiry signal. After the underwater target responds, the position of the underwater target is calculated by measuring the time difference of the sound wave signal from the element to the target and other information using geometric relationships. This technology plays an important role in many fields such as marine resource development, underwater archaeology, and underwater vehicle navigation.

[0003] At present, many methods for underwater target positioning are based on the Bayesian Kalman filter model, which determines the target trajectory by calculating the likelihood function of the estimated point and the measured point, which is optimal for linear Gaussian systems. However, for nonlinear and non-Gaussian systems, such algorithms usually introduce large errors and cause the algorithm to fail.

[0004] Particle filtering is a nonlinear filtering technology based on the Monte Carlo method. It uses a large number of particles to approximate the posterior probability distribution of the system state. These particles propagate in the state space according to the system dynamic model and update the weights according to the observed values. Although the resampling step in the particle filter can solve the problem of particle degradation, it also has shortcomings. The resampling process will reduce the diversity of particles by copying particles by weight, causing particle impoverishment, causing particles to concentrate in high-weight areas, and then some potential global optimal solution-related information may be lost, resulting in low positioning accuracy. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of low positioning accuracy of the existing particle filtering method, and propose a long baseline positioning method based on improved adaptive firefly optimized particle filtering.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a long baseline positioning method based on improved adaptive firefly optimized particle filtering, the method specifically comprises the following steps:

[0007] Step 1: Initialize the state vector of each particle, and record the initial state vector of the nth particle as and are the horizontal position and velocity of the nth particle at the initial moment, and are the vertical position and velocity of the nth particle at the initial moment, respectively, [·] T represents transposition, n=1,2,…,N, N is the total number of particles;

[0008] Step 2: Initialization time t=1;

[0009] Step 3: Calculate the state vector of the nth particle at time t based on the state vector of the nth particle at time t-1;

[0010] According to the state vector of each particle at time t, the particle arrival time equation is established, the likelihood function is established according to the particle arrival time, and then the weight w of each particle is calculated according to the likelihood function ratio t n ;

[0011] Sort the weights of each particle in descending order, select the first p particles as valid particles, discard the remaining Np particles, and randomly generate Np new particles in the state space, and set the weights of the generated new particles to w new ;

[0012] Normalize the weights of the effective particles and newly generated particles at time t, and use the state vectors and normalized weights of the effective particles and newly generated particles at time t to form a particle set;

[0013] Step 4: Use the state vector of each particle in the particle set as the initial position of each firefly individual in the firefly population, divide the entire search area evenly into K areas and number the divided areas, and then set the maximum number of iterations L of the firefly algorithm;

[0014] Step 5, initialize the number of iterations l = 1;

[0015] Step 6: Randomly select a fixed proportion of firefly individuals from the kth area, and migrate the selected firefly individuals to the k+1th area;

[0016] After migration, the firefly individuals in each area update their positions according to the local optimal solution;

[0017] Step 7: Whether the set maximum number of iterations L is reached;

[0018] If the maximum number of iterations L is reached, execute step 11;

[0019] If the maximum number of iterations L is not reached, execute step eight;

[0020] Step 8: For any area, calculate the fluorescence brightness of each firefly in the area, and then determine the local optimal solution in the area according to the fluorescence brightness. Similarly, determine the local optimal solution in each area.

[0021] And determine whether the current number of iterations is an integer multiple of T;

[0022] If the current number of iterations is an integer multiple of T, a global optimal solution is determined based on the local optimal solutions in each region, and the determined global optimal solution is used as the local optimal solution of each region for the next iteration, and step ten is executed again;

[0023] If the current number of iterations is not an integer multiple of T, execute step nine;

[0024] Step 9, taking the local optimal solution in each region determined in step 8 as the local optimal solution of each region in the next iteration, and then executing step 10;

[0025] Step 10: Set l=l+1, and return to step 6;

[0026] Step 11: Calculate the target state at time t based on the positions of individual fireflies in all areas, then set t=t+1 and return to execute step 3.

[0027] Furthermore, the initial state vector The values ​​in are selected from the state space, in which the velocity ranges from [0, V max ], the position range is [0,R max ], R max Indicates the maximum distance allowed between a particle and the position (X, Y) with the maximum likelihood value.

[0028] Furthermore, the state vector of the nth particle at time t is calculated based on the state vector of the nth particle at time t-1; specifically:

[0029]

[0030] in, represents the state vector of the nth particle at time t-1, represents the state vector of the nth particle at time t, w t is the process noise at time t, and f(·) is the state transition function.

[0031] Furthermore, the particle arrival time equation is established according to the state vector of each particle at time t, the likelihood function is established according to the particle arrival time, and the weight of each particle is calculated according to the likelihood function ratio. The specific process is:

[0032] Step 31. Arrival time of the nth particle at time t for:

[0033]

[0034] in, is the time when the direct wave of the nth particle reaches the mth buoy at time t, and are the state vector of the nth particle at time t The horizontal and vertical positions of is the underwater sound speed, x m,t and m,t are the horizontal and vertical positions of the mth buoy at time t respectively;

[0035] Step 32: According to calculate

[0036]

[0037] in, is the sampling point of the nth particle at the mth buoy at time t, f s is the sampling frequency, floor() means rounding down;

[0038] Step 3. Define the likelihood function of the nth particle at time t as

[0039]

[0040] Where E[·] is the output matrix of the matched filter of the nth particle, m = 1, 2, …, M, and M is the total number of buoys;

[0041] Step 3 and 4: Weight of the nth particle for:

[0042]

[0043] in, represents the likelihood function of the n′th particle at time t, and N is the total number of particles.

[0044] Furthermore, the weight of the new particle generated in step 3 is:

[0045]

[0046] Among them, ∈ is a positive factor.

[0047] Furthermore, the specific process of step six is ​​as follows:

[0048] The set of state vectors of individual fireflies in the kth region is recorded as in, are the state vectors of the first, second, ..., Sth firefly individuals in the kth region, respectively, and S is the total number of fireflies in the kth region;

[0049] 0.05S firefly individuals are randomly selected from the firefly individuals in the kth area, and the selected firefly individuals are migrated to the k+1th area.

[0050] Furthermore, when the number of iterations l=1, the local optimal solution in the kth region for:

[0051]

[0052] in, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The initial position of each firefly, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The brightness of an individual firefly;

[0053] When the number of iterations l-1≠l′T, the local optimal solution in the kth region of the lth iteration for:

[0054]

[0055] Where l' is a positive integer, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The position of the individual fireflies after the l-1th iteration, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The brightness of an individual firefly;

[0056] When the number of iterations l-1 = l′T, the local optimal solution in the kth region of the lth iteration for:

[0057]

[0058] Furthermore, the first, second, third, ..., Sth k The brightness of a firefly The calculation method is:

[0059]

[0060] in, is the normalized weight of the particle corresponding to the jth firefly individual in the kth region, I 0 Indicates the maximum light intensity of fireflies;

[0061] The first, second, third, ..., Sth regions in the kth region k The brightness of a firefly They are:

[0062]

[0063] Where γ is the absorption coefficient, e is the base of the natural logarithm, and r j It means that after the l-1th iteration, the position of the jth firefly in the kth region is different from the local optimal solution. The Euclidean distance between .

[0064] Furthermore, the positions of the individual fireflies in each area are updated according to the local optimal solution, specifically:

[0065]

[0066] in, represents the position of the jth firefly individual in the kth region after the lth iteration update, represents the position of the jth firefly individual in the kth region after the l-1th iteration update, β represents the attraction, α(l) is the step factor, and rand is a random number distributed between [0,1];

[0067]

[0068] Among them, β 0 is the maximum attraction;

[0069] α(l)=α 0 ×e -ql

[0070] Among them, α 0 is the initial step size, q=0.01.

[0071] Furthermore, the target state at time t is calculated based on the positions of individual fireflies in all areas, specifically:

[0072]

[0073] Among them, x L,n It represents the position of the nth firefly individual in the overall area after the Lth iteration; represents the target state at time t, Represents the normalized weight of the particle corresponding to the nth firefly individual in the overall area.

[0074] The beneficial effects of the present invention are:

[0075] 1. The firefly algorithm is used to replace the resampling process in the particle filter method. By introducing the firefly algorithm into the particle filter algorithm, low-weight particles are moved to other particles and new random particles are introduced. This alleviates the problem of loss of sample validity and diversity and the resulting particle depletion caused by the continuous abandonment of low-weight particles by resampling and supplementation by weighted copying particles, thereby ensuring the validity and diversity of particle samples and the accuracy of positioning results.

[0076] 2. Add particle weights to the firefly brightness formula. The higher the weight, the closer the particle is to the real state. Low-brightness particles move toward high-brightness particles, which improves the accuracy of the fusion algorithm. Adaptively adjust the step factor in the position update step. In the early stage of iteration, the firefly brightness is relatively dispersed, and the step factor is longer under parameter control. After iteration, the brightness is relatively concentrated, and the step factor is reduced under parameter control for fine search.

[0077] 3. The firefly algorithm search area is evenly divided into multiple areas. The fireflies in each area iterate independently without waiting for the calculation results of other areas. The original calculation process is transformed into parallel processing, which speeds up the search speed as a whole and covers a larger search space in a shorter time. In addition, the areas communicate with each other at regular intervals, and the local optimal solutions are compared with each other, so that the searches between areas promote each other, which not only greatly improves the calculation speed, but also avoids the final result from falling into a single local optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 The present invention is a flow chart of a long baseline positioning method based on an improved adaptive firefly optimized particle filter. DETAILED DESCRIPTION

[0079] Specific implementation method 1: Combination Figure 1 The present embodiment is described as follows. The present embodiment describes a long baseline positioning method based on an improved adaptive firefly optimized particle filter, and the method specifically comprises the following steps:

[0080] Step 1: Initialize the state vector of each particle, and record the initial state vector of the nth particle as and are the horizontal position and velocity of the nth particle at the initial moment, and are the vertical position and velocity of the nth particle at the initial moment, respectively, [·] T represents transposition, n=1,2,…,N, N is the total number of particles;

[0081] Step 2: Initialization time t=1;

[0082] Step 3: Calculate the state vector of the nth particle at time t based on the state vector of the nth particle at time t-1;

[0083] According to the state vector of each particle at time t, the particle arrival time equation is established, the likelihood function is established according to the particle arrival time, and then the weight of each particle is calculated according to the likelihood function ratio.

[0084] Sort the weights of each particle in descending order, select the first p particles as valid particles, discard the remaining Np particles, and randomly generate Np new particles in the state space, and set the weights of the generated new particles to w new ;

[0085] Normalize the weights of the effective particles and newly generated particles at time t, and use the state vectors and normalized weights of the effective particles and newly generated particles at time t to form a particle set

[0086] Step 4: The state vector of each particle in the particle set is used as the initial position of each individual firefly in the firefly population, and the initial position of each individual firefly is recorded as x 0,1 ,x 0,2 ,x 0,3 ,…,x 0,N , divide the entire search area evenly into K areas and number the divided areas (for example, divide the entire area into R rows and Q columns of grids, R×Q=K, and use the Q grids in the first row as the 1st to Qth areas after division, and use the Q grids in the second row as the Q+1th to 2Qth areas after division, and so on, but not limited to the above division method), and then set the maximum number of iterations L of the firefly algorithm;

[0087] Step 5, initialize the number of iterations l = 1;

[0088] Step 6: Randomly select a fixed proportion of firefly individuals from the kth area, and migrate the selected firefly individuals to the k+1th area;

[0089] After migration, the firefly individuals in each area update their positions according to the local optimal solution (determined by the previous iteration);

[0090] Step 7: Whether the set maximum number of iterations L is reached;

[0091] If the maximum number of iterations L is reached, execute step 11;

[0092] If the maximum number of iterations L is not reached, execute step eight;

[0093] Step 8: For any area, calculate the fluorescence brightness of each firefly in the area, and then determine the local optimal solution in the area according to the fluorescence brightness. Similarly, determine the local optimal solution in each area.

[0094] And determine whether the current number of iterations is an integer multiple of T;

[0095] If the current number of iterations is an integer multiple of T, a global optimal solution is determined based on the local optimal solutions in each region (i.e., the local optimal solution with the largest brightness is selected from the local optimal solutions in each region, and the selected local optimal solution is used as the global optimal solution), and then the determined global optimal solution is used as the local optimal solution of each region for the next iteration (for position update), and then step ten is executed;

[0096] If the current number of iterations is not an integer multiple of T, execute step nine;

[0097] Step 9, taking the local optimal solution in each region determined in step 8 as the local optimal solution of each region in the next iteration, and then executing step 10;

[0098] Step 10: Set l=l+1, and return to step 6;

[0099] Step 11: Calculate the target state at time t based on the positions of individual fireflies in all areas, then set t=t+1 and return to execute step 3.

[0100] The present invention aims at the problems of sample validity, loss of diversity and particle impoverishment caused by the particle filter resampling process. By introducing the firefly algorithm, low-weight particles are moved to other particles, and new random particles are added when using the firefly algorithm to avoid the particle impoverishment phenomenon, thereby ensuring the validity and diversity of particle samples and thus ensuring the accuracy of positioning results. In addition, when using the firefly algorithm, the original process is transformed into a parallel processing module through regional division, which greatly improves the calculation speed; and the regions regularly exchange information and migrate, which also avoids the final result from falling into a single local optimal solution.

[0101] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the initial state vector The values ​​in are selected from the state space, in which the velocity ranges from [0, V max], the position range is [0,R max ], R max Indicates the maximum distance allowed between a particle and the position (X, Y) with the maximum likelihood value.

[0102] The other steps and parameters are the same as those in the first embodiment.

[0103] In this embodiment, the speed is the speed in the Cartesian coordinate system. The approximate position of the target in space can be known in advance, and the position corresponding to the maximum likelihood probability value is taken as (X, Y). The azimuth and heading are evenly distributed between 0° and 360°, that is, the particle position can be a circle with the position (X, Y) as the center and a distance from the position (X, Y) less than R max Any position of .

[0104] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that the state vector of the nth particle at time t is calculated based on the state vector of the nth particle at time t-1; specifically:

[0105]

[0106] in, represents the state vector of the nth particle at time t-1, represents the state vector of the nth particle at time t, w t is the process noise at time t (w t is a Gaussian distribution with a mean of 0 and a variance of q), and f(·) is the state transfer function.

[0107] The other steps and parameters are the same as those in the first or second embodiment.

[0108] Specific implementation method 4: This implementation method is different from specific implementation methods 1 to 3 in that the particle arrival time equation is established according to the state vector of each particle at time t, the likelihood function is established according to the particle arrival time, and the weight of each particle is calculated according to the likelihood function ratio. The specific process is:

[0109] Step 31. Arrival time of the nth particle at time t for:

[0110]

[0111] in, is the time when the direct wave of the nth particle reaches the mth buoy at time t, and are the state vector of the nth particle at time t The horizontal and vertical positions of is the underwater sound speed, x m,t and m,t are the horizontal and vertical positions of the mth buoy at time t respectively;

[0112] Step 32: According to calculate

[0113]

[0114] in, is the sampling point of the nth particle at the mth buoy at time t, f s is the set sampling frequency, floor() means rounding down;

[0115] Step 3. Define the likelihood function of the nth particle at time t as

[0116]

[0117] Where E[·] is the output matrix of the matched filter of the nth particle, m = 1, 2, …, M, and M is the total number of buoys;

[0118] Step 3 and 4: Weight of the nth particle for:

[0119]

[0120] in, represents the likelihood function of the n′th particle at time t, and N is the total number of particles.

[0121] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0122] Specific implementation method 5: This implementation method is different from one of the specific implementation methods 1 to 4 in that the weight of the new particle generated in step 3 is:

[0123]

[0124] Here, ∈ is a small positive factor.

[0125] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0126] Since the resampling process of the particle filtering method continuously discards low-weight particles and supplements them through weighted copying particles, resulting in a lack of particle diversity, the coverage of the entire state space is reduced. The present invention randomly generates new particles in the state space on the basis of retaining a part of valid particles to avoid the problem of particle sample impoverishment, generates a firefly population based on a particle set including the newly generated particles and their weights, and sets a maximum number of iterations L.

[0127] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the specific process of step 6 is as follows:

[0128] The set of state vectors of individual fireflies in the kth region is recorded as in, are the state vectors of the first, second, ..., Sth firefly individuals in the kth region, respectively, and S is the total number of fireflies in the kth region;

[0129] 0.05S firefly individuals are randomly selected from the firefly individuals in the kth area, and the selected firefly individuals are migrated to the k+1th area.

[0130] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0131] It should be noted that the present invention first randomly determines the firefly individuals that need to migrate in each area according to the migration ratio, and then migrates the firefly individuals that need to migrate in the kth area to the k+1th area, and migrates the firefly individuals that need to migrate in the Kth area to the 1st area, and the migration ratio is 0.05.

[0132] Specific implementation method 7: This implementation method is different from any one of the specific implementation methods 1 to 6 in that when the number of iterations l=1, the local optimal solution in the kth region for:

[0133]

[0134] in, They are the 1st, 2nd, 3rd, ..., Sth in the kth region after migration. k The initial position of each firefly, They are the 1st, 2nd, 3rd, ..., Sth in the kth region after migration. k The brightness of an individual firefly;

[0135] When the number of iterations l-1≠l′T, the local optimal solution in the kth region of the lth iteration for:

[0136]

[0137] Where l' is a positive integer, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The position of the individual fireflies after the l-1th iteration, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The brightness of an individual firefly;

[0138] When the number of iterations l-1 = l′T, the local optimal solution in the kth region of the lth iteration for:

[0139]

[0140] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0141] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that the first, second, third, ..., Sth in the kth region k The brightness of a firefly The calculation method is:

[0142]

[0143] in, is the normalized weight of the particle corresponding to the jth firefly individual in the kth region, I 0 Indicates the maximum light intensity of fireflies;

[0144] The first, second, third, ..., Sth regions in the kth region k The brightness of a firefly They are:

[0145]

[0146] Where γ is the absorption coefficient, e is the base of the natural logarithm, and r j It means that after the l-1th iteration, the position of the jth firefly in the kth region is different from the local optimal solution. The Euclidean distance between .

[0147] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0148] In the firefly algorithm, the brighter the firefly, the more it can attract other fireflies to approach it; in the particle filter, the higher the particle weight, the higher its accuracy and the closer it is to the true value. Introducing the particle weight in the brightness calculation formula can effectively improve the accuracy of the calculation.

[0149]

[0150] Among them, x i =(x i1 ,x i2 ,…,x iJ ) is the position of the i-th firefly; r best =(r best1 ,r best2 ,…,r bestJ ) is the location of the optimal solution.

[0151] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that the positions of the fireflies in each area are updated according to the local optimal solution, specifically:

[0152]

[0153] in, represents the position of the jth firefly individual in the kth region after the lth iteration update, represents the position of the jth firefly individual in the kth region after the l-1th iteration update, β represents the attraction, α(l) is the step factor, and rand is a random number distributed between [0,1];

[0154]

[0155] Among them, β 0 is the maximum attraction;

[0156] Since the step size affects the quality of search results during search, a fixed step size often cannot provide the most accurate search results. Based on this, based on the firefly algorithm position update formula, the adaptive step size factor is introduced into the calculation:

[0157] α(l)=α 0 ×e -ql

[0158] Among them, α 0 is the initial step size, q=0.01.

[0159] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0160] The method of this embodiment is used to update the target position. The number of iterations in the initial stage is small. At this time, the brightness of the fireflies is relatively dispersed. Under the control of parameters, the step factor is longer. After iteration, the brightness is relatively concentrated. At this time, the step factor is reduced under the control of parameters for fine search.

[0161] Specific implementation method 10: This implementation method is different from the first to ninth specific implementation methods in that the target state at time t is calculated based on the positions of individual fireflies in all areas, specifically:

[0162]

[0163] Among them, x L,n It represents the position of the nth firefly individual in the overall area after the Lth iteration; represents the target state at time t, Represents the normalized weight of the particle corresponding to the nth firefly individual in the overall area.

[0164] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0165] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A long baseline positioning method based on improved adaptive firefly optimized particle filter, characterized in that: The method specifically comprises the following steps: Step 1: Initialize the state vector of each particle, and record the initial state vector of the nth particle as and are the horizontal position and velocity of the nth particle at the initial moment, and are the vertical position and velocity of the nth particle at the initial moment, respectively, [·] T represents transposition, n=1,2,…,N, N is the total number of particles; Step 2: Initialization time t=1; Step 3: Calculate the state vector of the nth particle at time t based on the state vector of the nth particle at time t-1; According to the state vector of each particle at time t, the particle arrival time equation is established, the likelihood function is established according to the particle arrival time, and then the weight of each particle is calculated according to the likelihood function ratio. Sort the weights of each particle in descending order, select the first p particles as valid particles, discard the remaining Np particles, and randomly generate Np new particles in the state space, and set the weights of the generated new particles to w new ; Normalize the weights of the effective particles and newly generated particles at time t, and use the state vectors and normalized weights of the effective particles and newly generated particles at time t to form a particle set; Step 4: Use the state vector of each particle in the particle set as the initial position of each firefly individual in the firefly population, divide the entire search area evenly into K areas and number the divided areas, and then set the maximum number of iterations L of the firefly algorithm; Step 5, initialize the number of iterations l = 1; Step 6: Randomly select a fixed proportion of firefly individuals from the kth area, and migrate the selected firefly individuals to the k+1th area; After migration, the firefly individuals in each area update their positions according to the local optimal solution; Step 7: Whether the set maximum number of iterations L is reached; If the maximum number of iterations L is reached, execute step 11; If the maximum number of iterations L is not reached, execute step eight; Step 8: For any area, calculate the fluorescence brightness of each firefly in the area, and then determine the local optimal solution in the area according to the fluorescence brightness. Similarly, determine the local optimal solution in each area. And determine whether the current number of iterations is an integer multiple of T; If the current number of iterations is an integer multiple of T, a global optimal solution is determined based on the local optimal solutions in each region, and the determined global optimal solution is used as the local optimal solution of each region for the next iteration, and step ten is executed again; If the current number of iterations is not an integer multiple of T, execute step nine; Step 9, taking the local optimal solution in each region determined in step 8 as the local optimal solution of each region in the next iteration, and then executing step 10; Step 10: Set l=l+1, and return to step 6; Step 11: Calculate the target state at time t based on the positions of individual fireflies in all areas, then set t=t+1 and return to execute step 3.

2. The method according to claim 1, characterized in that: The initial state vector The values ​​in are selected from the state space, in which the velocity ranges from [0, V max ], the position range is [0,R max ], R max Indicates the maximum distance allowed between a particle and the position (X, Y) with the maximum likelihood value.

3. The method of long baseline positioning based on improved adaptive firefly optimized particle filtering according to claim 2, characterized in that: The state vector of the nth particle at time t is calculated according to the state vector of the nth particle at time t-1; specifically: in, represents the state vector of the nth particle at time t-1, represents the state vector of the nth particle at time t, w t is the process noise at time t, and f(·) is the state transition function.

4. The method of long baseline positioning based on improved adaptive firefly optimized particle filtering according to claim 3 is characterized in that: The particle arrival time equation is established according to the state vector of each particle at time t, the likelihood function is established according to the particle arrival time, and the weight of each particle is calculated according to the likelihood function ratio. The specific process is: Step 31. Arrival time of the nth particle at time t for: in, is the time when the direct wave of the nth particle reaches the mth buoy at time t, and are the state vector of the nth particle at time t The horizontal and vertical positions of is the underwater sound speed, x m,t and m,t are the horizontal and vertical positions of the mth buoy at time t respectively; Step 32: According to calculate in, is the sampling point of the nth particle at the mth buoy at time t, f s is the sampling frequency, floor() means rounding down; Step 3. Define the likelihood function of the nth particle at time t as Where E[·] is the output matrix of the matched filter of the nth particle, m = 1, 2, …, M, and M is the total number of buoys; Step 3 and 4: Weight of the nth particle for: in, represents the likelihood function of the n′th particle at time t, and N is the total number of particles.

5. The method of long baseline positioning based on improved adaptive firefly optimized particle filtering according to claim 4 is characterized in that: The weight of the new particle generated in step 3 is: Among them, ∈ is a positive factor.

6. The method of long baseline positioning based on improved adaptive firefly optimized particle filter according to claim 1, characterized in that: The specific process of step six is ​​as follows: The set of state vectors of individual fireflies in the kth region is recorded as in, are the state vectors of the first, second, ..., Sth firefly individuals in the kth region, respectively, and S is the total number of fireflies in the kth region; 0.05S firefly individuals are randomly selected from the firefly individuals in the kth area, and the selected firefly individuals are migrated to the k+1th area.

7. The method of long baseline positioning based on improved adaptive firefly optimized particle filtering according to claim 5, characterized in that: When the number of iterations l=1, the local optimal solution in the kth region for: in, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The initial position of each firefly, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The brightness of individual fireflies; When the number of iterations l-1≠l′T, the local optimal solution in the kth region of the lth iteration for: Where l' is a positive integer, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The position of the individual fireflies after the l-1th iteration, are the 1st, 2nd, 3rd, ..., Sth in the kth region respectively. k The brightness of individual fireflies; When the number of iterations l-1 = l′T, the local optimal solution in the kth region of the lth iteration k=1,2,…,K is:

8. The method for long baseline positioning based on improved adaptive firefly optimized particle filtering according to claim 7 is characterized in that: The first, second, third, ..., Sth regions in the kth region k The brightness of a firefly The calculation method is: in, is the normalized weight of the particle corresponding to the j-th firefly individual in the k-th region, and I0 represents the maximum light intensity of the firefly; The first, second, third, ..., Sth regions in the kth region k The brightness of a firefly They are: Where γ is the absorption coefficient, e is the base of the natural logarithm, and r j It means that after the l-1th iteration, the position of the jth firefly in the kth region is different from the local optimal solution. The Euclidean distance between .

9. The method of long baseline positioning based on improved adaptive firefly optimized particle filtering according to claim 8, characterized in that: The fireflies in each area are updated according to the local optimal solution, specifically: in, represents the position of the jth firefly individual in the kth region after the lth iteration update, represents the position of the jth firefly individual in the kth region after the l-1th iteration update, β represents the attraction, α(l) is the step factor, and rand is a random number distributed between [0,1]; Among them, β0 is the maximum attraction; α(l)＝α0×e -ql Among them, α0 is the initial step size, and q=0.

01.

10. The long baseline positioning method based on improved adaptive firefly optimized particle filtering according to claim 9, characterized in that: The target state at time t is calculated based on the positions of individual fireflies in all areas, specifically: Among them, x L,n It represents the position of the nth firefly individual in the overall area after the Lth iteration; represents the target state at time t, Represents the normalized weight of the particle corresponding to the nth firefly individual in the overall area.

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