Multi-information fusion ambiguity resolution positioning method based on mixed variable differential evolution

Abstract

The invention discloses a multi-information fusion ambiguity resolution positioning method based on mixed variable differential evolution, and belongs to the technical field of long-baseline underwater acoustic positioning. According to the invention, the problem of low precision of target position calculation in the prior art is solved. According to the method, a joint time delay-Doppler frequency shift observation model is constructed, the position, the speed and the fuzzy cycle number of a moving target platform are uniformly incorporated into a maximum likelihood estimation framework, and a mixed variable optimization problem is established; an improved differential evolution algorithm is introduced to solve a mixed variable optimization problem, and unified evolution search is realized through a mode of'continuous optimization + discrete rounding '. And a restart mechanism is designed, and when stagnation or long-term non-convergence occurs in the evolution process, the population is automatically reset based on the guidance of a historical optimal solution, so that local optimum is effectively avoided. Moreover, the method can give consideration to the collaborative search of continuous and discrete variables, and can remarkably improve the precision and stability of long baseline positioning. The method can be applied to long-baseline underwater acoustic positioning.

Description

Technical Field

[0001] This invention belongs to the field of long baseline underwater acoustic localization technology, specifically involving a multi-information fusion defuzzification localization method based on mixed variable differential evolution. Background Technology

[0002] Underwater acoustic positioning technology relies on the propagation characteristics of sound waves in water to achieve precise positioning of underwater targets by measuring the propagation delay, phase, or Doppler frequency shift between the platform and a reference point. Long baseline (LBL) systems are widely used for navigation and positioning of underwater vehicles, unmanned underwater vehicles, and underwater observation platforms due to their large measurement coverage and high positioning accuracy. However, under high frame rates or large-scale conditions, traditional LBL positioning methods based on time delay measurements are susceptible to periodic ambiguity and geometric dilution effects, leading to decreased solution accuracy and even significant deviations.

[0003] Traditional methods often rely on single time delay measurements to construct geometric intersection models. However, as the array range expands or the platform speed increases, periodic ambiguity becomes significant, often requiring additional prior constraints to aid in the solution. In practical applications, the uncertainty of signal propagation paths and interference from measurement noise render positioning methods relying solely on time delay measurements unreliable. Furthermore, existing anti-ambiguity methods often employ methods such as show of hands or reference position marking, which have low accuracy in resolving distance ambiguity and struggle to achieve precise positioning within the range of long-baseline arrays.

[0004] Doppler information can provide radial velocity compensation in the direction of target motion, thus mitigating positioning errors caused by time delay ambiguity to some extent. The nonlinear optimization problem solved by fusing two types of observations exhibits mixed-variable characteristics: it includes both continuous variables such as target position and velocity, and discrete variables related to periodic ambiguity. However, existing optimization algorithms struggle to simultaneously consider the joint search of continuous and discrete variables, easily getting trapped in local optima, resulting in low accuracy in target position calculation and impacting the performance of target position calculation. Summary of the Invention

[0005] The purpose of this invention is to address the problem that existing methods are difficult to coordinate the search of continuous and discrete variables, are prone to getting trapped in local optima, and thus have low accuracy in solving the target location. Therefore, this invention proposes a multi-information fusion defuzzy localization method based on mixed variable differential evolution.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] A multi-information fusion unfuzzy localization method based on mixed variable differential evolution, the method specifically includes the following steps:

[0008] Step 1: Establish a moving target transceiver anomaly model within a long baseline array, and then design a fitness function based on the moving target transceiver anomaly model that includes time delay observations, Doppler frequency shift observations, moving target position, moving target velocity, and time delay ambiguity cycle number.

[0009] Step 2: Calculate the maximum number of ambiguity periods within the array range based on the acoustic beacon pulse transmission period and the speed of sound in water;

[0010] Step 3: Based on the selected long baseline array coordinate range, the upper limit of the moving target platform's speed in the water, and the maximum number of fuzzy cycles calculated, the boundary constraints are used to initialize the individuals in the population.

[0011] Step 4: Initialize the number of iterations ;

[0012] Step 5: Perform relaxation mutation and crossover operations on all individuals in the population;

[0013] Step 6: Calculate the first... The fitness function values ​​of all individuals in the population are obtained in the second iteration, and a selection operation is performed based on the calculated fitness function values ​​to obtain the third iteration. All individuals after the next iteration update;

[0014] Step Seven, Judgment Whether the minimum fitness function value of all individuals in the population after the update obtained in the next iteration is less than the preset threshold;

[0015] If it is less than the preset threshold, then output the first... After the next iteration update, the individual corresponding to the minimum fitness function value in the population will have its position parameters output as the localization result of the moving target.

[0016] If the value is not less than the preset threshold, then a stagnation check is performed:

[0017] If the stall condition is met, continue to step eight;

[0018] Otherwise, if the stagnation condition is not met, proceed to step nine;

[0019] Step 8: Obtain the search result with the smallest fitness function value from the historical search results. Individuals, and then from One individual is randomly selected from the total number of individuals, and Gaussian perturbation is applied to this selected individual to generate... Individuals, using generated Individuals and Acquisition Each individual becomes a new initial population, and then the process returns to step four.

[0020] Step 9: Determine if the current iteration has reached the set maximum number of iterations;

[0021] If the maximum number of iterations is reached, return to step three.

[0022] If the maximum number of iterations has not been reached, then let Return to step five.

[0023] Furthermore, the moving target transceiver anomaly model within the long baseline array is as follows:

[0024] (1)

[0025] in, This indicates the speed at which a signal travels through water. Represents the position coordinates of the moving target. Indicates the current speed of the moving target. The heading angle of a moving target. Indicates the first in the array The current position coordinates of each primitive. Indicates the first The transmission time from the signal transmitted by each element to the signal received by the target platform.

[0026] Furthermore, the design process of the fitness function is as follows:

[0027] Step 11: Based on the moving target transmit / receive anomaly model, obtain the relationship between latency and the position and velocity of the moving target platform:

[0028] (2)

[0029] in, This represents the position vector of the moving target platform. The superscript T indicates transpose. This represents the velocity vector of the moving target platform. , Represents the rectangular coordinates of a moving target in space. Velocity in the axial direction, Represents the rectangular coordinates of a moving target in space. Velocity in the axial direction, Represents the rectangular coordinates of a moving target in space. Velocity in the axial direction, Indicates the first The position vector of each primitive ;

[0030] Expanding the left and right sides of equation (2) by squaring them simultaneously yields:

[0031] (3)

[0032] Steps 1 and 2: Establish the first The relationship between the observation delay and the actual delay for each primitive element is as follows:

[0033] (7)

[0034] in, Indicates the first The observation delay corresponding to each primitive Indicates the first The number of fuzzy cycles of each primitive relative to the moving target platform. For synchronization period, Indicates the first The time delay observation error of each element;

[0035] By rearranging formula (7), we obtain the time delay observations and the unknown parameters of the platform. And the coupling parameter model between the number of fuzzy periods:

[0036] (8)

[0037] in, , Represents a continuous variable consisting of the position coordinates and velocity of the moving target platform;

[0038] Substitute formula (3) into the right side of the coupling parameter model to calculate the observation delay corresponding to each primitive;

[0039] Step 13: Establish the first The observed Doppler frequency shift corresponding to each primitive element Compared with the true Doppler frequency shift Relationship:

[0040] (12)

[0041] in, Indicates the first The Doppler frequency shift observation error corresponding to each element;

[0042] True Doppler Shift for:

[0043] (13)

[0044] in, Indicates the first The center frequency of the signal transmitted by each element; Indicates the relationship between the target platform and the first The radial velocity of the moving target platform along the line connecting the individual elements;

[0045] (14)

[0046] in, Represents the L2 norm;

[0047] Substituting equation (14) into equation (12), we obtain the first... Doppler frequency shift observations corresponding to each element Unknown parameters of the platform Coupled parameter model:

[0048] (15)

[0049] The Doppler frequency shift observations corresponding to each element are calculated according to the coupling parameter model of equation (15);

[0050] Step 1, Section 4: Calculate the mean value of the time delay observation error based on the time delay observations corresponding to each primitive element. and standard deviation The mean value of the Doppler frequency shift observation error is calculated based on the Doppler frequency shift observations corresponding to each primitive element. and standard deviation ;

[0051] Next, calculate the likelihood function based on time delay and Doppler frequency shift information. :

[0052] (16)

[0053] in, It is a constant term;

[0054] Equation (16) can be simplified as follows:

[0055] (17)

[0056] in, ;

[0057] (18)

[0058] Step 15: Time Delay Observation Error Vector and Doppler frequency shift observation error vector The corresponding covariance matrix and They are respectively:

[0059] (19)

[0060] (20)

[0061] in, Represents a diagonal matrix. Indicates the first The mean square error of the measurement delay of each primitive element Indicates the first The mean square error of the measured Doppler frequency shift of each element;

[0062] Equation (17) can be rewritten as:

[0063] (twenty one)

[0064] Here, the superscript -1 represents the inverse of the matrix;

[0065] (twenty two)

[0066] (twenty three)

[0067] in, , express A discrete vector composed of the number of fuzzy cycles of each primitive relative to the moving target platform;

[0068] Establish the fitness function for the differential evolution algorithm:

[0069] (twenty four)

[0070] in, This represents the objective function controlled by time delay. This represents the objective function controlled by Doppler frequency offset. Indicates the weighting coefficient;

[0071] (25)

[0072] (26)

[0073] in, This represents the time delay calculated based on the position, velocity, and number of fuzzy cycles in the current iteration of the differential evolution algorithm. This represents the Doppler frequency shift calculated based on the position, velocity, and number of ambiguity cycles in the current iteration of the differential evolution algorithm. , .

[0074] Furthermore, the specific process of step two is as follows:

[0075] (27)

[0076] in, This indicates the preset maximum underwater acoustic range within a long-baseline underwater acoustic system. This indicates the target's acoustic beacon pulse transmission period. This indicates rounding the variable up. This represents the maximum number of ambiguity periods within the array range.

[0077] Furthermore, the specific process of step three is as follows:

[0078] (28)

[0079] in, For population size, , This represents the dimension of the mixture variable parameters in each individual. Indicates the first in the initial population The first individual dimensional components, for A random number within the interval, Indicates the first The upper bound of the boundary of the dimensional component. Indicates the first Lower bound of the dimensional component;

[0080] Initialize to:

[0081] (29)

[0082] in, .

[0083] Furthermore, the specific process of step five is as follows:

[0084] (30)

[0085] in, As a variable factor, , and Indicates from the first Three individuals randomly selected from the population satisfy the following conditions: , , and They represent , and The Middle The value of the dimensional component, Indicates the first step after the crossover operation. The first individual The values ​​of the dimensional components;

[0086] Perform relaxation and mutation operations on the discrete variable part of the fuzzy cycle number of the primitive:

[0087] (31)

[0088] The first Individuals obtained in the next iteration With variant individuals Perform a crossover operation to generate crossover individuals:

[0089] (32)

[0090] in, Indicates the first The crossover operation of the nth iteration produces the first Among the individuals, the first The values ​​of the dimensional components;

[0091] Relaxation operations are performed on the discrete variable part:

[0092] (33)

[0093] Where CR is a constant, This indicates the range of population vector dimensions. The selected integer, Indicates the number of relaxation operations after the first relaxation operation. Among the individuals, the first The value of the dimensional component.

[0094] Furthermore, the specific process of step six is ​​as follows:

[0095] (34)

[0096] in, Indicates the first The population obtained in the nth iteration The fitness function value of each individual. Indicates the first The population obtained in the nth iteration The fitness function value of each individual. Indicates the first The population obtained in the nth iteration Individual.

[0097] Furthermore, the stagnation state check specifically involves determining whether formula (35) is satisfied:

[0098] (35)

[0099] in, Indicates the first The minimum fitness function value of all individuals in the population after the next iteration update. Indicates the first The iteration continues to the... The minimum fitness function value of all individuals in the population after the next iteration update. This indicates the calculation of absolute value. This indicates the set threshold.

[0100] If equation (35) is satisfied, then the stagnation state is satisfied; otherwise, the stagnation state is not satisfied.

[0101] Furthermore, the Gaussian perturbation generation of the randomly selected individuals... Individuals, specifically:

[0102] (36)

[0103] in, This refers to randomly selected individuals. Indicates the first A random perturbation vector, Indicates the first generation generated by Gaussian perturbation Individual, .

[0104] Furthermore, the random perturbation vector for:

[0105] (37)

[0106] in, Represents a random perturbation vector The first in One element, For dimensional indexing, It is a scale factor. This represents a Gaussian distribution with a mean of 0 and a standard deviation of 1.

[0107] The beneficial effects of this invention are:

[0108] This invention constructs a joint time-delay-Doppler frequency shift observation model, unifying the position, velocity, and number of ambiguity cycles of the moving target platform within a maximum likelihood estimation framework, and establishes a mixed-variable optimization problem. In solving this problem, an improved differential evolution algorithm is introduced, achieving a unified evolutionary search through "continuous optimization + discrete rounding." A restart mechanism is also designed; when the evolutionary process stalls or fails to converge for an extended period, the population is automatically reset based on historical optimal solutions, effectively avoiding local optima traps. This method can simultaneously address the collaborative search of continuous and discrete variables, significantly improving the accuracy and stability of long-baseline positioning even in the presence of noise and periodic ambiguity, providing a feasible solution for high-precision navigation in complex underwater environments.

[0109] Meanwhile, the method of the present invention also has the advantages of low computational cost, no need to obtain the initial position information of the target, good robustness, and high adaptability. Attached Figure Description

[0110] Figure 1 This is a flowchart of a multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to the present invention;

[0111] Figure 2 This is the acoustic navigation scenario for the distributed mobility platform of the present invention;

[0112] Figure 3 The original motion state is simulated using a pre-defined long baseline.

[0113] Figure 4 This is a simulation situation diagram for long-baseline, non-range-ambiguous positioning.

[0114] Figure 5 A positioning simulation situation diagram to resolve distance ambiguity in the show-of-hands voting method;

[0115] Figure 6 A simulation situation diagram for resolving distance ambiguity using the reference position marking method;

[0116] Figure 7 This is a localization simulation diagram based on multi-information fusion defuzzification using mixed variable differential evolution according to the present invention;

[0117] Figure 8 A graph showing the horizontal distance deviation of the simulation positioning results;

[0118] Figure 9 Simulation matrix distribution of the accuracy rate of the show-of-hands voting method in solving fuzzy issues;

[0119] Figure 10 To solve the fuzzy accuracy histogram for the show-of-hands voting method;

[0120] Figure 11The simulation matrix distribution of the accuracy of fuzzy resolution using the reference position marking method;

[0121] Figure 12 The simulation matrix distribution of the accuracy of fuzzy resolution using the reference position marking method;

[0122] Figure 13 This is a simulation matrix distribution diagram of the defuzzification accuracy of a multi-information fusion localization method based on mixed variable differential evolution according to the present invention.

[0123] Figure 14 Histogram of defuzzification accuracy of a multi-information fusion localization method based on mixed variable differential evolution according to the present invention.

[0124] Figure 15 A simulation array distribution diagram for the acoustic navigation accuracy of the show-of-hands voting method;

[0125] Figure 16 A simulation array distribution diagram for the accuracy of acoustic navigation positioning using the reference position marking method;

[0126] Figure 17 The image shows the distribution of the acoustic navigation accuracy simulation array for a multi-information fusion positioning method based on hybrid variable differential evolution according to the present invention. Detailed Implementation

[0127] Specific implementation method one: Combining Figure 1 This embodiment describes a multi-information fusion unfuzzy localization method based on mixed-variable differential evolution, which specifically includes the following steps:

[0128] Step 1: Establish a moving target transceiver anomaly model within a long baseline array, and then design a fitness function expression based on the moving target transceiver anomaly model, which includes time delay observations, Doppler frequency shift observations, moving target position, moving target velocity, and time delay ambiguity cycle number.

[0129] First, establish a model of the transmitting and receiving outliers of moving targets within a long baseline array:

[0130] (1)

[0131] in, This indicates the speed at which a signal travels through water. Represents the position coordinates of the moving target. Indicates the current speed of the moving target. The heading angle of a moving target. Indicates the first in the array The current position coordinates of each primitive. Indicates the first The transmission time from the transmitted signal of the first element to the received signal of the target platform, i.e., the transmission time of the first element. The actual latency corresponding to each primitive.

[0132] Secondly, the design process of the fitness function is as follows:

[0133] Step 11: Based on the moving target transmit / receive anomaly model, obtain the relationship between latency and the position and velocity of the moving target platform:

[0134] (2)

[0135] in, This represents the position vector of the moving target platform. The superscript T indicates transpose. This represents the velocity vector of the moving target platform. , Represents the rectangular coordinates of a moving target in space. Velocity in the axial direction, Represents the rectangular coordinates of a moving target in space. Velocity in the axial direction, Represents the rectangular coordinates of a moving target in space. Velocity in the axial direction, Indicates the first The position vector of each primitive ;

[0136] Expanding the left and right sides of equation (2) by squaring them simultaneously yields:

[0137] (3)

[0138] Equation (3) reflects the propagation delay. With unknown platform parameters The relationship between them, ;

[0139] Steps 1 and 2: Denote the vector composed of the actual time delays corresponding to each primitive as:

[0140] (4)

[0141] in, Indicates the total number of primitives. Let them represent the first primitive, the second primitive, ..., the third primitive, respectively. The actual latency corresponding to each primitive;

[0142] The vector composed of the observation delays corresponding to each primitive element is denoted as:

[0143] (5)

[0144] in, Let them represent the first primitive, the second primitive, ..., the third primitive, respectively. The observation delay corresponding to each primitive;

[0145] For long baseline positioning systems, the observation delay vector With the true time delay vector The relational expression satisfies:

[0146] (6)

[0147] in, Represents the time delay observation error vector. A vector representing the number of fuzzy cycles of each primitive relative to the target platform. For synchronization period;

[0148] Then establish the first The relationship between the observation delay and the actual delay for each primitive element is as follows:

[0149] (7)

[0150] in, Indicates the first The observation delay corresponding to each primitive Indicates the first The number of fuzzy cycles of each primitive relative to the moving target platform. For synchronization period, Indicates the first The time delay observation error of each element;

[0151] By rearranging formula (7), we obtain the time delay observations and the unknown parameters of the platform. And the coupling parameter model between the number of fuzzy periods:

[0152] (8)

[0153] in, , Represents a continuous variable consisting of the position coordinates and velocity of the moving target platform;

[0154] Substitute formula (3) into the right side of the coupling parameter model to calculate the observation delay corresponding to each primitive;

[0155] Step 13: Combine the vectors formed by the observed Doppler frequency shifts corresponding to each primitive element. Recorded as:

[0156] (9)

[0157] in, Let them represent the first primitive, the second primitive, ..., the third primitive, respectively. The observed Doppler frequency shift corresponding to each primitive element;

[0158] The vector composed of the real Doppler frequency shifts corresponding to each primitive element Recorded as:

[0159] (10)

[0160] in, Let them represent the first primitive, the second primitive, ..., the third primitive, respectively. The actual Doppler frequency shift corresponding to each element;

[0161] vector with vector The relational expression satisfies:

[0162] (11)

[0163] in, This represents the Doppler frequency shift observation error vector;

[0164] Then establish the first The observed Doppler frequency shift corresponding to each primitive element Compared with the true Doppler frequency shift Relationship:

[0165] (12)

[0166] in, Indicates the first The Doppler frequency shift observation error corresponding to each element;

[0167] True Doppler Shift for:

[0168] (13)

[0169] in, Indicates the first The center frequency of the signal transmitted by each element; Indicates the relationship between the target platform and the first The radial velocity of the moving target platform along the line connecting the individual elements;

[0170] (14)

[0171] in, Represents the L2 norm;

[0172] Substituting equation (14) into equation (12), we obtain the first... Doppler frequency shift observations corresponding to each element Unknown parameters of the platform Coupled parameter model:

[0173] (15)

[0174] The Doppler frequency shift observations corresponding to each element are calculated according to the coupling parameter model of equation (15);

[0175] Step 1, Section 4: Calculate the mean value of the time delay observation error based on the time delay observations corresponding to each primitive element. and standard deviation The mean value of the Doppler frequency shift observation error is calculated based on the Doppler frequency shift observations corresponding to each primitive element. and standard deviation ;

[0176] Next, calculate the likelihood function based on time delay and Doppler frequency shift information. :

[0177] (16)

[0178] in, It is a constant term;

[0179] Equation (16) can be simplified as follows:

[0180] (17)

[0181] in, ;

[0182] (18)

[0183] Step 15: Time Delay Observation Error Vector and Doppler frequency shift observation error vector The corresponding covariance matrix and They are respectively:

[0184] (19)

[0185] (20)

[0186] in, Represents a diagonal matrix. Indicates the first The mean square error of the measurement delay of each primitive element Indicates the first The mean square error of the measured Doppler frequency shift of each element and It can be actually measured;

[0187] Equation (17) can be rewritten using the observed quantity and observation error as follows:

[0188] (twenty one)

[0189] Here, the superscript -1 represents the inverse of the matrix;

[0190] (twenty two)

[0191] (twenty three)

[0192] in, , express A discrete vector composed of the number of fuzzy cycles of each primitive relative to the moving target platform;

[0193] Establish the fitness function for the differential evolution algorithm:

[0194] (twenty four)

[0195] in, This represents the objective function controlled by time delay. This represents the objective function controlled by Doppler frequency offset. Indicates the weighting coefficient;

[0196] (25)

[0197] (26)

[0198] in, This represents the time delay calculated based on the position, velocity, and number of fuzzy cycles in the current iteration of the differential evolution algorithm. This represents the Doppler frequency shift result calculated based on the position, velocity, and number of ambiguity cycles in the current iteration of the differential evolution algorithm.

[0199] To perform defuzzy localization, this invention also needs to obtain the maximum number of fuzzy periods within the array range, i.e.:

[0200] Step 2: Calculate the maximum number of ambiguity periods within the array range based on the acoustic beacon pulse transmission period and the underwater sound velocity measured by hydrology.

[0201] (27)

[0202] in, This indicates the maximum preset underwater acoustic range within the long-baseline underwater acoustic system (determined based on the array configuration of the long-baseline positioning system). This indicates the target's acoustic beacon pulse transmission period. This indicates rounding the variable up. This represents the maximum number of ambiguity periods within the array range.

[0203] Then, the population optimization algorithm is used in this invention to solve for the target's location. The specific solution process includes steps three to nine, namely:

[0204] Step 3: Based on the selected long baseline array coordinate range, the upper limit of the moving target platform's speed in the water, and the maximum number of fuzzy cycles calculated, the boundary constraints are used to initialize the individuals in the population.

[0205] The specific process of step three is as follows:

[0206] (28)

[0207] in, For population size, , This represents the dimension of the mixture variable parameters in each individual. Indicates the first in the initial population The first individual dimensional components, for A random number within the interval, Indicates the first The upper bound of the boundary of the dimensional component. Indicates the first Lower bound of the dimensional component;

[0208] In the specific implementation process, considering the special characteristics of the underwater environment and engineering realities, this invention utilizes a high-precision depth gauge (i.e., pressure sensor) mounted on an AUV (Autonomous Underwater Vehicle) to directly acquire the target's high-precision depth information z. Since the measurement accuracy of the depth gauge is typically much higher than that of acoustic positioning, the target's depth position is considered in the construction of the hybrid variable differential evolution algorithm. and the vertical velocity derived from it It is usually set to constant depth navigation, that is Treated as known constants, they are not included in the optimization variables of individual populations. This approach reduces the 6-dimensional search problem in three-dimensional space (3D position + 3D velocity) to a 4-dimensional search problem in the horizontal plane (horizontal position). , and horizontal speed , While ensuring the three-dimensional rigor of the physical model, it significantly reduces the computational complexity of the algorithm and improves the convergence speed. In each individual, the first four components are continuous variables consisting of the position and velocity of the moving target platform.

[0209] For by The discrete variable, composed of the fuzzy period number of the transmission delay of each primitive, is initialized as follows:

[0210] (29)

[0211] in, ;

[0212] Step 4: Initialize the number of iterations ;

[0213] Step 5: Perform relaxation mutation and crossover operations on all individuals in the population; the specific process of step 5 is as follows:

[0214] (30)

[0215] in, As a variable factor, , and Indicates from the first Three individuals randomly selected from the population satisfy the following conditions: , , and They represent , and The Middle The value of the dimensional component, Indicates the first step after the crossover operation. The first individual The values ​​of the dimensional components;

[0216] Perform relaxation mutation on the discrete variable portion of the mixed variable that contains the number of fuzzy cycles of the primitives:

[0217] (31)

[0218] The first Individuals obtained in the next iteration With variant individuals Perform a crossover operation to generate crossover individuals:

[0219] (32)

[0220] in, Indicates the first The crossover operation of the nth iteration produces the first Among the individuals, the first The values ​​of the dimensional components;

[0221] Relaxation operations are performed on the discrete variable part:

[0222] (33)

[0223] CR is a constant (which can be set according to actual conditions, and the parameter copying is controlled within the range of constants specified by the user). This indicates the range of population vector dimensions. The selected integer, Indicates the number of relaxation operations after the first relaxation operation. Among the individuals, the first The values ​​of the dimensional components;

[0224] When satisfied or The binomial crossover operator copies the corresponding element of the mutation vector to the vector. Ensure that at least one element differs from the target vector of the parent or previous generation.

[0225] It should be noted that when performing relaxation mutation and crossover operations, this invention can also constrain the operation results by setting upper and lower boundaries of the parent population mixing variable. Taking a matrix containing 4 primitives as an example, the upper boundary is:

[0226]

[0227] The lower boundary is:

[0228]

[0229] in, The maximum speed of the set moving target. The set minimum speed of the moving target. The maximum number of fuzzy cycles obtained from the calculation;

[0230] When variables obtained during relaxation mutation and crossover operations exceed the upper and lower bound constraints, for example, when the value of a variable exceeds the upper bound, the value of the variable is adjusted to the upper bound; when the value of a variable is below the lower bound, the value of the variable is adjusted to the lower bound.

[0231] Step 6: Calculate the first... The fitness function values ​​of all individuals in the population are obtained in the second iteration, and a selection operation is performed based on the calculated fitness function values ​​to obtain the third iteration. All individuals after the next iteration update;

[0232] (34)

[0233] in, Indicates the first The population obtained in the nth iteration The fitness function value of each individual. Indicates the first The population obtained in the nth iteration The fitness function value of each individual. Indicates the first The population obtained in the nth iteration Individual;

[0234] Step Seven, Judgment Whether the minimum fitness function value of all individuals in the population after the update obtained in the next iteration is less than the preset threshold;

[0235] If it is less than the preset threshold, then output the first... After the next iteration update, the individual corresponding to the minimum fitness function value in the population will have its position parameters output as the localization result of the moving target.

[0236] If it is not less than a preset threshold, a stagnation check is performed, specifically determining whether formula (35) is satisfied:

[0237] (35)

[0238] in, Indicates the first The minimum fitness function value of all individuals in the population after the next iteration update. Indicates the first The iteration continues to the... The minimum fitness function value of all individuals in the population after the next iteration update. This indicates the calculation of absolute value. This indicates the set threshold.

[0239] If equation (35) is satisfied, then the stagnation state is satisfied (the algorithm is considered to be trapped in a local optimum), and step eight is continued; otherwise, the stagnation state is not satisfied, and step nine is continued.

[0240] Step 8: Obtain the search result with the smallest fitness function value from the historical search results. Individuals (it should be noted that this was obtained) (There are no duplicate individuals among the individuals), and then from... One individual is randomly selected from the total number of individuals, and a Gaussian perturbation is applied to the randomly selected individual:

[0241] (36)

[0242] in, This refers to randomly selected individuals. Indicates the first A random perturbation vector, Indicates the first generation generated by Gaussian perturbation Individual, ;

[0243] Each dimension of the random perturbation vector is generated through a Gaussian perturbation. for:

[0244] (37)

[0245] in, Represents a random perturbation vector The first in One element, For dimensional indexing, It is a scaling factor (which can be set to a small constant). ), This represents a Gaussian distribution with a mean of 0 and a standard deviation of 1.

[0246] Using Gaussian perturbation Individuals and Acquisition Each individual becomes a new initial population, and then the process returns to step four.

[0247] Step 9: Determine if the current iteration has reached the set maximum number of iterations;

[0248] If the maximum number of iterations is reached, return to step three.

[0249] If the maximum number of iterations has not been reached, then let Return to step five.

[0250] Experimental Section

[0251] like Figure 2 As shown, a simulation experiment was designed: four primitives were arranged in a square array, with their positions at (0,0) meters, (0,2000) meters, (2000,2000) meters, and (2000,0) meters respectively. The maximum propagation distance was chosen to be 3 km, meaning the maximum propagation distance from the moving target to the acoustic beacon was 3 km. The average speed of sound in water was denoted as c = 1500 m / s. The simulation set the target's navigation state as CV motion, the speed of the moving target platform was set to 10 m / s, and the target heading angle was set to 35°. Clocks were synchronized between each primitive and the moving target platform, and the synchronous transmission period of the signal was set to 0.1 s. The transmission frequencies of the underwater acoustic transceivers on the four primitives were set to 9 kHz, 11 kHz, 13 kHz, and 15 kHz respectively. The time delay observation was... With Doppler frequency shift observation They are statistically independent and all follow a Gaussian distribution with zero mean. and .

[0252] To ensure the invention can correctly search for the ambiguity period number from the transmitted acoustic beacon signal to the target platform within the array range, 19 was chosen as the maximum ambiguity period number for subsequent design. The population size was set to 300, the maximum number of iterations to 400, the fitness function decision threshold to 10, and the platform motion duration to 150s. The initial motion state of the platform was obtained as follows: Figure 3 As shown, the trajectory points obtained from the initial defuzzification are as follows: Figure 4 As shown in Table 1, the measurement error settings are as follows:

[0253] Table 1 Standard deviation of measurement error

[0254]

[0255] like Figure 4 As shown, due to the short pulse transmission period, i.e. T=0.1s, the traditional long baseline non-resistant range ambiguity positioning method produces severe range ambiguity linearity, resulting in multiple possible positions in the positioning result, making it impossible to achieve accurate target positioning.

[0256] To achieve anti-range ambiguity localization of targets in simulation experiments, the show-of-hands voting method and the reference position marking method are introduced and compared with the multi-information fusion unambiguity localization method based on mixed variable differential evolution of this invention. The basic principle of the show-of-hands voting method is to first exhaustively enumerate all possible solutions, then establish a criterion using redundant primitive information, and weight each solution. The solution with the most votes is selected as the true solution. This method utilizes redundant primitives in two ways: one is that redundant primitives do not participate in the position calculation, and the true solution is determined by comparing the back-calculated time delay with the measured time delay; the other is that all primitives are combined to solve the problem, and the region with the highest frequency of occurrence is taken as the true value region. The reference position marking method is a priori method for unambiguous range localization, which uses reference position information to determine the number of range ambiguity cycles before solving the platform position. This method is based on the "nearest is true" criterion: based on the maximum effective distance... A fuzzy period is divided into A fuzzy position is defined, with the fuzzy position closest to the reference position being the actual platform position.

[0257] Figure 5 and Figure 6 The images show the situational maps for resolving distance fuzzy positioning using the show-of-hands voting method and the reference position marking method, respectively. Figure 7 The localization simulation image is obtained using the multi-information fusion defuzzification method based on mixed variable differential evolution proposed in this invention. Figure 8The motion situation positioning error results show that the multi-information fusion positioning method based on mixed variable differential evolution can achieve accurate positioning throughout the entire flight by simultaneously optimizing position, velocity, and ambiguity cycle number, and fusing two types of observation information: time delay and Doppler frequency shift. Moreover, the positioning trajectory is highly consistent with the actual trajectory, and the root mean square positioning error is 2.5m, which is far superior to traditional methods such as raising hands and reference position marking.

[0258] To verify the accuracy of the differential evolution algorithm in solving the fuzzy cycle number of the target platform, we conducted... Within the array, coordinate points are selected at 50m intervals to verify the effectiveness of the algorithm in resolving distance ambiguity within the array, and to test the stability of the algorithm's accuracy. Using 500 Monte Carlo experiments, the calculation of the ambiguity period equal to the true ambiguity period is considered a correct resolution. In M Monte Carlo experiments, the number of times the ambiguity is correctly resolved is denoted as m. The resolution accuracy is then defined as:

[0259]

[0260] The calculated distributions of the unfuzzy resolution accuracy of the show-of-hands voting method within the matrix range are as follows: Figure 9 and Figure 10 As shown, the accuracy distribution of the reference position marking method in unambiguity resolution within the matrix range is as follows: Figure 11 and Figure 12 As shown, the multi-information fusion unfuzzy localization method based on mixed variable differential evolution of the present invention has the following unfuzzy accuracy distributions within the matrix range: Figure 13 and Figure 14 As shown.

[0261] from Figure 13 As can be seen from the heatmap color distribution, the method of this invention presents a bright yellow color, representing a high accuracy rate (90%-100%), in most areas within the array range, indicating that most areas have an extremely high deblurring accuracy. In contrast, in Figure 9 The method of voting by raising hands and Figure 11 In the reference position marking method, although the bright yellow high-accuracy area is dominant, it is interspersed with many blue and green low-accuracy areas, and the distribution is more dispersed, especially the low-accuracy points are more concentrated in a certain central area; for example, Figure 13 As shown, the high accuracy of the unfuzzy localization method of the present invention is more evenly and concentrated along the target movement direction, and the low accuracy points are very few and randomly distributed, showing that the method of the present invention has stronger stability and robustness throughout the entire array range.

[0262] Depend on Figure 14It can be seen that the number of sample cells with a defuzzification accuracy range of 90%-100% using the method of this invention reached 1086, accounting for 71.4% of the total sample size. Compared with the 40.4% accuracy of the show-of-hands method and the 1.4% accuracy of the reference position marking method, the method of this invention has an overwhelming advantage in defuzzification accuracy. This demonstrates that the present invention can achieve over 90% error-free calculation of the fuzzy cycle number of each element for the vast majority of coordinate points within the matrix range, exhibiting high reliability and stability in distance fuzzy positioning.

[0263] To investigate the magnitude of the positioning error when the algorithm can correctly resolve distance ambiguity within the array range, the root mean square error (RMSE) is used to characterize the accuracy of the platform's acoustic navigation. Let the platform's position information be denoted as... Its estimated value is denoted as , This indicates the number of times the coordinate point was correctly resolved in the fuzzy solution; therefore, the navigation accuracy is: ;

[0264] After removing positioning results with large deviations in position and distance due to de-ambiguity errors, the positioning accuracy distributions of the show-of-hands voting method and the reference position marking method within the array range are calculated as follows: Figure 15 , Figure 16 As shown, the positioning accuracy distribution of the multi-information fusion unfuzzy localization method based on mixed variable differential evolution in this invention within the array range is as follows: Figure 17 As shown.

[0265] In the positioning accuracy distribution map under correct defuzzification conditions, the bluer the color, the higher the positioning accuracy; the yellower the color, the lower the positioning accuracy. From Figure 15 and Figure 16 It can be seen that the global root mean square error (RMSE) of the correctly resolved ambiguity using the show-of-hands voting method is 7.157m, while the positioning error of the reference position marking method is mainly concentrated in the 10m to 30m range, with discrete high error points, and its RMSE is 10.867m. In contrast, the hybrid variable differential evolutionary positioning method of this invention, when correctly resolved ambiguity, has a positioning error concentrated between 1.4m and 3m, with a RMSE of 2.105m, achieving an order-of-magnitude improvement compared to traditional methods. This significant improvement in accuracy proves that the multi-information fusion and optimization mechanism of the algorithm of this invention not only ensures a high ambiguity resolution accuracy but also optimizes error propagation in the precise positioning stage, enabling it to have stable and reliable meter-level positioning capability throughout the entire array range.

[0266] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A multi-information fusion unfuzzy localization method based on mixed-variable differential evolution, characterized in that, The method specifically includes the following steps: Step 1: Establish a moving target transceiver anomaly model within a long baseline array, and then design a fitness function based on the moving target transceiver anomaly model that includes time delay observations, Doppler frequency shift observations, moving target position, moving target velocity, and time delay ambiguity cycle number. Step 2: Calculate the maximum number of ambiguity periods within the array range based on the acoustic beacon pulse transmission period and the speed of sound in water; Step 3: Based on the selected long baseline array coordinate range, the upper limit of the moving target platform's speed in the water, and the maximum number of fuzzy cycles calculated, the boundary constraints are used to initialize the individuals in the population. Step 4: Initialize the number of iterations ; Step 5: Perform relaxation mutation and crossover operations on all individuals in the population; Step 6: Calculate the first... The fitness function values ​​of all individuals in the population are obtained in the second iteration, and a selection operation is performed based on the calculated fitness function values ​​to obtain the third iteration. All individuals after the next iteration update; Step Seven, Judgment Whether the minimum fitness function value of all individuals in the population after the update obtained in the next iteration is less than the preset threshold; If it is less than the preset threshold, then output the first... After the next iteration update, the individual corresponding to the minimum fitness function value in the population will have its position parameters output as the localization result of the moving target. If the value is not less than the preset threshold, then a stagnation check is performed: If the stall condition is met, continue to step eight; Otherwise, if the stagnation condition is not met, proceed to step nine; Step 8: Obtain the search result with the smallest fitness function value from the historical search results. Individuals, and then from One individual is randomly selected from the total number of individuals, and Gaussian perturbation is applied to this selected individual to generate... Individuals, using generated Individuals and Acquisition Each individual becomes a new initial population, and then the process returns to step four. Step 9: Determine if the current iteration has reached the set maximum number of iterations; If the maximum number of iterations is reached, return to step three. If the maximum number of iterations has not been reached, then let Return to step five.

2. The multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to claim 1, characterized in that, The moving target transceiver anomaly model within the long baseline array is as follows: (1) in, This indicates the speed at which a signal travels through water. Represents the position coordinates of the moving target. Indicates the current speed of the moving target. The heading angle of a moving target. Indicates the first in the array The current position coordinates of each primitive. Indicates the first The transmission time from the signal transmitted by each element to the signal received by the target platform.

3. The multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to claim 2, characterized in that, The design process of the fitness function is as follows: Step 11: Based on the moving target transmit / receive anomaly model, obtain the relationship between latency and the position and velocity of the moving target platform: (2) in, This represents the position vector of the moving target platform. The superscript T indicates transpose; This represents the velocity vector of the moving target platform. , Represents the rectangular coordinates of a moving target in space. Velocity in the axial direction, Represents the rectangular coordinates of a moving target in space. Velocity in the axial direction, Represents the rectangular coordinates of a moving target in space. Velocity in the axial direction; Indicates the first The position vector of each primitive ; Expanding the left and right sides of equation (2) by squaring them simultaneously yields: (3) Steps 1 and 2: Establish the first The relationship between the observation delay and the actual delay for each primitive element is as follows: (7) in, Indicates the first The observation delay corresponding to each primitive Indicates the first The number of fuzzy cycles of each primitive relative to the moving target platform. For synchronization period, Indicates the first The time delay observation error of each element; By rearranging formula (7), we obtain the time delay observations and the unknown parameters of the platform. And the coupling parameter model between the number of fuzzy periods: (8) in, , Represents a continuous variable consisting of the position coordinates and velocity of the moving target platform; Substitute formula (3) into the right side of the coupling parameter model to calculate the observation delay corresponding to each primitive; Step 13: Establish the first The observed Doppler frequency shift corresponding to each primitive element Compared with the true Doppler frequency shift Relationship: (12) in, Indicates the first The Doppler frequency shift observation error corresponding to each element; True Doppler Shift for: (13) in, Indicates the first The center frequency of the signal transmitted by each element; Indicates the relationship between the target platform and the first The radial velocity of the moving target platform along the line connecting the individual elements; (14) in, Represents the L2 norm; Substituting equation (14) into equation (12), we obtain the first... Doppler frequency shift observations corresponding to each element Unknown parameters of the platform Coupled parameter model: (15) The Doppler frequency shift observations corresponding to each element are calculated according to the coupling parameter model of equation (15); Step 1, Section 4: Calculate the mean value of the time delay observation error based on the time delay observations corresponding to each primitive element. and standard deviation The mean value of the Doppler frequency shift observation error is calculated based on the Doppler frequency shift observations corresponding to each primitive element. and standard deviation ; Next, calculate the likelihood function based on time delay and Doppler frequency shift information. : (16) in, It is a constant term; Equation (16) can be simplified as follows: (17) in, ; (18) Step 15: Time Delay Observation Error Vector and Doppler frequency shift observation error vector The corresponding covariance matrix and They are respectively: (19) (20) in, Represents a diagonal matrix. Indicates the first The mean square error of the measurement delay of each primitive element Indicates the first The mean square error of the measured Doppler frequency shift of each element; Equation (17) can be rewritten as: (21) Here, the superscript -1 represents the inverse of the matrix; (22) (23) in, , express A discrete vector composed of the number of fuzzy cycles of each primitive relative to the moving target platform; Establish the fitness function for the differential evolution algorithm: (24) in, This represents the objective function controlled by time delay. This represents the objective function controlled by Doppler frequency offset. Indicates the weighting coefficient; (25) (26) in, This represents the time delay calculated based on the position, velocity, and number of fuzzy cycles in the current iteration of the differential evolution algorithm. This represents the Doppler frequency shift calculated based on the position, velocity, and number of ambiguity cycles in the current iteration of the differential evolution algorithm. , .

4. The multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to claim 3, characterized in that, The specific process of step two is as follows: (27) in, This indicates the preset maximum underwater acoustic range within a long-baseline underwater acoustic system. This indicates the target's acoustic beacon pulse transmission period. This indicates rounding the variable up. This represents the maximum number of ambiguity periods within the array range.

5. The multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to claim 4, characterized in that, The specific process of step three is as follows: (28) in, For population size, , This represents the dimension of the mixture variable parameters in each individual. Indicates the first in the initial population The first individual dimensional components, for A random number within the interval, Indicates the first The upper bound of the boundary of the dimensional component. Indicates the first Lower bound of the dimensional component; Initialize to: (29) in, .

6. The multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to claim 5, characterized in that, The specific process of step five is as follows: (30) in, As a variable factor, , and Indicates from the first Three individuals randomly selected from the population satisfy the following conditions: , , and They represent , and The Middle The value of the dimensional component, Indicates the first step after the crossover operation. The first individual The values ​​of the dimensional components; Perform relaxation and mutation operations on the discrete variable part of the fuzzy cycle number of the primitive: (31) The first Individuals obtained in the next iteration With variant individuals Perform a crossover operation to generate crossover individuals: (32) in, Indicates the first The crossover operation of the nth iteration produces the first Among the individuals, the first The values ​​of the dimensional components; Relaxation operations are performed on the discrete variable part: (33) Where CR is a constant, This indicates the range of population vector dimensions. The selected integer, Indicates the number of relaxation operations after the first relaxation operation. Among the individuals, the first The value of the dimensional component.

7. The multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to claim 6, characterized in that, The specific process of step six is ​​as follows: (34) in, Indicates the first The population obtained in the nth iteration The fitness function value of each individual. Indicates the first The population obtained in the nth iteration The fitness function value of each individual. Indicates the first The population obtained in the nth iteration Individual.

8. The multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to claim 7, characterized in that, The stagnation state check specifically involves determining whether formula (35) is satisfied: (35) in, Indicates the first The minimum fitness function value of all individuals in the population after the next iteration update. Indicates the first The iteration continues to the... The minimum fitness function value of all individuals in the population after the next iteration update. This indicates the calculation of absolute value. This indicates the set threshold. If equation (35) is satisfied, then the stagnation state is satisfied; otherwise, the stagnation state is not satisfied.

9. The multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to claim 8, characterized in that, The Gaussian perturbation generated from the randomly selected individuals Individuals, specifically: (36) in, This refers to randomly selected individuals. Indicates the first A random perturbation vector, Indicates the first generation generated by Gaussian perturbation Individual, .

10. The multi-information fusion unfuzzy localization method based on mixed variable differential evolution according to claim 9, characterized in that, The random perturbation vector for: (37) in, Represents a random perturbation vector The first in One element, For dimensional indexing, It is a scale factor. This represents a Gaussian distribution with a mean of 0 and a standard deviation of 1.

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