Inertial navigation method and system based on group coevolution

Abstract

The invention discloses an inertial navigation method and system based on group coevolution, and relates to the technical field of inertial navigation, and the method comprises the following steps: carrying out coarse alignment of double-vector attitude determination under a solidification coordinate system according to inertial navigation data; determining an optimization variable, and constructing a target function for initial alignment; solving a target function of initial alignment by utilizing a group coevolution algorithm to obtain an optimal variable group, and further calculating an attitude angle obtained based on a group coevolution coarse alignment method; on the basis, fine alignment of Kalman filtering is carried out, and after initial alignment of inertial navigation is completed, the carrier is switched into a navigation state to determine position coordinates. According to the method, initial alignment is performed based on the group coevolution algorithm, so that the orientation precision and robustness of inertial navigation can be effectively improved, and the navigation positioning precision is further improved.

Description

Technical Field

[0001] The present application relates to the technical field of inertial navigation, and particularly to an inertial navigation method and system based on group co-evolution. Background Art

[0002] Before an inertial navigation system is used for vehicle navigation, initial alignment must be performed to determine the initial values of navigation parameters such as attitude, azimuth, speed, and position, among which the initial alignment of azimuth is the most critical. In fact, inertial navigation initial alignment is a process of finding a reference navigation coordinate system to determine the spatial orientation of the vehicle coordinate system relative to the navigation coordinate system. The commonly used alignment scheme is to perform coarse alignment based on double-vector attitude determination in a fixed coordinate system and then perform fine alignment based on Kalman filtering. However, the coarse alignment based on double-vector attitude determination does not make full use of past data and can only obtain a relatively rough attitude matrix, often with a certain misalignment angle error, where the azimuth misalignment angle can reach dozens of angular minutes, thus affecting the orientation and positioning accuracy of inertial navigation. Optimal solution of the attitude matrix by fully using historical measurement data to minimize the misalignment angle error plays an important role in improving the initial alignment accuracy and is also of great benefit to the improvement of positioning accuracy. This belongs to an optimization problem.

[0003] Optimization refers to the process of obtaining the global optimal solution from multiple feasible solutions with the minimum time and computational cost when making problem decisions. This has attracted widespread attention in engineering applications such as medicine, health, economy, and technology, as well as path planning, parameter identification, and image segmentation. With the emergence of more nonlinear, large-scale, high-dimensional, and complex constraint problems containing incomplete information, it is becoming increasingly difficult to find the optimal solution. In most application scenarios, optimization has become a non-deterministic polynomial (NP-hard) problem. The time required for traditional accurate calculation methods is exponentially increasing and it is difficult to obtain the global optimal solution. Metaheuristic algorithms inspired by nature came into being in the 1980s. As an approximate calculation method, metaheuristic algorithms do not need to understand the specific characteristics of the problem, can effectively use information in the problem search space, and iteratively find the optimal solution in a relatively short time. They have the advantages of simple calculation steps, relatively small amount of calculation, easy combination of quantitative and qualitative analysis, and strong versatility. In recent years, metaheuristic algorithms have flourished, and metaheuristic optimization algorithms designed to simulate certain phenomena or behaviors in nature have emerged in an endless stream, such as the genetic algorithm (GA) designed to simulate biological genetics, the Kepler optimization algorithm (KOA) proposed based on the laws of planetary motion, the particle swarm optimization algorithm (PSO) that imitates the collective behavior of fish or bird flocks, and the rich-poor optimization algorithm (PRO) based on human efforts to achieve a better life. The hybrid improvement strategy of the ant colony optimization algorithm and the genetic algorithm, the particle swarm optimization algorithm and the gray wolf optimization algorithm, the sparrow search algorithm and the bird flock optimization algorithm is more common, but the improvement of the optimization effect is very limited. According to the No Free Lunch Theorem (NFL), each algorithm has its own type of problem that can be solved efficiently, and no algorithm can solve all problems with the same performance.

[0004] Therefore, how to effectively break through the limitations of a single algorithm model and further improve the accuracy and stability of optimization, especially to be able to universally apply it to solving different types of optimization problems with outstanding performance, is a technical problem that needs to be urgently solved in the current field of optimization algorithms. Summary of the invention

[0005] The purpose of this application is to provide an inertial navigation method and system based on swarm collaborative evolution, which can solve the problems of low optimization accuracy, poor stability and difficulty in achieving universality that cannot be overcome when using a single algorithm for optimization and solution, further improve the orientation accuracy and robustness of inertial navigation, and thus improve positioning accuracy.

[0006] To achieve the above objectives, this application provides the following solutions: In a first aspect, the present application provides an inertial navigation method based on group collaborative evolution, comprising: Based on inertial navigation data, the rough alignment in the fixed coordinate system is completed using the dual-vector attitude determination algorithm; Determine the optimization variables and construct the objective function for the initial alignment based on the optimization variables; Use the group co-evolution algorithm to solve the objective function of the initial alignment to obtain the optimal variable group; Based on the optimal variable group, calculate the attitude transformation matrix obtained by the group co-evolution rough alignment method; Based on the attitude transformation matrix, use Kalman filtering for fine alignment to determine the attitude matrix; The carrier switches to the navigation state, and the position coordinates are determined based on the attitude matrix for navigation solution.

[0007] Optionally, the rough alignment includes determining the attitude transformation matrix between the carrier inertial system and the navigation inertial system.

[0008] Optionally, the attitude transformation matrix is: ; Wherein, is the attitude transformation matrix; is the gravity vector in the navigation inertial system at time is the gravity vector in the navigation inertial system at time is the specific force measurement value vector in the carrier inertial system at time is the specific force measurement value vector in the carrier inertial system at time

[0009] Optionally, the objective function is: ; Wherein, m is the number of non-coplanar vectors measured under the static base condition; is the gravity vector in the navigation inertial system of the i-th; is the specific force measurement value vector in the carrier inertial system of the i-th.

[0010] Optionally, the use of the group co-evolution algorithm to solve the objective function of the initial alignment to obtain the optimal variable group includes: Initialize the basic parameters of the group co-evolution algorithm; the basic parameters include: the target population size Popsize, the total iteration number threshold IterNum, the co-evolution timing CENum, and the merger timing MergerNum; Let the outer loop iteration number j = 1; Obtain N basic algorithms; the types of the N basic algorithms are all different; Let the number of basic algorithms n = N; The population is initialized to obtain the initial total population; For each basic algorithm, allocate the corresponding initial small population from the initial total population; Determine the initial performance evaluation metrics for each basic algorithm respectively; any initial performance evaluation metric is obtained after preliminarily optimizing the basic algorithm using the corresponding initial small population; Determine that the initial performance evaluation metric is the performance evaluation metric of the corresponding basic algorithm at the 0th iteration; Expand the population size of the initial total population to the target population size Popsize to obtain the population at the 0th iteration; Use the population at the (j - 1)th iteration and the performance evaluation metrics of different basic algorithms at the (j - 1)th iteration to perform N - 1 rounds of iterative optimization on the basic algorithms to obtain the optimal basic algorithm at the jth iteration; Determine the total number of iterations; ; where is the total number of iterations, and u is a variable; Judge whether the total number of iterations reaches the total iteration number threshold IterNum to obtain the judgment result; If the judgment result is no, then increase the value of the outer loop iteration number j by 1 and return to the step "Use the population at the (j - 1)th iteration and the performance evaluation metrics of different basic algorithms at the (j - 1)th iteration to perform N - 1 rounds of iterative optimization on the basic algorithms to obtain the optimal basic algorithm at the jth iteration"; If the judgment result is yes, then determine the optimal variable group from the individuals corresponding to the optimal fitness value in the optimal basic algorithm at the jth iteration.

[0011] Optionally, using the population at the (j - 1)th iteration and the performance evaluation metrics of different basic algorithms at the (j - 1)th iteration to perform N - 1 rounds of iterative optimization on the basic algorithms to obtain the optimal basic algorithm at the jth iteration includes: Take the population at the (j - 1)th iteration as the population at the 0th iteration; Take the performance evaluation metrics of different basic algorithms at the (j - 1)th iteration as the performance evaluation metrics of different basic algorithms at the 0th iteration; Let the inner loop iteration number q = 1; Based on the performance evaluation metrics of each basic algorithm at the (q - 1)th iteration, use the roulette wheel method to determine the population allocation quantity for each basic algorithm; Based on the population allocation quantity, determine the small population of each basic algorithm at the (q - 1)th iteration from the population at the (q - 1)th iteration; Based on the equal running time mechanism, use the small population of each basic algorithm at the (q - 1)th iteration to perform iterative optimization on the corresponding basic algorithm respectively until the iterative optimization times reach the co - evolution opportunity CENum; Based on the co-evolution mechanism, calculate the fitness values of all individuals; the fitness values are the objective function values of the initial alignment; the co-evolution mechanism includes: a sharing mechanism, a communication mechanism, and an elimination and renewal mechanism; the elimination and renewal mechanism is used to update the small populations assigned to each basic algorithm, and obtain the small populations of each basic algorithm at the q-th iteration; Determine the performance evaluation metrics of the n basic algorithms at the q-th iteration respectively; Determine that the set of the small populations of the n basic algorithms at the q-th iteration is the population at the q-th iteration; Increase the value of the iteration count q by 1, and return to the step "Based on the performance evaluation metrics of each basic algorithm at the (q - 1)-th iteration, use the roulette wheel method to determine the population allocation quantity of each basic algorithm" until the value of the iteration count q reaches the merger opportunity MergerNum; Arrange the basic algorithms in descending order according to the performance evaluation metrics at the q-th iteration; Take the small population corresponding to the n-th basic algorithm and the small population corresponding to the 1st basic algorithm as the updated small population corresponding to the 1st basic algorithm at the q-th iteration; Delete the n-th basic algorithm, and decrease the value of the basic algorithm quantity n by 1; Take the performance evaluation metrics at the q-th iteration as the performance evaluation metrics of the corresponding basic algorithm at the 0-th iteration; Take the set of the small populations of all basic algorithms at the q-th iteration as the population at the 0-th iteration; Return to the step "Set the inner loop iteration count q = 1" until the basic algorithm quantity n is equal to 1, and obtain the optimal basic algorithm at the j-th iteration; Determine that the population at the q-th iteration is the population at the j-th iteration; Determine that the performance evaluation metrics of different basic algorithms at the q-th iteration are the performance evaluation metrics of different basic algorithms at the j-th iteration.

[0012] Optionally, the multiple basic algorithms include the sand cat swarm optimization algorithm, the sparrow search algorithm, the spider wasp optimization algorithm, the particle swarm algorithm, and the Kepler optimization algorithm.

[0013] Optionally, the performance evaluation metric is: ; In the formula, represents the performance evaluation metric of the n-th basic algorithm; represents the prior performance index of the n-th basic algorithm; represents the absolute accuracy index of the n-th basic algorithm; represents the relative accuracy index of the n-th basic algorithm; Denote the optimization efficiency index of the nth basic algorithm; Denote the fluctuation index of the nth basic algorithm; Denote the comprehensive performance index of the nth basic algorithm; and Both denote the model empirical coefficient.

[0014] Optionally, the attitude matrix is: where is the attitude matrix; is the transformation matrix from the navigation inertial system to the navigation coordinate system at the initial moment; is the transformation matrix from the vehicle coordinate system to the vehicle inertia at the initial moment.

[0015] In a second aspect, the present application provides an inertial navigation system based on group co-evolution, including: A coarse alignment module, configured to perform coarse alignment in the fixed coordinate system based on inertial navigation data by using a dual-vector attitude determination algorithm; A target function construction module, configured to determine optimization variables and construct a target function for initial alignment based on the optimization variables; A target function module, configured to solve the target function of initial alignment by using a group co-evolution algorithm to obtain an optimal variable group; An attitude transformation matrix determination module, configured to calculate an attitude transformation matrix obtained by the group co-evolution coarse alignment method based on the optimal variable group; A fine alignment module, configured to perform fine alignment by using Kalman filtering based on the attitude transformation matrix to determine the attitude matrix; A coordinate determination module, configured to transfer the vehicle into the navigation state and complete the determination of the position coordinates based on the attitude matrix for navigation solution.

[0016] According to the specific embodiments provided by the present application, the following technical effects are disclosed in the present application: The present application provides an inertial navigation method and system based on group co-evolution. By simulating processes such as competition, cooperation, and evolution among social groups, a variety of meta-heuristic algorithms are comprehensively used, enabling them to cooperate closely and co-evolve, thereby forming a group co-evolution algorithm that efficiently integrates the advantages of various algorithms. Through the cooperation of multiple co-evolution mechanisms, the algorithm can effectively jump out of local optimal solutions and achieve accurate convergence. The exploration ability and development ability of the algorithm are more balanced. Compared with single algorithms and other advanced algorithms, the proposed algorithm has significant advantages in convergence accuracy. It integrates the advantages of various basic algorithms and has a certain universality in solving various problems, especially more successful in solving complex optimization problems. It has important reference value for problems such as large-scale parallel computing, parameter identification, task planning, and decision optimization, strongly promoting the fundamental transformation of meta-heuristic algorithms and the research progress of multi-algorithm co-evolution, and thus improving the positioning and orientation accuracy and robustness of inertial navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0018] Figure 1 It is a flowchart of an inertial navigation method based on group co-evolution in an embodiment of the present application; Figure 2 It is a flowchart of the group co-evolution algorithm in an embodiment of the present application; Figure 3 It is the first schematic diagram of the optimization result of a test function in an embodiment of the present application; Figure 4 It is the second schematic diagram of the optimization result of a test function in an embodiment of the present application; Figure 5 It is the third schematic diagram of the optimization result of a test function in an embodiment of the present application; Figure 6 It is the fourth schematic diagram of the optimization result of a test function in an embodiment of the present application; Figure 7 It is the fitness value evolution curve diagram of the algorithm executed 100 times in an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0020] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0021] Embodiment 1 As Figure 1 shown, Embodiment 1 provides an inertial navigation method based on group co-evolution, including: Step 101: Based on inertial navigation data, use the double-vector attitude determination algorithm to complete the rough alignment in the fixed coordinate system.

[0022] For the rough alignment of double-vector attitude determination in the fixed coordinate system based on inertial navigation data. Two important inertial coordinate systems need to be defined for the rough alignment in the fixed coordinate system. One is the initial carrier inertial system (b0), which coincides with the carrier coordinate system (b system) at the initial moment of alignment and then has no rotation relative to the inertial space. The attitude matrix is calculated in real time according to the attitude update algorithm from the measurement values of the gyroscope and is used to represent the transformation relationship between the two coordinate systems. The other is the initial navigation inertial system (n0), which coincides with the navigation coordinate system (n system) at the initial moment of alignment and then has no rotation relative to the inertial space. The n system rotates around a fixed axis relative to the n0 system, and the attitude matrix can be calculated in real time according to the earth's angular velocity of rotation. Therefore, the key to the initial rough alignment method in the fixed coordinate system is to solve the azimuth relationship between the b0 system and the n0 system, that is, the constant matrix .

[0023] The gravity vector in the n0 system and its specific force measurement value vector in the b0 system can be directly obtained through measurement or calculation. Two matrix equations are established for the two vectors at the half-alignment moment t1 and the end-alignment moment t2, and then the attitude transformation matrix can be solved using the double-vector attitude determination algorithm, that is, .

[0024] Among them, is the attitude transformation matrix. is the gravity vector in the navigation inertial system at the moment. is the gravity vector in the navigation inertial system at the is the specific force measurement value vector in the carrier inertial system at time is the specific force measurement value vector in the carrier inertial system at time

[0025] Step 102: Determine the optimization variables and construct the objective function for initial alignment based on the optimization variables.

[0026] Determine the optimization variables and construct the objective function for initial alignment. The optimization variables are the attitude angles including the pitch angle α, roll angle β, and azimuth angle γ in because the attitude angles correspond one-to-one with the attitude matrix

[0027] Assume that m non-coplanar vectors are measured under static base conditions and measured in the n0 system and b0 system. Due to the existence of measurement errors, the following relationship is approximately satisfied: .

[0028] where the attitude transformation matrix is obtained from the optimization variables , and through transformation. The difference between both ends of the equal sign reflects the inconsistency error of the same physical vector in two coordinate systems. To quantitatively describe the "optimal" performance, the objective function is constructed here as: .

[0029] where m is the number of non-coplanar vectors measured under static base conditions. is the gravity vector in the i-th navigation inertial system. is the specific force measurement value vector in the i-th carrier inertial system.

[0030] Step 103: Use the group co-evolution algorithm to solve the objective function of initial alignment and obtain the optimal variable group.

[0031] Step 103 includes: Step 103-1: Initialize the basic parameters of the group co-evolution algorithm. The basic parameters include: the target population size Popsize, the total iteration number threshold IterNum, the co-evolution opportunity CENum, and the merger opportunity MergerNum.

[0032] Step 103-2: Let the number of outer loop iterations \(j = 1\).

[0033] Step 103-3: Obtain \(N\) basic algorithms. The types of the \(N\) basic algorithms are all different. The multiple basic algorithms include the sand cat swarm optimization algorithm, the sparrow search algorithm, the spider wasp optimization algorithm, the particle swarm algorithm, and the Kepler optimization algorithm.

[0034] Step 103-4: Let the number of basic algorithms \(n = N\).

[0035] Step 103-5: Initialize the population to obtain the initial total population.

[0036] Step 103-6: Allocate the corresponding initial small population for each basic algorithm from the initial total population.

[0037] Step 103-7: Determine the initial performance evaluation metrics for each basic algorithm respectively. Any initial performance evaluation metric is obtained after preliminarily optimizing the basic algorithm using the corresponding initial small population. The performance evaluation metrics are: 。

[0038] In the formula, represents the performance evaluation metric of the \(n\)th basic algorithm. represents the prior performance index of the \(n\)th basic algorithm. represents the absolute accuracy index of the \(n\)th basic algorithm. represents the relative accuracy index of the \(n\)th basic algorithm. represents the optimization efficiency index of the \(n\)th basic algorithm. represents the fluctuation index of the \(n\)th basic algorithm. represents the comprehensive performance index of the \(n\)th basic algorithm. and both represent the model experience coefficients.

[0039] Step 103-8: Determine that the initial performance evaluation metric is the performance evaluation metric of the corresponding basic algorithm at the 0th iteration.

[0040] Step 103-9: Expand the population size of the initial total population to the target population size Popsize to obtain the population at the 0th iteration.

[0041] Step 103-10: Use the population at the \((j - 1)\)th iteration and the performance evaluation metrics of different basic algorithms at the \((j - 1)\)th iteration to perform \(N - 1\) rounds of iterative optimization on the basic algorithms to obtain the optimal basic algorithm at the \(j\)th iteration.

[0042] Step 103-11: Determine the total number of iterations. 。Among them is the total number of iterations, and \(u\) is a variable.

[0043] Step 103-12: Determine whether the total number of iterations reaches the total iteration number threshold IterNum to obtain a judgment result.

[0044] Step 103-13: If the judgment result is no, increase the value of the outer loop iteration number j by 1 and return to Step 103-10.

[0045] Step 103-14: If the judgment result is yes, determine the optimal variable group corresponding to the individual with the optimal fitness value in the optimal basic algorithm at the j-th iteration.

[0046] Step 103-10 includes: Step 103-10-1: Use the population at the (j - 1)-th iteration as the population at the 0-th iteration.

[0047] Step 103-10-2: Use the performance evaluation metrics of different basic algorithms at the (j - 1)-th iteration as the performance evaluation metrics of different basic algorithms at the 0-th iteration.

[0048] Step 103-10-3: Let the inner loop iteration number q = 1.

[0049] Step 103-10-4: Based on the performance evaluation metrics of each basic algorithm at the (q - 1)-th iteration, use the roulette wheel method to determine the population allocation quantity of each basic algorithm.

[0050] Step 103-10-5: Based on the population allocation quantity, determine the small population of each basic algorithm at the (q - 1)-th iteration from the population at the (q - 1)-th iteration.

[0051] Step 103-10-6: Based on the equal running time mechanism, use the small population of each basic algorithm at the (q - 1)-th iteration to perform iterative optimization on the corresponding basic algorithm respectively until the number of iterative optimization reaches the co-evolution opportunity CENum.

[0052] Step 103-10-7: Based on the co-evolution mechanism, calculate the fitness value of all individuals. The fitness value is the objective function value of the initial alignment. The co-evolution mechanism includes: sharing mechanism, communication mechanism, and elimination and recruitment mechanism. The elimination and recruitment mechanism is used to update the small population allocated to each basic algorithm to obtain the small population of each basic algorithm at the q-th iteration.

[0053] Step 103-10-8: Determine the performance evaluation metrics of n basic algorithms at the q-th iteration respectively.

[0054] Step 103-10-9: Determine that the set of the small populations of n basic algorithms at the q-th iteration is the population at the q-th iteration.

[0055] Step 103-10-10: Increase the value of the iteration count q by 1, and return to Step 103-10-4 until the value of the iteration count q reaches the merger opportunity MergerNum.

[0056] Step 103-10-12: Sort the basic algorithms in descending order according to the performance evaluation metric at the q-th iteration.

[0057] Step 103-10-13: Use the small population corresponding to the n-th basic algorithm and the small population corresponding to the 1st basic algorithm as the small population corresponding to the 1st basic algorithm at the updated q-th iteration.

[0058] Step 103-10-14: Delete the n-th basic algorithm, and decrease the value of the basic algorithm count n by 1.

[0059] Step 103-10-15: Use the performance evaluation metric at the q-th iteration as the performance evaluation metric for the corresponding basic algorithm at the 0-th iteration.

[0060] Step 103-10-16: Use the set of small populations corresponding to all basic algorithms at the q-th iteration as the population at the 0-th iteration.

[0061] Step 103-10-17: Return to the step "Set the inner loop iteration count q = 1" until the basic algorithm count n equals 1, to obtain the optimal basic algorithm at the j-th iteration.

[0062] Step 103-10-18: Determine the population at the q-th iteration as the population at the j-th iteration.

[0063] Step 103-10-19: Determine the performance evaluation metrics of different basic algorithms at the q-th iteration as the performance evaluation metrics of different basic algorithms at the j-th iteration.

[0064] Step 104: Based on the optimal variable group, calculate the attitude transformation matrix obtained by the group co-evolution coarse alignment method. The attitude matrix is: .

[0065] Where, is the attitude matrix. is the transformation matrix from the navigation inertial system to the navigation coordinate system at the initial moment. is the transformation matrix from the vehicle coordinate system to the vehicle inertial system at the initial moment.

[0066] Step 105: Based on the attitude transformation matrix, use Kalman filtering for fine alignment to determine the attitude matrix.

[0067] Step 106: The vehicle enters the navigation state, and based on the attitude matrix, perform navigation solution to complete the determination of the position coordinates.

[0068] Co - evolution is a very important phenomenon from both the perspectives of natural science and social science. With the development of human society to the present, it no longer focuses on individual interests, but increasingly emphasizes co - evolution based on common interests, which includes information sharing, team restructuring, individual mobilization, elimination and recruitment within a group, information exchange, team collaboration, assessment and competition and annexation between groups, as well as the process of selection, distribution, and resource tilt of the market environment towards dominant groups. The swarm co - evolution algorithm (SCEA) designs five co - evolution mechanisms of sharing and communication, assessment, selection and distribution, elimination and recruitment, and annexation and monopoly based on multiple basic optimization algorithms. The specific method is as follows: Select a basic optimization algorithm and complete parameter initialization, perform pre - optimization with a small population and a small number of times to provide a basis for algorithm evaluation and population distribution; then each basic algorithm performs iterative optimization; when the co - evolution opportunity arrives, successively execute the mechanisms of sharing, communication, and elimination and recruitment, and re - evaluate the algorithm and distribute the population according to the optimization results; when the annexation opportunity arrives, perform an annexation operation on the algorithm until the global optimal solution is output when the algorithm reaches the maximum number of iterations. This algorithm realizes the efficient integration and co - evolution of multiple algorithms, making it have more prominent optimization accuracy, stability, and universality.

[0069] Such as Figure 2 , the swarm co - evolution algorithm includes: Step 1: Initialization; Initialize the model parameters of the selected basic algorithm and define the basic parameters of the swarm co - evolution algorithm.

[0070] Step 2: Population initialization; Define the dimension and upper and lower limit intervals of the feasible solution according to the problem to be optimized, and randomly generate some feasible solutions within the search space.

[0071] Step 3: Preliminary pre - optimization; Allocate the same initial small population to each basic algorithm in advance, perform preliminary iteration for several times for pre - optimization, evaluate the performance of the basic algorithm through assessment, and provide a prior probability and a basis for population distribution for in - depth iterative optimization.

[0072] Step 4: Iterative optimization; Expand the population size to Popsize, and allocate the initial population for each basic algorithm according to the performance evaluation of the algorithm. Then, perform in - depth iterative optimization according to the equal running - time mechanism. When the co - evolution opportunity arrives, execute co - evolution mechanisms such as sharing, communication, and elimination and recruitment. After calculating the fitness value of individuals, re - evaluate the performance of the algorithm and redistribute the population individuals. When the annexation opportunity arrives, the algorithm with the worst performance will no longer execute, and the population individuals belonging to it will be absorbed by the algorithm with the best performance until a monopoly situation where only one algorithm remains is reached.

[0073] Step 5: Record the position of the best population individual and its optimal solution at the current iteration number.

[0074] Step 6: Determine whether the maximum number of iterations has been reached. If the algorithm termination condition is satisfied, output the current optimal solution; otherwise, return to Step 4 to continue the iterative optimization search.

[0075] Furthermore, in Step 1, the parameter initialization of the basic algorithm is obtained by referring to the best model parameters provided by the respective algorithm proposers. The prior probability of the basic algorithm is initially assigned with equal probability, and other model parameters are set according to actual experience.

[0076] Furthermore, in Step 2, the implementation method for initializing a population of d dimension with a size of Popsize is as follows: (1) where represents the i -th j dimensional variable of the individual i ∈ [1, Popsize], j ∈ [1, d , ub j and lb j respectively represent the upper and lower limits of this variable, and rand is a random number between 0 and 1.

[0077] Furthermore, in Step 3, the specific implementation method for the performance evaluation and assessment of each basic algorithm after preliminary iterative optimization is as follows: Based on the fitness evolution curve of the algorithm, which reflects the historical performance and future trends of the algorithm, and using this as an important basis for the assessment, algorithms with outstanding performance can obtain more population resource inclination.

[0078] The specific indicators considered include: Prior performance indicator P p : Different algorithms have their own unique advantages and applicable problem types. The suitability between the problem to be solved and the selected algorithm is quantitatively evaluated through the prior indicator P p , and , N represents the number of selected basic algorithms.

[0079] Absolute accuracy indicator A 1 and relative accuracy indicator A 2: They are respectively used to describe the maximum effect of fitness improvement relative to all algorithms after iterative evolution and the average effect of fitness value improvement relative to their respective algorithms after iterative optimization. Their implementation methods are as follows: (2) (3) In the formula, f i,j represents the fitness function value of the i th generation of the j th algorithm, Iter is the number of iterations up to now.

[0080] Optimization efficiency index E : The slope of the fitness value evolution curve can characterize the optimization effect of the algorithm. Calculate the average evolution slope within the number of iterations as a measure of the optimization efficiency of the algorithm. The larger this value is, the higher the optimization efficiency and the better the optimization performance of the algorithm. The calculation formula is as follows: (4) In the formula, K i,j is the evolution slope of the i th generation of the j th algorithm, mean (·) is the function for calculating the mean value.

[0081] Fluctuation index D : The fluctuation performance index is used to measure the dynamic dependence degree of the algorithm on the random initial value and the evolutionary operation. The smaller its value is, the higher the approximation degree of the algorithm to the optimal solution and the better the optimization performance of the algorithm. Its implementation method is as follows: (5) Comprehensive performance index S : Its calculation method is shown in the following formula. The performance of the algorithm is comprehensively evaluated by the area of the region formed by the iteration curve and the coordinate axes. The smaller the area of this region is, the better the comprehensive optimization performance of the algorithm.

[0082] (6) Normalize the above 6 indicators for the assessment of the algorithm performance and use them as the basis for the next population selection and allocation. Its specific implementation method is: (7) In the formula, c 1 and c 2 are the model empirical coefficients. The 5 indicators are in different magnitudes, so normalization processing is required, and the mean value after normalization is 1 / N . c 1 is taken as 5 / N , if the normalized indicator is greater than the average value, it indicates that this algorithm is more excellent than other algorithms. Then the evaluation result of the algorithm should be further increased on the basis of the prior probability. Otherwise, it will have a decaying effect on the prior probability, and the amplitude of increase or decay is closely related to the gap between each indicator and the mean value.c 2 is used to scale the model calculation value.

[0083] Furthermore, in step 4, the detailed implementation method of iterative optimization is as follows: Step 4.1: Initialize some populations on the basis of the preliminary optimization population size to increase the population size to Popsize, and according to the algorithm evaluation results of the preliminary optimization, select and allocate the initial populations for each basic algorithm respectively. The implementation process of selection and allocation is as follows: Define score as the normalized algorithm evaluation result, which is also the proportion of the strength of a certain algorithm in the entire algorithm group. Determine the number allocated to each algorithm by the roulette wheel method. The core idea is that the score higher, the larger the sector area it occupies in the circle, and the higher the probability that the algorithm is selected. A total of M= 1000 landing tests are carried out, and the number of times of falling in the area occupied by each algorithm is counted m , and the number of individuals allocated to this algorithm is Popsize × m / M . During the selection and allocation process, try to keep the population stable on the basis of the original algorithm population, and transfer the individuals that the algorithm needs to reduce from the back to the front to the algorithm population that needs to increase individuals in turn.

[0084] Step 4.2: Conduct in-depth iterative optimization according to the equal running time mechanism. This is because algorithms with lower running time costs can run more times in the same time. Therefore, iterative optimization is carried out by assigning the corresponding number of iterations to each algorithm according to the inverse ratio of the running time of each algorithm.

[0085] Step 4.3: When the co-evolution opportunity is reached, execute co-evolution operators such as sharing, communication, elimination, and recruitment, and calculate the fitness values of the corresponding individuals.

[0086] Step 4.4: After co-evolution, perform iterative optimization. Before the next co-evolution, re-evaluate and sort the algorithm performance according to the assessment method in step 3, and select and allocate the corresponding populations for each algorithm according to step 4.1 based on the algorithm evaluation results, and then return to step 4.2 to continue optimization.

[0087] Step 4.5: When the annexation opportunity is reached, annex the algorithm with the worst performance in step 4.4. The algorithm will not be executed in the next iterative optimization, and the population individuals belonging to it will be absorbed by the algorithm with the best performance until a monopoly situation where only one algorithm remains, otherwise return to step 4.2 to continue optimization.

[0088] Furthermore, in step 4.3, the specific implementation method of the co-evolution mechanism of sharing, communication, elimination, and recruitment is as follows: Step 4.3.1: The sharing mechanism is realized by the process of sharing and communicating the optimal individuals and replacing the worst individuals, that is, N each algorithm selects p optimal individuals and shares them with other algorithms, and itself will also receive ( N -1)× p optimal individuals of the other algorithms and eliminates the individuals with the worst fitness values ( N -2)× p , and each no longer retains its original optimal individuals.

[0089] Step 4.3.2: The communication mechanism refers to the operation process in which two individuals generate two new individuals through arithmetic operations, so as to increase the diversity of the population, improve the global search ability of the algorithm and the ability to jump out of the local optimum. When implementing, real number coding and arithmetic crossover are adopted. The specific process is as follows: Suppose the two crossover individuals are and , and determine whether to perform the crossover operation with the crossover probability P c . When performing the crossover, then select some variables in the parent individuals to perform arithmetic crossover with the probability P c . First, randomly generate d random real numbers in the interval [0, P c and round them, and then find the positions where the values are 1 P 1, P 2,..., P m , which are the variables to be crossed. Then randomly generate m random real numbers in the interval [0, 1] a i ( i = P 1, P 2,..., P m ). After the crossover operation, the two offspring can be expressed as: (8) The arithmetic crossover of adaptive crossover changes adaptively according to the fitness distribution state of the population P c , so as to achieve a balance between exploitation and exploration. When the fitness of the population individuals tends to be consistent or tends to the local optimum, make P c increase, and when the population fitness is relatively scattered, make P c decrease. At the same time, for individuals with fitness higher than the average fitness of the population, corresponding to lowerP c , enabling these individuals to be protected and enter the next generation, while individuals with fitness below the average correspond to higher P c , causing this part of the individuals to be eliminated, P c The calculation of is shown in the following formula.

[0090] (9) In the formula, P c1 and P c2 are the upper and lower limit ranges of the adaptive crossover operator respectively, f max is the maximum fitness value in the population, f avg is the average fitness value of each generation of the population, f is the larger fitness value among the two individuals to be crossed.

[0091] Step 4.3.3 Discard individuals who cannot contribute more to the team through the end-elimination mechanism, and at the same time incorporate new individuals to make up for the vacancies. Define the ratio of end-elimination to new inclusion as P E , directly eliminate individuals with a proportion of the lower rankings in each algorithm after sorting the population fitness values by P E , and initialize the same number of new individuals to supplement the original population for the next iteration optimization.

[0092] The sand cat swarm optimization algorithm (SCSO), sparrow search algorithm (SSA), spider wasp optimization algorithm (SWO), particle swarm optimization algorithm (PSO), and Kepler optimization algorithm (KOA) are selected as the basic algorithms to specifically illustrate the swarm co-evolution algorithm shown in this embodiment.

[0093] S1: Initialization; Initialize according to the model parameters provided by the respective algorithm proposers, and then define the basic parameters of the swarm co-evolution algorithm, including the population size Popsize = 100, the number of iterations IterNum = 5000, the co-evolution opportunity CENum = 500, the merger opportunity MergerNum = 1000, the communication probability P c = 0.2, the elimination and new inclusion ratio P E = 0.2, and assign equal probabilities to the prior probabilities of the selected basic algorithms.

[0094] S2: Population initialization; clarify the dimension and upper and lower limit intervals of the feasible solutions according to the problem to be optimized, and randomly generate a certain number of feasible solutions within the search space according to Equation (1).

[0095] S3: Preliminary pre-optimization; pre-allocate the same initial small population of size 10 to the 5 selected basic algorithms, and perform preliminary iteration 20 times for pre-optimization. Evaluate the performance of the basic algorithms through the assessment mechanism provided in step 3 of the invention content, and use the results as the prior probability and population allocation basis for in-depth iterative optimization.

[0096] S4: Iterative optimization; add an initialized population to expand the population size to Popsize = 100; S4-1: According to the algorithm performance evaluation in S3, allocate the respective initial populations to each basic algorithm using the selection and allocation implementation method described in step 4.1; S4-2: Set the respective iteration times for each basic algorithm according to the equal running time mechanism, and perform in-depth iterative optimization according to their respective algorithm processes; S4-3: When the iteration times Iter reach the co-evolution opportunity, that is Iter= CENum, implement the co-evolution of the algorithm according to the sharing mechanism described in step 4.3.1, the communication mechanism described in step 4.3.2, and the elimination and recruitment mechanism described in step 4.3.3 respectively.

[0097] S4-4: After the co-evolution is completed, continue with iterative optimization. Before the next implementation of co-evolution, re-evaluate and rank the algorithm performance by executing the assessment provided in step 3 again, and then re-allocate the population to each algorithm according to the selection and allocation method provided in step 4.1, and then return to S4-2 to continue iterative optimization.

[0098] S4-5: When the iteration times Iter reach the annexation opportunity, that is Iter= MergerNum, the algorithm with the worst performance evaluation in S4-4 will no longer be executed, and the individuals of its affiliated population will be absorbed by the algorithm ranked first in performance until a monopoly situation where only one algorithm remains is reached.

[0099] S5: Record the position of the best population individual and its optimal solution at the current iteration times; S6: When the maximum iteration times is reached, that is Iter = IterNum, the algorithm terminates and outputs the global optimal solution, otherwise return to S4 to continue iterative optimization.

[0100] Embodiment 2 The proposed swarm co-evolution algorithm is tested through four different types of functions in the CEC2022 test set. The detailed information is given in Table 1, which provides significant and diverse search obstacles for algorithm testing and fully verifies the convergence accuracy, stability and universality of the algorithm's optimization effect.

[0101] Table 1 Test results of different types of functions on the swarm co-evolution algorithm

[0102] In order to verify the advancement and feasibility of the proposed swarm collaborative evolution algorithm (SCEA), the optimization results are compared with the selected single basic algorithm and other 7 advanced metaheuristic algorithms, namely, raccoon optimization algorithm (COA), gray wolf optimization algorithm (GWO), whale optimization algorithm (WOA), pelican optimization algorithm (POA), dandelion optimization algorithm (DOA), star bird optimization algorithm (NOA) and Ludo game group intelligence algorithm (LGSI). The population size and the number of iterations are set to the same value to ensure the objectivity and fairness of the comparative experiment. Each algorithm is run independently on each test function 100 times, and the average value, optimal value and standard deviation of the optimization results are recorded, and the algorithm performance is ranked based on this. In order to enable technicians in this field to see the experimental results more intuitively, the results of the comparative test are shown in Tables 2 and 3. Figures 3 - 6 shown.

[0103] Table 2 Performance comparison of different algorithms

[0104] From the test results, it can be seen that the proposed swarm co-evolution algorithm has significantly improved the optimization accuracy compared with a single basic algorithm, and is also more advanced than other optimization algorithms, which verifies the effectiveness of the co-evolution mechanism between multiple algorithms. For test functions of different types and characteristics, the comprehensive performance of the swarm co-evolution algorithm can be at the forefront, indicating that the proposed algorithm integrates the advantages of various basic algorithms and has a certain universality in the face of various optimization problems.

[0105] Example 3 The proposed algorithm is applied to inertial navigation to verify the practical application effect of the swarm collaborative evolution algorithm and the effectiveness of improving the orientation accuracy of inertial navigation. The inertial navigation system is fixedly installed on the vehicle, the vehicle engine is in the starting state, and there are disturbances such as people opening and closing the door, getting on and off the vehicle. Ten groups of inertial navigation data under the condition of 5-minute static base shaking are collected, and initial alignment tests of four alignment schemes are carried out, including 1-minute coarse alignment, 5-minute fine alignment, 1-minute coarse alignment + SCEA optimal alignment, and 1-minute coarse alignment + SCEA optimal alignment + 5-minute fine alignment.

[0106] The results of the orientation test of the inertial navigation method are shown in Table 3. We focus on the azimuth alignment accuracy. The results show that the root mean square error and standard deviation of the 10 groups of alignment tests can be improved from 0.4049° and 0.4268° to 0.3057° and 0.3222° respectively by further optimizing the swarm co-evolution algorithm on the basis of rough alignment. It can be seen that the proposed swarm co-evolution algorithm is very successful in the application of the initial alignment problem of inertial navigation. After using this result as the initial value of fine alignment and further implementing fine alignment based on Kalman filtering, the root mean square error and standard deviation can be greatly improved from 0.2173° and 0.229° to 0.038° and 0.0401° respectively, which effectively verifies the feasibility, advancement and robustness of the inertial navigation method based on swarm co-evolution under the condition of static base shaking. Figure 7 The fitness value evolution curve of 100 executions in the inertial navigation directional optimization process is given. The objective function achieved a minimum value of 0.2875 and an average value of 0.2883, and the standard deviation was as low as 4.1712e-4. It can be seen that the swarm collaborative evolution algorithm is an efficient, advanced and stable optimization algorithm.

[0107] Table 3 Results of orientation test using inertial navigation method

[0108] Example 4 The embodiment provides an inertial navigation system based on group collaborative evolution, including: The coarse alignment module is used to complete the coarse alignment in the solidified coordinate system based on the inertial navigation data and using the dual-vector attitude determination algorithm.

[0109] The objective function construction module is used to determine the optimization variables and construct the initial alignment objective function based on the optimization variables.

[0110] The objective function module is used to solve the objective function of the initial alignment using the swarm co-evolution algorithm to obtain the optimal variable group.

[0111] The posture conversion matrix determination module is used to calculate the posture conversion matrix obtained by the group co-evolution rough alignment method based on the optimal variable group.

[0112] The precise alignment module is used to perform precise alignment based on the attitude conversion matrix and use Kalman filtering to determine the attitude matrix.

[0113] The coordinate determination module is used to switch the carrier into the navigation state and perform navigation solution based on the attitude array to complete the determination of the position coordinates.

[0114] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0115] Specific examples are used in this article to elaborate on the principles and implementation manners of the present application. The descriptions of the above embodiments are only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. An inertial navigation method based on group co-evolution, characterized in that, Including: Based on inertial navigation data, use the double-vector attitude determination algorithm to complete the rough alignment in the fixed coordinate system; Determine the optimization variables and construct the objective function for the initial alignment based on the optimization variables; Use the group co-evolution algorithm to solve the objective function of the initial alignment to obtain the optimal variable group; Based on the optimal variable group, calculate the attitude transformation matrix obtained by the group co-evolution rough alignment method; Based on the attitude transformation matrix, use Kalman filtering for fine alignment to determine the attitude matrix; The carrier enters the navigation state, and the position coordinates are determined based on the attitude matrix through navigation calculation.

2. The inertial navigation method based on group co-evolution according to claim 1, characterized in that, The rough alignment includes determining the attitude transformation matrix between the carrier inertial system and the navigation inertial system.

3. The inertial navigation method based on group co-evolution according to claim 1, characterized in that, The attitude transformation matrix is: ； Among them, is the attitude transformation matrix; is the gravity vector in the navigation inertial system at time is the gravity vector in the navigation inertial system at time is the specific force measurement value vector in the vehicle inertial system at time is the specific force measurement value vector in the vehicle inertial system at time 4. The inertial navigation method based on group co-evolution according to claim 3, characterized in that, The objective function is: ； where m is the number of non-coplanar vectors measured under the condition of a static base; is the gravity vector in the i-th navigation inertial system; is the specific force measurement value vector in the i-th vehicle inertial system.

5. The inertial navigation method based on group co-evolution according to claim 1, characterized in that, The step of using the group co-evolution algorithm to solve the objective function of the initial alignment to obtain the optimal variable group includes: Initialize the basic parameters of the group co-evolution algorithm; the basic parameters include: the target population size Popsize, the total iteration number threshold IterNum, the co-evolution opportunity CENum, and the merger opportunity MergerNum; Let the outer loop iteration number j = 1; Obtain N basic algorithms; the types of the N basic algorithms are all different; Let the number of basic algorithms n = N; Initialize the population to obtain the initial total population; Assign the corresponding initial small population to each basic algorithm from the initial total population; Determine the initial performance evaluation quantity of each basic algorithm respectively; any initial performance evaluation quantity is obtained after the initial small population is used to perform preliminary optimization on the basic algorithm; Determine that the initial performance evaluation quantity is the performance evaluation quantity of the corresponding basic algorithm at the 0th iteration; Expand the population size of the initial total population to the target population size Popsize to obtain the population at the 0th iteration; Use the population at the (j - 1)th iteration and the performance evaluation quantities of different basic algorithms at the (j - 1)th iteration to perform N - 1 rounds of iterative optimization on the basic algorithms to obtain the optimal basic algorithm at the jth iteration; Determine the total number of iterations; ; where is the total number of iterations and u is a variable; Judge whether the total iteration number reaches the total iteration number threshold IterNum to obtain the judgment result; If the judgment result is no, then increase the value of the outer loop iteration number j by 1 and return to the step "Use the population at the (j - 1)th iteration and the performance evaluation quantities of different basic algorithms at the (j - 1)th iteration to perform N - 1 rounds of iterative optimization on the basic algorithms to obtain the optimal basic algorithm at the jth iteration"; If the judgment result is yes, then determine the individual corresponding to the optimal fitness value in the optimal basic algorithm at the jth iteration to obtain the optimal variable group.

6. The inertial navigation method based on group co-evolution according to claim 5, characterized in that, The step of using the population at the (j - 1)th iteration and the performance evaluation quantities of different basic algorithms at the (j - 1)th iteration to perform N - 1 rounds of iterative optimization on the basic algorithms to obtain the optimal basic algorithm at the jth iteration includes: Take the population at the (j - 1)th iteration as the population at the 0th iteration; Take the performance evaluation quantities of different basic algorithms at the (j - 1)th iteration as the performance evaluation quantities of different basic algorithms at the 0th iteration; Let the inner loop iteration number q = 1; Based on the performance evaluation quantities of each basic algorithm at the (q - 1)th iteration, use the roulette wheel method to determine the population allocation quantity of each basic algorithm; Based on the population allocation quantity, determine the small populations of each basic algorithm at the (q - 1)-th iteration from the population at the (q - 1)-th iteration. Based on the equal running time mechanism, use the small populations of each basic algorithm at the (q - 1)-th iteration to perform iterative optimization on the corresponding basic algorithm respectively until the number of iterative optimization times reaches the co-evolution opportunity CENum. Based on the co-evolution mechanism, calculate the fitness values of all individuals; the fitness value is the objective function value of the initial alignment; the co-evolution mechanism includes: a sharing mechanism, a communication mechanism, and an elimination and renewal mechanism; the elimination and renewal mechanism is used to update the small populations allocated to each basic algorithm to obtain the small populations of each basic algorithm at the q-th iteration. Determine the performance evaluation metrics of the n basic algorithms at the q-th iteration respectively. Determine the set of the small populations of the n basic algorithms at the q-th iteration as the population at the q-th iteration. Increase the value of the iteration number q by 1, and return to the step "Based on the performance evaluation metrics of each basic algorithm at the (q - 1)-th iteration, use the roulette wheel method to determine the population allocation quantity of each basic algorithm" until the value of the iteration number q reaches the merger opportunity MergerNum. Arrange the basic algorithms in descending order according to the performance evaluation metrics at the q-th iteration. Take the small population corresponding to the n-th basic algorithm and the small population corresponding to the 1st basic algorithm as the updated small population corresponding to the 1st basic algorithm at the q-th iteration. Delete the n-th basic algorithm, and decrease the value of the basic algorithm quantity n by 1. Take the performance evaluation metrics at the q-th iteration as the performance evaluation metrics of the corresponding basic algorithm at the 0-th iteration. Take the set of the small populations of all basic algorithms at the q-th iteration as the population at the 0-th iteration. Return to the step "Let the inner loop iteration number q = 1" until the basic algorithm quantity n is equal to 1 to obtain the optimal basic algorithm at the j-th iteration. Determine the population at the q-th iteration as the population at the j-th iteration. Determine the performance evaluation metrics of different basic algorithms at the q-th iteration as the performance evaluation metrics of different basic algorithms at the j-th iteration.

7. The inertial navigation method based on group co-evolution according to claim 5, wherein, The multiple basic algorithms include the sand cat swarm optimization algorithm, the sparrow search algorithm, the spider wasp optimization algorithm, the particle swarm algorithm, and the Kepler optimization algorithm.

8. The inertial navigation method based on group co-evolution according to claim 5, wherein, The performance evaluation metric is: ； In the formula, represents the performance evaluation measure of the nth basic algorithm; represents the prior performance index of the nth basic algorithm; represents the absolute accuracy index of the nth basic algorithm; represents the relative accuracy index of the nth basic algorithm; represents the optimization efficiency index of the nth basic algorithm; represents the fluctuation index of the nth basic algorithm; represents the comprehensive performance index of the nth basic algorithm; and both represent the model empirical coefficients.

9. The inertial navigation method based on group co-evolution according to claim 3, wherein, The attitude matrix is: Among them, is the attitude matrix; is the transformation matrix from the navigation inertial system to the navigation coordinate system at the initial moment; is the transformation matrix from the vehicle coordinate system to the vehicle inertial system at the initial moment.

10. An inertial navigation system based on group co-evolution, wherein, Including: A coarse alignment module, which is used to complete the coarse alignment in the fixed coordinate system based on the inertial navigation data by using the double-vector attitude determination algorithm. An objective function construction module, which is used to determine the optimization variables and construct the objective function of the initial alignment based on the optimization variables. An objective function module, which is used to solve the objective function of the initial alignment by using the group co-evolution algorithm to obtain the optimal variable group. An attitude transformation matrix determination module, which is used to calculate the attitude transformation matrix obtained by the group co-evolution coarse alignment method based on the optimal variable group. A fine alignment module, which is used to perform fine alignment by using Kalman filtering based on the attitude transformation matrix to determine the attitude matrix. A coordinate determination module, which is used to transfer the carrier into the navigation state and complete the determination of the position coordinates based on the attitude matrix for navigation solution.

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