GNSS integer ambiguity estimation method and device based on improved particle swarm optimization

Abstract

The present invention provides a GNSS integer ambiguity estimation method and device based on improved particle swarm optimization, which is used to achieve rapid and accurate estimation of high-dimensional integer ambiguities. The method includes parameterizing floating-point ambiguities and their variance-covariance matrices with integer Gaussian transformations; establishing an ambiguity search objective function by minimizing the residual quadratic form of the optimal integer candidate vector as the fitness; directly rounding the floating-point ambiguities to obtain the initial search value; combining the floating-point ambiguities and mean square error after integer Gaussian transformation to determine the search space for each ambiguity component; setting an improved particle swarm optimization method, setting dynamic inertia weights, dynamic learning factors, boundary detection and control, adaptive iteration, and scale factor improvement models; and performing optimal and suboptimal integer ambiguity candidate vector estimation and obtaining the corresponding residual quadratic form. The present invention can be used for ambiguity resolution of undifferenced ambiguities, dual-frequency, and ionosphere-free combination models, and can also be extended to other GNSS integer ambiguity estimation problems.

Description

Technical Field

[0001] The present invention relates to the field of GNSS navigation and positioning technology, and in particular to a GNSS integer ambiguity estimation technical solution. Background Art

[0002] GNSS technology provides continuous, accurate, and real-time precise location information. In recent years, emerging technologies have placed greater demands on location services with higher scale and reliability, leading to an urgent need for fast, high-precision positioning services. Rapid and accurate fixation of GNSS ambiguities is a prerequisite for fast, high-precision positioning. The core task of integer ambiguity determination is to convert the floating-point ambiguities obtained from parameter estimation into integers using a certain mapping relationship. This is an integer estimation problem.

[0003] The least-squares ambiguity reduction and correlation adjustment (LAMBDA) method has been widely studied and used due to its high success rate and efficiency. It is often applied to integer ambiguity determination problems with high precision or strong correlation. However, this method typically uses the integer solution obtained by sequential rounding as the initial point for layer-by-layer node enumeration and relies heavily on the conditional variance of the floating-point ambiguities to establish the search space. This reduces the search error tolerance, especially in the initial positioning phase when the floating-point solution accuracy is low, increasing the risk of incorrect fixation or fixation failure. Therefore, it is necessary to further study integer ambiguity fast estimation methods with global optimization capabilities to ensure the global optimality of the integer candidate vectors and use this as an effective constraint to further improve positioning accuracy and convergence speed.

[0004] In contrast, behavioral intelligent optimization algorithms have achieved remarkable success in many fields due to their global search capabilities, suggesting their potential for application in integer ambiguity estimation. Particle swarm optimization (PSO) has garnered widespread attention due to its advantages, such as a small number of control parameters and fast computational speed, offering a solution to the aforementioned problems. However, classical PSO methods employ fixed control parameters and suffer from imbalanced global and local search capabilities. The swarm may quickly converge to a local optimum and fluctuate around the global optimum. It is also prone to overlooking previously unreached regions within the high-dimensional ambiguity space.

[0005] Based on this, it is necessary to study a new GNSS integer ambiguity estimation technology based on the classic particle swarm optimization method to quickly and accurately estimate the high-dimensional ambiguity integer vector to achieve fast and high-precision positioning. Summary of the Invention

[0006] In order to solve the above technical problems, the present invention provides a GNSS integer ambiguity estimation technical solution based on improved particle swarm optimization.

[0007] The technical solution provided by the present invention provides a GNSS integer ambiguity estimation method based on improved particle swarm optimization, which is used to achieve fast and accurate estimation of high-dimensional integer ambiguity, including the following process:

[0008] Integer Gaussian transform parameterization of floating-point ambiguities and their variance-covariance matrices;

[0009] The ambiguity search objective function is established by minimizing the residual quadratic form of the optimal integer candidate vector as the fitness. The floating-point ambiguity is directly rounded to estimate the initial value of the search. The search space of each ambiguity component is determined by combining the floating-point ambiguity and the mean square error after integer Gaussian transformation.

[0010] An improved particle swarm optimization method is set up, including setting dynamic inertia weight, dynamic learning factor, boundary detection and control, adaptive iteration and scale factor improvement model based on the classic particle swarm optimization algorithm, supporting global search in high-dimensional ambiguity space and extracting the global optimal solution of integer ambiguity candidate vectors;

[0011] The optimal and suboptimal integer ambiguity candidate vectors are estimated based on the improved particle swarm optimization method, and the corresponding residual quadratic form is obtained.

[0012] Moreover, the integer Gaussian transform parameterization is to first decompose the ambiguity variance-covariance matrix to obtain a conversion matrix, and then perform Gaussian transform on the floating-point ambiguity and its accuracy that eliminates the hardware delay between the receiver and the satellite.

[0013] Moreover, the establishment of the ambiguity search objective function, the determination of the search initial value and the search space are carried out in the following manner: the ambiguity search objective function is established with the quadratic form of the integer candidate vector residual as a function and the minimum function value as a target; each floating-point ambiguity component after integer Gaussian transformation is rounded to an integer to determine the search initial value; the floating-point ambiguity components after integer Gaussian transformation are combined, and the left and right closed intervals of the component are obtained by 3 times the ambiguity mean error and rounding up and down operations, and the hyperspace of the integer ambiguity candidate vector search is cyclically determined, and it is assumed that the space has a confidence probability close to 100% and contains the true ambiguity vector.

[0014] Moreover, the dynamic inertia weight improvement model sets the inherited weight of the particle along the inertia direction to change dynamically with the iterative evolution process of the particle, which is divided into three stages and determined by the following method:

[0015] In the early evolution process, the inertia weight is set as a convex function. The characteristic that the convex function decreases more slowly than the linear function is used to reduce the decrease rate of the particle's flight speed, so that the particles can conduct a large-scale search in the entire hyperspace in the early stage.

[0016] In the mid-term evolution process, the inertia weight uses a linear function to accelerate the convergence of all particles in the population, reduce the particle search range, and make particles search near the existing optimal integer vector;

[0017] In the later evolution process, the inertia weight is mutated to make the particles jump out of the optimal region and search for potential solutions in the area outside the existing optimal integer vector to ensure that the particles will not fall into the local optimum;

[0018] If the integer optimal solution has been searched in the first two steps, the existence of the third step will not change the final estimation result; if the search in the first two steps falls into a local optimum, the third step can be adjusted.

[0019] Moreover, the dynamic learning factor improvement model includes individual learning factors and social learning factors, which are used to ensure that the individual historical optimum and the population historical optimum have different weights at different evolutionary stages, and are determined as follows:

[0020] Set initial and end values ​​for individual learning factors and social learning factors respectively;

[0021] A functional relationship is established between the learning factor and the current number of iterations, the maximum number of iterations, and the initial and final values ​​of the learning factor; in the early evolutionary process, the individual learning factor plays a dominant role; and in the later stage, the influence of the social learning factor increases.

[0022] Moreover, the improved boundary detection and control model is used to prevent particles from crossing the boundary beyond the search space of the GNSS integer solution, otherwise the out-of-bounds particles lose the meaning of the solution, thereby leading to an erroneous fixed solution, which is determined by the following method:

[0023] After the current particle completes the position update, determine whether it exceeds the upper and lower limits of the search interval;

[0024] If a particle crosses the boundary, the flight speed of the particle is adjusted again. During this process, a random number can be introduced to randomly change the flight direction of the particle while adjusting the speed.

[0025] After adjusting the speed, update the position again;

[0026] The loop repeats until all particles in the current iteration are within the search space.

[0027] Moreover, the adaptive iterative improvement model introduces the concept of aggregation degree, which is used to reflect the aggregation degree of all particles in the current iteration, and is determined as follows:

[0028] Establishing a clustering function by combining particle states, the dimensions of integer candidate vectors, and population size, wherein the particle states are the positions of the integer candidate vectors;

[0029] After each iteration, the aggregation degree of the population is calculated to characterize the distance between all individuals in the current iteration; if the aggregation degree is less than the corresponding threshold, the iterative evolution ends, otherwise the search continues.

[0030] Moreover, the improved proportional factor model adopts a certain proportion of dominant particles to replace the traditional consistent population historical optimal solution, which can further prevent the search results from falling into the local optimum. It is determined by the following method:

[0031] Select some particles with smaller fitness function values ​​in the current iteration as the set of dominant particles, and support quickly obtaining the set by sorting in ascending order of fitness function values;

[0032] Calculate the distance between the current particle and each dominant particle, select the dominant particle with the closest distance as the historical global optimal particle, and replace the population's historical global optimal particle with the dominant particle to update the speed.

[0033] Furthermore, the process of estimating the integer ambiguity candidate vector based on the improved particle swarm optimization method adopts the following method, wherein the input is the floating-point ambiguity with the hardware delay between the receiver and the satellite eliminated, the ambiguity variance-covariance matrix, and the preset control parameters of the improved particle swarm optimization method;

[0034] Subsequently, based on the integer Gaussian transform parameterization, an improved particle swarm optimization method is used to perform integer estimation following the search objective function in the search space;

[0035] The final output is the optimal and suboptimal integer ambiguity candidate vectors and the corresponding residual quadratic form.

[0036] On the other hand, the present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, the steps of the GNSS integer ambiguity estimation method based on improved particle swarm optimization as described above are implemented.

[0037] The beneficial effects brought about by the technical solution provided by the present invention include at least:

[0038] The present invention provides a GNSS integer ambiguity estimation technology solution based on improved particle swarm optimization. The present invention ensures the global optimality of the integer ambiguity candidate vector and further reduces the risk of ambiguity fixation failure or incorrect fixation by using the improved particle swarm optimization method in a high-dimensional ambiguity space. The method provided by the present invention has the characteristics of inherent parallelism, global optimality, adaptability, and robustness. It can achieve accurate resolution of integer ambiguities more quickly. In addition, it can ensure that integer estimation is successfully achieved for more epochs and more satellites. Ultimately, the obtained integer unconstrained information is used to effectively improve positioning accuracy and shorten initialization time. The method provided by the present invention has a certain degree of universality. It can not only be used for undifferenced ambiguity integer estimation of precise single-point positioning based on dual-frequency ionosphere-free combination, but can also be extended to GNSS integer ambiguity estimation problems of single-difference ambiguity, double-difference ambiguity, multi-frequency, multi-system or non-combination models, providing a technical reference for solving the accuracy and timeliness problems of GNSS precise positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the present invention or related technologies, the following briefly introduces the drawings required for use in the embodiments or related technical descriptions. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0040] Figure 1 1 is a flow chart of a GNSS integer ambiguity estimation method based on improved particle swarm optimization according to an embodiment of the present invention;

[0041] Figure 2 1 is a schematic structural diagram of a GNSS integer ambiguity estimation device based on improved particle swarm optimization provided by an embodiment of the present invention;

[0042] Figure 3 It is a structural diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0043] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0044] The terms "including" and "having" and any variations thereof in the description and claims of the present invention and the accompanying drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or modules is not limited to the listed steps or modules, but may optionally include steps or modules not listed, or may optionally include other steps or modules inherent to the process, method, product, or apparatus.

[0045] It should be noted that the terms "first" and "second" as used herein are merely used to distinguish similar objects and do not represent a specific ordering of the objects. It is understood that the terms "first" and "second" may interchangeably represent a specific order or precedence, where permitted. It should be understood that the objects distinguished by "first" and "second" may be interchangeable, where appropriate, such that the embodiments of the present invention described herein may be implemented in an order other than that described or illustrated herein.

[0046] It can be understood that the GNSS integer ambiguity estimation method based on improved particle swarm optimization provided in an embodiment of the present invention is applied to the field of navigation and positioning technology, and improves the positioning accuracy and convergence speed of GNSS users (users include but are not limited to mobile phones, tablets, navigators and other devices) by quickly restoring the integer characteristics of the carrier phase ambiguity.

[0047] The present invention is described in detail below with reference to specific embodiments.

[0048] See also Figure 1 , an embodiment of the present invention provides a GNSS integer ambiguity estimation method based on improved particle swarm optimization, comprising the following steps:

[0049] S101, performing integer Gaussian transformation parameterization on the floating-point ambiguity and its variance-covariance matrix that eliminates the hardware delay between the receiver and the satellite, thereby reducing the correlation between the ambiguity components and improving the efficiency of subsequent integer estimation.

[0050] The integer Gaussian transform parameterization is first performed by L T After DL decomposition obtains the transformation matrix, Gaussian transformation is performed on the floating-point ambiguity and its accuracy that eliminates the hardware delay between the receiver and the satellite, so as to reduce the correlation of the ambiguity and improve the efficiency of subsequent integer vector estimation. Specifically, based on the translation invariance of the ambiguity normalization domain, the floating-point ambiguity is firstly transformed using the “remove-restore” technique. Transform to a decimal between (-1,1) to unify the magnitude of the multidimensional ambiguity components:

[0051]

[0052] in, is the fractional part of the floating point ambiguity, and ia is the integer part.

[0053] Specifically, in order to reduce the correlation between ambiguity components and improve the search efficiency of integer ambiguity candidate vectors, the ambiguity variance-covariance matrix Carry out L T DL decomposition, after obtaining the transformation matrix, the floating-point ambiguity and its precision are parameterized by integer Gaussian transformation:

[0054]

[0055] Where Z is a full-rank transformation matrix; and are the floating-point ambiguity vector after Gaussian transformation and down-correlation and its corresponding variance-covariance matrix.

[0056] S102, establish the ambiguity search objective function with minimizing the residual quadratic form of the optimal integer candidate vector as the fitness; round the ambiguity to obtain the initial search value; combine the floating-point ambiguity after integer Gaussian transformation and its error to determine the search space of each ambiguity component.

[0057] The establishment of the fuzzy search objective function, the determination of the search initial value and the search space are carried out in the following manner, including:

[0058] The process of resolving integer candidate vectors must take into account the floating-point ambiguity accuracy and inter-component correlation. When these conditions are met, the nearest integer to the floating-point ambiguity is estimated. Therefore, the ambiguity search objective function is established, using the quadratic form of the residual of the integer candidate vector as a function and minimizing the function value.

[0059] By performing a rounding operation on each floating-point ambiguity component after integer Gaussian transformation, the search initial value can be determined to improve the efficiency of subsequent integer vector search.

[0060] By combining the floating-point ambiguity components after integer Gaussian transformation, taking 3 times the ambiguity mean error and performing rounding operations, we can obtain the left and right closed intervals of the component, loop through and determine the hyperspace for searching integer ambiguity candidate vectors, and obtain a confidence probability close to 100% that the search space contains the true ambiguity vector.

[0061] Specifically, the ambiguity resolution using the integer least squares estimation principle can be expressed as a mixed integer model:

[0062]

[0063] Where E(·) and D(·) represent the expectation and variance operators respectively; y is the observation vector, Q yyis the corresponding variance-covariance matrix; a is the unknown integer ambiguity vector, n represents the number of integer ambiguities to be determined; b is the real vector of non-ambiguous parameters in the GNSS positioning model (including coordinate position, receiver clock error, ionosphere, troposphere parameters, etc.), its dimension is p, represents an integer, represents a real number; A and B are both full-rank coefficient matrices.

[0064] Understandably, the orthogonal decomposition method is widely used to solve the mixed integer model, obtaining:

[0065]

[0066] in, is the residual vector of the observation value; and are the real and integer ambiguity vectors, respectively; and denote the real and integer solutions of the non-ambiguous parameters respectively; represents the residual quadratic form taking into account the variance-covariance matrix.

[0067] It can be understood that since the residual vector is independent of the integer solutions a and b, the first term can be ignored; and when b is equal to When , the third term can be considered as zero. Therefore, the above formula can be simplified to:

[0068]

[0069] in, for and Therefore, the process of solving the optimal integer ambiguity candidate vector is to continuously search for the integer vector that satisfies the above formula in a hyperspace.

[0070] It can be understood that since the integer transformation reduces the correlation, the above optimization problem can be rewritten as:

[0071]

[0072] in, is the optimal integer ambiguity vector to be sought.

[0073] The above formula is the search objective function actually followed by the subsequent integer ambiguity estimation.

[0074] Subsequently, specifically, in order to further improve the search efficiency, the floating point ambiguity is directly rounded to obtain the initial search value:

[0075]

[0076] Where z0 is the initial value vector, and round(·) indicates rounding to the nearest integer.

[0077] Specifically, the fuzzy search space can be defined as:

[0078]

[0079] Among them, [inf j ,sup j ] represents the search interval of the j-th dimension ambiguity, which is a left and right closed interval; and Represents floor and ceiling operations respectively; is the j-th dimension floating point ambiguity after integer Gaussian transformation; is the mean square error of the j-th dimension ambiguity, that is, the diagonal element of the variance-covariance matrix in the j-th dimension.

[0080] It can be understood that the search space determined by the above formula contains the complete integer Gaussian transformed ellipse, and the 3 times mean square error and rounding up and rounding down operations can make it more than 99.7% confident that the search space contains the true ambiguity vector.

[0081] S103, based on the classic particle swarm optimization algorithm, adopts five improved models, including dynamic inertia weight, dynamic learning factor, boundary detection and control, adaptive iteration, and scaling factor, to achieve global search in high-dimensional ambiguity space, ensure the global optimality of integer ambiguity candidate vectors, and take into account both computational accuracy and efficiency.

[0082] Specifically, the particle swarm optimization algorithm is a biomimetic heuristic derived from the foraging patterns of birds. It leverages information sharing among a certain number of particles, each characterized by position and velocity, to enable the movement of the entire swarm to evolve from disorder to order within the problem-solving space, ultimately achieving the optimal solution. The fundamental behavior of particles is to emulate the success of neighboring particles and their own past successes. This collective behavior manifests as a search for optimal regions within a high-dimensional search space according to specific search rules.

[0083] During the iteration process, each particle in the population needs to continuously update its own speed and position information according to the corresponding control parameters; in addition, during the iterative evolution of the entire population, each particle not only needs to rely on its own historical state to adjust its evolutionary state, but also needs to refer to the state information of other particles in the population to achieve the optimal overall result.

[0084] The particle swarm optimization process is specifically manifested as follows: the position of each particle in the swarm represents a potential integer ambiguity candidate vector. The position of the particle is the encoded representation of the solution, and the velocity of the particle represents the change in position. Each particle searches for the optimal solution in the multidimensional space according to the preset search objective function, and records the best position reached as the individual historical optimal solution. Then according to the maximum or minimum value of the fitness function Determine the historical optimal population of the current iteration The particle position and velocity update can be expressed as:

[0085]

[0086] Among them, the ordinal number j is the dimension identifier; and denote the position and velocity of the i-th particle at the t-th iteration, respectively; round(·) denotes a rounding operation, the purpose of which is to keep the particle position an integer; ω is an inertia weight parameter, which is a non-negative number; c1 and c2 denote the individual learning factor and the social learning factor, respectively; r1 and r2 are random numbers between (0,1); is the individual historical optimum, corresponding to the historical maximum or minimum fitness function value achieved by particle i; It is the historical optimum of the population, corresponding to the historical maximum or minimum fitness function value of the entire population.

[0087] Understandably, the classical particle swarm optimization algorithm uses fixed control parameters to make particles maintain a certain state of motion, which can easily miss the optimal area and thus fail to search for the optimal solution. In other words, it can easily lead to It is not always possible to gradually approach the true global optimum, especially in high-dimensional search spaces. Therefore, five improvements are made to the classic particle swarm optimization algorithm, and an improved method that is more suitable for GNSS multi-system integer ambiguity estimation is proposed. The detailed improved model is as follows:

[0088] (1) Specifically, the dynamic inertia weight improvement model sets the inherited weight of the particle along the inertia direction to change dynamically with the iterative evolution process of the particle, which can be expressed as:

[0089]

[0090] Among them, ω is the inertia weight, maxIts is the maximum number of iterations, and t is the current number of iterations.

[0091] Understandably, the dynamic inertia weight improvement model divides the evolution process into three stages:

[0092] ① In the early evolution process, the inertia weight is set as a convex function. The characteristic that the convex function decreases more slowly than the linear function is used to reduce the decrease rate of the particle flight speed, so that the particles can search in a global larger range as much as possible in the early stage.

[0093] ② In the mid-term evolution process, the inertia weight uses a linear function to accelerate the convergence of all particles in the population, reduce the particle search range, and make the particles search near the existing optimal integer vector;

[0094] ③ In the later evolution process, the inertia weight is mutated to make the particles jump out of the optimal region and search for possible potential solutions in the area outside the existing optimal integer vector to ensure that the particles will not fall into the local optimum;

[0095] It can be understood that if the integer optimal solution has been searched in the first two steps, the existence of the third step will not change the final estimation result; if the search in the first two steps falls into a local optimum, the third step can be adjusted.

[0096] (2) Specifically, the dynamic learning factor improvement model includes individual learning factors and social learning factors, both of which are used to reflect the learning and reference of particles from the previous iteration or historical iterations during each iteration. Whether the selection of their values ​​is reasonable determines whether particles can communicate effectively and whether they have sufficient optimization capabilities.

[0097] The dynamic learning factor improvement model ensures that the individual historical optimum and the population historical global optimum have different weights at different evolutionary stages. This is determined by the following methods, including:

[0098] Set initial and end values ​​for individual learning factors and social learning factors respectively;

[0099] Establish a functional relationship between the learning factor and the current number of iterations, the maximum number of iterations, and the initial and final values ​​of the learning factor; in the early evolutionary process, the individual learning factor dominates; while in the later stage, the influence of the social learning factor increases. The functional relationship of the dynamic learning factor can be expressed as:

[0100]

[0101] in, and are the initial and final values ​​of the individual learning factor c1; and are the initial and final values ​​of the social learning factor c2 respectively.

[0102] Understandably, the improved model of dynamic learning factors makes individual learning factors dominate in the early stages of evolution, while the influence of social learning factors increases in the later stages. This effectively enables individuals to fully adapt their flight direction and speed based on their own experience in the early stages, enhancing their search capabilities. Meanwhile, in the later stages, they can adapt their flight direction and speed based on the experience of the entire population, ensuring global learning capabilities.

[0103] (3) Specifically, after each iteration, the improved boundary detection and control model can prevent particles from crossing the boundary and exceeding the search space of the GNSS integer solution. Otherwise, the out-of-bounds particles lose the meaning of the solution and lead to an erroneous fixed solution. The boundary detection and control process is as follows:

[0104] After the current particle completes the position update, first determine whether the particle exceeds the upper and lower limits of the defined search interval:

[0105]

[0106] Among them, inf j with sup j are the lower and upper limits of the defined j-th dimension fuzzy search interval respectively.

[0107] If the particle crosses the boundary, adjust the flying speed of the particle again:

[0108]

[0109] Where r3 and r4 are random numbers between (0, 1). The purpose of introducing random numbers is to randomly change the flight direction of out-of-bounds particles while adjusting the speed, thereby improving the global search capability.

[0110] After adjusting the speed, update the position again:

[0111]

[0112] The loop repeats until all particles in the current iteration are within the search space.

[0113] (4) It is understandable that the number of iterations of the classical particle swarm optimization algorithm is usually a fixed constant. When the number of iterations is greater than the given maximum number of iterations maxIts, the search is terminated, which will undoubtedly have an adverse effect on the parameter solution: on the one hand, the preset maxIts is usually a large integer, and the global optimal solution may have been searched before maxIts is reached. The subsequent iterative process not only has no gain on the parameter estimation results, but also increases the computational time; on the other hand, when the iteration reaches maxIts, it is not ruled out that the individual has not yet found the global optimum, but the iteration must be terminated, which will significantly reduce the accuracy of the final parameter estimation.

[0114] Taking into account the differences in GNSS data quality at each observation epoch, the dimensions of the ambiguity vector to be solved, and the inevitable randomness of the search process, the number of iterations of the ambiguity resolution process for each epoch should not be the same, but should be determined adaptively by the population.

[0115] Specifically, the adaptive iterative improvement model introduces the concept of density, which characterizes the degree of aggregation of all particles in the current iteration by combining the particle state (i.e., the position of the integer candidate vector), the dimension of the integer candidate vector, and the population size, and then characterizes the convergence of the evolutionary process to achieve the purpose of adaptive search times and improve computational efficiency. t It can be expressed as:

[0116]

[0117] Among them, Nsize is the population size; represents the particle position, is the average position vector of all particles in the current iteration population, and its dimension is the number of integer ambiguities to be calculated, n. For its elements.

[0118] After each iteration, the population aggregation is calculated. If the aggregation is less than the set aggregation threshold, the iterative evolution ends, otherwise the next search continues.

[0119] (5) It is understandable that the historical optimal population that all particles in the swarm approach when the speed is updated is consistent, which is When multiple local optima appear in a high-dimensional search space, the search process is prone to fall into local optimality.

[0120] Specifically, the scale factor improvement model uses a certain proportion M of dominant particles to replace the traditional consistent population historical optimal solution, which can further prevent the search results from falling into local optimality. The specific improvement model is as follows:

[0121] First, select Nsize*M particles with smaller fitness function values ​​in the current iteration as the set of dominant particles (the set can be quickly obtained by sorting in ascending order of fitness function values), which is recorded as:

[0122]

[0123] in, Represents the set of dominant particles, whose number is Nsize*M, where M is the scale factor.

[0124] Then calculate the distance dis between the current particle and each dominant particle k :

[0125] dis k ,1≤k≤Nsize*M;

[0126] Where k is an integer between [1, Nsize*M].

[0127] Then select the dominant particle closest to the current individual as the population history optimal of the current particle, that is, GSW = min(dis)∈Mbest t . And replace the dominant particle with the global optimal population history To update the speed:

[0128]

[0129] in, represents the velocity of the i-th particle at the t+1-th iteration, GSW is the dominant particle closest to the current particle, and min(dis) represents the minimum distance.

[0130] Understandably, the scaling factor improvement model ensures that the historical global optimal value of each particle in the population during the speed update may not be consistent, but will always belong to one of the top Nsize*M dominant particles. This ensures that the top Nsize*M dominant particles have equal weight in social attributes, that is, the i-th particle only converges to the dominant model closest to it, thus preventing it from falling into local extremes.

[0131] S104, performing optimal and suboptimal integer ambiguity candidate vector estimation based on an improved particle swarm optimization method, and obtaining the corresponding residual quadratic form.

[0132] Specifically, when determining the initial search value z0 of the ambiguity vector, the search space [inf j ,sup j After finding the objective function, the improved particle swarm optimization method is activated to complete the integer least-squares mapping of ambiguities from the real domain to the integer domain. The input is the floating-point ambiguities that eliminate hardware delays between the receiver and satellite, the ambiguity variance-covariance matrix, and the preset control parameters of the improved particle swarm optimization method. The output is the optimal and suboptimal integer ambiguity candidate vectors and the corresponding residual quadratic form.

[0133] For example, the recommended settings of the preset control parameters are shown in Table 1:

[0134] Table 1 Recommended preset control parameters for the improved particle swarm optimization method

[0135]

[0136] It can be understood that once the optimal integer ambiguity vector is obtained and suboptimal integer solutions After that, an ambiguity check can be performed to determine whether the obtained integer ambiguity can be accepted as the correct ambiguity value.

[0137] In some embodiments, the widely used Ratio-test can be used to perform ambiguity confirmation testing. The Ratio-test is defined as the ratio T of the suboptimal integer solution residual quadratic form to the optimal integer solution residual quadratic form:

[0138]

[0139] If the integer ambiguity passes the test, the optimal integer ambiguity vector Convert to the original ambiguity domain:

[0140]

[0141] in, This is the final estimated integer ambiguity vector. Update the unambiguous parameter b as constraint information to obtain a fixed solution; otherwise, maintain the ambiguous floating-point solution.

[0142] In some embodiments, the GPS / Galileo / BDS triple-system dual-frequency precise single-point positioning ambiguity fixed solution using the embodiments of the present invention can achieve positioning accuracies of 1.21 / 2.17 / 3.82 cm in the E / N / U directions, respectively, which are better than the 1.47 / 2.29 / 4.44 cm of the LAMBDA solution method; in terms of convergence time, the LAMBDA method requires 11.72 minutes, which can be shortened by 7.25% to only 10.87 minutes using the embodiments of the present invention.

[0143] Among them, E stands for EAST, N stands for NORTH, and U stands for UP, which means the vertical upward direction.

[0144] See next Figure 2 , which is a schematic diagram of the structure of a GNSS integer ambiguity estimation device based on improved particle swarm optimization, provided by an exemplary embodiment of the present invention. The device can be implemented as all or part of a terminal through software, hardware, or a combination of both, or can be integrated into a server as an independent module. The GNSS integer ambiguity estimation device in this embodiment of the present invention can be applied to a terminal or the cloud. The device 20 includes an integer estimation preprocessing module 210 and an integer ambiguity estimation module 220, wherein:

[0145] an integer estimation preprocessing module for determining an integer Gaussian transform conversion matrix based on the ambiguity variance-covariance matrix, and de-correlating the floating-point ambiguities and their variance-covariance matrices according to the conversion matrix;

[0146] The integer estimation preprocessing module is further used to determine the ambiguity search objective function; directly round the floating point ambiguity to obtain the search initial value; and obtain the search space of each ambiguity component;

[0147] The integer ambiguity estimation module is used to estimate the optimal and suboptimal integer ambiguity candidate vectors and the corresponding residual quadratic forms based on the improved particle swarm optimization method.

[0148] It should be noted that the apparatus 20 provided in the above embodiment, when performing GNSS integer ambiguity estimation, is illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus provided in the above embodiment and the embodiment of GNSS integer ambiguity estimation based on improved particle swarm optimization are based on the same concept. The implementation process is detailed in the method embodiment and is not repeated here.

[0149] An embodiment of the present invention further provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any of the above-mentioned method embodiments when executing the program.

[0150] Figure 3 An example of a physical structure diagram of an electronic device is shown in FIG. Figure 3 As shown, the electronic device may include: a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other via the communications bus. The processor may invoke logic instructions in the memory to execute a GNSS integer ambiguity estimation method based on an improved particle swarm optimization.

[0151] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the GNSS integer ambiguity estimation method based on improved particle swarm optimization provided by the above-mentioned methods. The computer program is implemented to execute the GNSS integer ambiguity estimation method based on improved particle swarm optimization provided by the above-mentioned methods when the computer program is executed by the processor.

[0152] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0153] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the existing technology can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or certain parts of the embodiments.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A GNSS integer ambiguity estimation method based on improved particle swarm optimization, characterized by: It is used to achieve fast and accurate estimation of high-dimensional integer ambiguity, including the following processes: Integer Gaussian transform parameterization of floating-point ambiguities and their variance-covariance matrices; The ambiguity search objective function is established by minimizing the residual quadratic form of the optimal integer candidate vector as the fitness. The floating-point ambiguity is directly rounded to estimate the initial value of the search. The search space of each ambiguity component is determined by combining the floating-point ambiguity and the mean square error after integer Gaussian transformation. An improved particle swarm optimization method is set up, including setting dynamic inertia weight, dynamic learning factor, boundary detection and control, adaptive iteration and scale factor improvement model based on the classic particle swarm optimization algorithm, supporting global search in high-dimensional ambiguity space and extracting the global optimal solution of integer ambiguity candidate vectors; The optimal and suboptimal integer ambiguity candidate vectors are estimated based on the improved particle swarm optimization method, and the corresponding residual quadratic form is obtained.

2. The GNSS integer ambiguity estimation method based on improved particle swarm optimization according to claim 1, characterized in that: The integer Gaussian transform parameterization is to first decompose the ambiguity variance-covariance matrix to obtain a conversion matrix, and then perform Gaussian transform on the floating-point ambiguity and its accuracy that eliminates the hardware delay between the receiver and the satellite.

3. The GNSS integer ambiguity estimation method based on improved particle swarm optimization according to claim 1, characterized in that: The establishment of the fuzzy search objective function, the determination of the search initial value and the search space are as follows: Establishing the ambiguity search objective function with the quadratic form of the integer candidate vector residual as a function and the minimum function value as a target; performing a rounding operation on each floating-point ambiguity component after integer Gaussian transformation to determine the search initial value; The floating-point ambiguity components after integer Gaussian transformation are combined with the ambiguity mean error tripled and rounded up and down to obtain the left and right closed intervals of the component. The hyperspace for searching integer ambiguity candidate vectors is cyclically determined, and it is assumed that this space contains the true ambiguity vector with a confidence probability close to 100%.

4. The GNSS integer ambiguity estimation method based on improved particle swarm optimization according to claim 1, characterized in that: The dynamic inertia weight improvement model sets the inherited weight of the particle along the inertia direction to change dynamically with the iterative evolution process of the particle. It is divided into three stages and is determined as follows: In the early evolution process, the inertia weight is set as a convex function. The characteristic that the convex function decreases more slowly than the linear function is used to reduce the decrease rate of the particle's flight speed, so that the particles can conduct a large-scale search in the entire hyperspace in the early stage. In the mid-term evolution process, the inertia weight uses a linear function to accelerate the convergence of all particles in the population, reduce the particle search range, and make particles search near the existing optimal integer vector; In the later evolution process, the inertia weight is mutated to make the particles jump out of the optimal region and search for potential solutions in the area outside the existing optimal integer vector to ensure that the particles will not fall into the local optimum; If the integer optimal solution has been searched in the first two steps, the existence of the third step will not change the final estimation result; if the search in the first two steps falls into a local optimum, the third step can be adjusted.

5. The GNSS integer ambiguity estimation method based on improved particle swarm optimization according to claim 1, characterized in that: The dynamic learning factor improvement model includes individual learning factors and social learning factors, which are used to ensure that the individual historical optimum and the population historical optimum have different weights at different evolutionary stages, and are determined as follows: Set initial and end values ​​for individual learning factors and social learning factors respectively; Establish a functional relationship between the learning factor and the current number of iterations, the maximum number of iterations, and the initial and final values ​​of the learning factor; This makes individual learning factors dominate in the early evolutionary process, while the influence of social learning factors increases in the later stage.

6. The GNSS integer ambiguity estimation method based on improved particle swarm optimization according to claim 1, characterized in that: The improved boundary detection and control model is used to prevent particles from crossing the boundary beyond the search space of the GNSS integer solution. Otherwise, the out-of-bounds particles lose the meaning of the solution, which leads to an erroneous fixed solution. It is determined by the following method: After the current particle completes the position update, determine whether it exceeds the upper and lower limits of the search interval; If a particle crosses the boundary, the flight speed of the particle is adjusted again. During this process, a random number can be introduced to randomly change the flight direction of the particle while adjusting the speed. After adjusting the speed, update the position again; The loop repeats until all particles in the current iteration are within the search space.

7. The GNSS integer ambiguity estimation method based on improved particle swarm optimization according to claim 1, characterized in that: The adaptive iterative improvement model introduces the concept of aggregation degree, which is used to reflect the aggregation degree of all particles in the current iteration, and is determined as follows: Establishing a clustering function by combining particle states, the dimensions of integer candidate vectors, and population size, wherein the particle states are the positions of the integer candidate vectors; After each iteration, the aggregation degree of the population is calculated to represent the distance between all individuals in the current iteration; If the aggregation degree is less than the corresponding threshold, the iterative evolution ends, otherwise the search continues.

8. The GNSS integer ambiguity estimation method based on improved particle swarm optimization according to claim 1, characterized in that: The scale factor improvement model uses a certain proportion of dominant particles to replace the traditional consistent population historical optimal solution, which can further prevent the search results from falling into the local optimum. It is determined by the following method: Select some particles with smaller fitness function values ​​in the current iteration as the set of dominant particles, and support quickly obtaining the set by sorting in ascending order of fitness function values; Calculate the distance between the current particle and each dominant particle, and select the dominant particle with the closest distance as the historical global optimal; The dominant particle is used to replace the global optimal population history and update the speed.

9. The GNSS integer ambiguity estimation method based on improved particle swarm optimization according to claim 1, characterized in that: The process of integer ambiguity candidate vector estimation based on the improved particle swarm optimization method is as follows: The input is the floating-point ambiguity that eliminates the hardware delay between the receiver and the satellite, the ambiguity variance-covariance matrix, and the preset control parameters of the improved particle swarm optimization method; Subsequently, based on the integer Gaussian transform parameterization, an improved particle swarm optimization method is used to perform integer estimation following the search objective function in the search space; The final output is the optimal and suboptimal integer ambiguity candidate vectors and the corresponding residual quadratic form.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the GNSS integer ambiguity estimation method based on improved particle swarm optimization are implemented as described in any one of claims 1 to 9.

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