A carrier phase localization method based on chaotic mapping sparrow regression search

Abstract

This invention relates to the field of satellite navigation technology, specifically to a carrier phase positioning method based on chaotic mapping sparrow regression search. In the process of searching for integer ambiguities, a chaotic mapping is used to initialize the sparrow population, optimize follower and watchdog strategies, introduce a memory regression model and a monitoring strategy based on the sparrows' foraging behavior, and introduce baseline constraints based on the carrier's coherence characteristics. Through these settings, this invention overcomes the problems of getting trapped in local optima and poor convergence in integer ambiguity search, improves the exploration and development performance of the search space, and achieves rapid integer ambiguity search. Furthermore, through three-dimensional experiments, multi-dimensional experiments, and RTK experiments in a real-world environment, this invention outperforms traditional methods in terms of real-time performance, effectiveness, and accuracy.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation technology, specifically to a carrier phase positioning method based on chaotic mapping sparrow regression search. Background Technology

[0002] Modern satellite navigation and positioning technologies can generally be divided into two categories: pseudorange positioning and carrier phase positioning. In pseudorange measurement, due to the limitation of C / A code chip length, the accuracy of pseudorange positioning is at the meter level, suitable for single-point positioning. However, in carrier phase measurement, the carrier wavelength is only tens of centimeters, and the accuracy of carrier phase positioning can be at the centimeter or millimeter level, suitable for high-precision positioning. With the increasing application of high-precision positioning, such as millimeter-level measurement and monitoring of geological disaster deformation, centimeter-level positioning during UAV flight, and centimeter-level intelligent driving of automobiles on roads, carrier phase-based positioning technology has become a research hotspot.

[0003] When using satellites to achieve high-precision positioning via carrier phase, the integer part of the carrier phase is an unknown random integer, called integer ambiguity. Integer ambiguity resolution (IAR) is crucial for GNSS positioning based on carrier phase. Traditional IAR algorithms suffer from problems such as complex search processes, excessively long search times, susceptibility to local optima, and poor convergence. Summary of the Invention

[0004] The purpose of this invention is to provide a carrier phase positioning method based on chaotic mapping sparrow regression search, which aims to solve the technical problems of complex and time-consuming integer ambiguity resolution search process in existing satellite carrier phase positioning processes.

[0005] To achieve the above objectives, this invention provides a carrier phase localization method based on chaotic mapping sparrow regression search, comprising the following steps:

[0006] Step 1: System initialization, initializing the population's number of individuals, individual dimensions, number of iterations, warning values, and search space range;

[0007] Step 2: Population initialization;

[0008] Step 3: Calculate and sort the initial population fitness values, and record the best and worst positions of individuals;

[0009] Step 4: Classify sparrows according to their fitness values ​​and update the positions of the corresponding sparrows;

[0010] Step 5: Calculate population density and complete individual migration;

[0011] Step 6: Repeat step 3 to update and record the best fitness value, average fitness value, and worst fitness value of the population;

[0012] Step 7: Determine whether the optimal fitness value, worst fitness value, and average fitness value of the population converge to a point. If they converge to a point, perform integer ambiguity resolution.

[0013] Otherwise, continue iterating;

[0014] Step 8: Determine if the number of iterations has reached the total number of iterations. If it has, terminate the iteration and output the integer ambiguity.

[0015] Otherwise, return to step 4.

[0016] Optionally, during the population initialization process, an initial population is generated through piecewise linear chaotic mapping to obtain an initial position with a sufficiently uniform distribution.

[0017] The piecewise linear chaotic mapping expression is:

[0018]

[0019] In the formula, p is a control parameter. By assigning an initial value to p, a random sequence with good statistical properties can be generated after iteration.

[0020] Optionally, the fitness function for calculating the initial population fitness value is to use the least squares method, fitting the fixed solution with the fuzzy floating-point solution, so that the floating-point solution reaches integer optimality. The cost function is:

[0021]

[0022] The fitness function is:

[0023] f(N)=b-lg(J(N))

[0024] In the formula, N is the double-difference ambiguity floating-point solution, and Q is the double-difference ambiguity fixed-point solution. -1 is the inverse of the corresponding covariance matrix, and b is a sufficiently large number such that the fitness function f(N) is always positive.

[0025] Optionally, the process of classifying sparrows based on fitness values ​​and updating the positions of the corresponding role sparrows includes the following steps:

[0026] Update the discoverer's location;

[0027] Update the position of the followers;

[0028] Update the location of the vigilant.

[0029] Optionally, during the process of updating and recording the optimal fitness value, average fitness value and worst fitness value of the population, the fitness value of the sparrow's new position is specifically calculated and sorted. The new position of each sparrow is compared with the remembered optimal position, the optimal value is selected and the global optimal position and corresponding fitness value are updated.

[0030] Optionally, regression foraging behavior can be introduced during the process of selecting the optimal value and updating the global optimal position. The strategy formula is as follows:

[0031]

[0032] In the formula, The optimal fitness value, X is the current fitness value. best To memorize the optimal position, X k+1 The current position is used; by introducing regression foraging behavior, the optimal foraging position during the search process is memorized.

[0033] Optionally, baseline constraints are introduced when performing integer ambiguity resolution search, and the constraints of double-difference integer ambiguity obtained by following the principle of GPS interferometer carrier attitude measurement are applied.

[0034] This invention provides a carrier phase localization method based on chaotic mapping sparrow regression search. During the integer ambiguity search process, a chaotic mapping is used to initialize the sparrow population, optimize follower and watchdog strategies, introduce a memory regression model and monitoring strategy based on sparrow foraging behavior, and introduce baseline constraints based on the carrier's coherence characteristics. Through these settings, this invention overcomes the problems of getting trapped in local optima and poor convergence in integer ambiguity search, improves the exploration and development performance of the search space, and achieves rapid integer ambiguity search. Furthermore, through three-dimensional experiments, multi-dimensional experiments, and RTK experiments in a real-world environment, this invention outperforms traditional methods in terms of real-time performance, effectiveness, and accuracy. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart illustrating a carrier phase localization method based on chaotic mapping sparrow regression search according to the present invention.

[0037] Figure 2 This is a schematic diagram of the antenna receiving a carrier wave according to the present invention.

[0038] Figure 3 This is a three-dimensional result diagram of integer ambiguity using the GA algorithm in a specific embodiment of the present invention.

[0039] Figure 4 This is a three-dimensional result diagram of integer ambiguity using the AGA algorithm in a specific embodiment of the present invention.

[0040] Figure 5 This is a three-dimensional result diagram of integer ambiguity using the SSA algorithm in a specific embodiment of the present invention.

[0041] Figure 6 This is a three-dimensional result diagram of integer ambiguity using the method of the present invention in a specific embodiment of the present invention.

[0042] Figure 7 This is a three-dimensional result diagram of integer ambiguity using the LAMBDA algorithm in a specific embodiment of the present invention.

[0043] Figure 8 This is a three-dimensional result diagram of integer ambiguity using the MLAMBDA algorithm in a specific embodiment of the present invention.

[0044] Figure 9 This is a baseline solution result diagram in a specific embodiment of the present invention.

[0045] Figure 10 This is a comparison chart of real-time dynamic positioning (RTK) errors using the method of the present invention in a specific embodiment of the present invention.

[0046] Figure 11 This is a comparison chart of the cumulative distribution curves of positioning errors in specific embodiments of the present invention. Detailed Implementation

[0047] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0048] Please see Figure 1 This invention provides a carrier phase localization method based on chaotic mapping sparrow regression search, comprising the following steps:

[0049] S1: System initialization, initializing the population's number of individuals, individual dimensions, number of iterations, warning values, and search space range;

[0050] S2: Population initialization;

[0051] S3: Calculate and sort the initial population fitness values, and record the best and worst positions of individuals;

[0052] S4: Classify sparrows according to their fitness values ​​and update the positions of the corresponding sparrows for each role;

[0053] S5: Calculate population density and complete individual migration;

[0054] S6: Repeat step S3 to update and record the best fitness value, average fitness value, and worst fitness value of the population;

[0055] S7: Determine whether the optimal fitness value, worst fitness value and average fitness value of the population converge to a point. If they converge to a point, perform integer ambiguity resolution.

[0056] Otherwise, continue iterating;

[0057] S8: Determine if the number of iterations has reached the total number of iterations. If it has, terminate the iteration and output the integer ambiguity.

[0058] Otherwise, return to step S4.

[0059] The following provides further explanation in conjunction with the specific implementation steps:

[0060] In step S1, the system is initialized, which involves initializing the population size, individual dimension, number of iterations, warning value, and search space range.

[0061] In step S2, a population initialization operation is performed, specifically by generating an initial population through a piecewise linear chaotic map (PWLCM) to obtain an initial position with a sufficiently uniform distribution.

[0062] The PWLCM mapping expression is:

[0063]

[0064] In the formula, p is a control parameter. By assigning an initial value to p, a random sequence with good statistical properties can be generated through iteration.

[0065] Step S3: Calculate the initial fitness values. Calculate and sort the initial population fitness values, recording the best and worst positions of individuals. Specifically, the fitness function uses the least squares method, fitting a fixed solution with an ambiguity floating-point solution to achieve integer optimality for the floating-point solution. The cost function is:

[0066]

[0067] The fitness function is:

[0068] f(N) = b - lg(J(N))

[0069] Wherein, is the floating-point solution of the double-difference ambiguity, N is the fixed solution of the double-difference ambiguity, Q -1 is the inverse matrix of the corresponding covariance matrix, and b is a sufficiently large number such that the fitness function f(N) is always positive.

[0070] Step S4, classify the sparrows according to the fitness value and update the positions of the sparrows with corresponding roles, which specifically includes the following steps:

[0071] Step S41, update the position of the discoverer:

[0072]

[0073] Wherein, is the current position of the i-th sparrow in the j-th dimension at the (t + 1)-th iteration, is the current position of the i-th sparrow in the j-th dimension at the t-th iteration. α ∈ (0, 1] is a uniformly random number. iter max is the maximum number of iterations, Q is a random number subject to a normal distribution. L is a 1×d matrix, and each element therein is 1. R2 (R2 ∈ [0, 1]) and ST (ST ∈ [0.5, 1]) respectively represent the warning value and the safety value. When no predator appears (R2 < ST), the discoverer can search this area; when a predator is discovered (R2 ≥ ST), the population needs to randomly move to a safe area;

[0074] Step S42, update the position of the follower:

[0075]

[0076] Wherein, [[ID=三十七]]is the current position of the i-th sparrow in the j-th dimension at the (t + 1)-th iteration, is the current position of the i-th sparrow in the j-th dimension at the t-th iteration, is the current position of the optimal discoverer at the (t + 1)-th iteration, and D is the population dimension;

[0077] Step S43, update the position of the vigilant:

[0078]

[0079] Wherein, is the current position of the i-th sparrow in the j-th dimension at the (t + 1)-th iteration, is the current position of the i-th sparrow in the j-th dimension at the t-th iteration, Let f be the globally optimal position at the t-th iteration. β is a random number following a normal distribution, and K∈[-1,1] is a uniformly random number. i f represents the fitness value of the current individual sparrow. g This represents the current globally optimal fitness value.

[0080] Step S5: Calculate the population density (den)

[0081]

[0082] In the formula, X a,k Let X be the current position of the a-th sparrow in the k-th dimension. b,k Let D be the current position of the b-th sparrow in the k-th dimension, where D is the population dimension.

[0083] When the population density is too high (den < p) m When this happens, individuals will migrate:

[0084]

[0085] In the formula, Let be the current position of the i-th sparrow in the j-th dimension at the (t+1)-th iteration. Let p be the current position of the i-th sparrow in the j-th dimension at the t-th iteration, δ be the sparrow population boundary, and p be the position of the i-th sparrow in the j-th dimension. m This is the migration threshold. After the migration is complete, the algorithm is less likely to get trapped in a local optimum.

[0086] In step S6, repeat step S3, calculate and sort the fitness values ​​of the sparrows' new positions, compare the new position of each sparrow with the best position in memory, select the best value and update the global best position and corresponding fitness value, and record the best fitness value, average fitness value and worst fitness value of the population.

[0087] Furthermore, during the process, regression foraging behavior is introduced, and its strategy formula is as follows:

[0088]

[0089] In the formula, The optimal fitness value, X is the current fitness value. best To memorize the optimal position, X k+1 The current position is shown; by introducing regression foraging behavior, the optimal foraging position during the search process is memorized. When the environment becomes harsh, the sparrows will return to the memorized optimal position, preventing the population from getting trapped in local optima and improving convergence accuracy.

[0090] Step S7: Determine whether the optimal, worst, and average fitness values ​​of the population converge to a single point. If they converge, perform integer ambiguity resolution; otherwise, continue iterating.

[0091] Step S8: Determine whether the number of iterations has reached the total number of iterations. If it has, terminate the iteration and output the integer ambiguity; otherwise, return to step S4.

[0092] Furthermore, when using the method of this invention for fuzzy search, baseline constraints are introduced to ensure the uniqueness of the results, reduce the search space, and improve search efficiency. According to Figure 2 A single-differential carrier phase equation can be established:

[0093]

[0094] In the formula, This is single-difference integer ambiguity, where L is the baseline vector, θ is the angle between the unit line of the line of sight vector e and the baseline vector L, and λ is the carrier wavelength. It is a single differential carrier phase;

[0095] Therefore, the dual-differential carrier phase equation is derived:

[0096]

[0097] Based on the principles of GPS interferometer carrier attitude measurement, It should be less than |L|. Substituting this into the above equation, the constraint equation for double-difference integer ambiguity can be described as follows:

[0098]

[0099] To illustrate the performance of this invention, specific embodiments are also provided for simulation experiments for verification:

[0100] Specifically, this paper compares six algorithms: Traditional Genetic Algorithm (GA), Adaptive Genetic Algorithm (AGA), Least-square AMBiguity Decorrelation Adjustment (LAMBDA), Modified Least-square AMBiguity Decorrelation Adjustment (MLAMBDA), Sparrow Search Algorithm (SSA), and the method of this invention. Three simulation examples are used for comparison and illustration.

[0101] Simulation Example 1: 3D IAR Experiment

[0102] The truth values ​​for the three-dimensional (3D) floating-point solution and integer ambiguity are as follows:

[0103]

[0104] The population has 20 individuals, an individual dimension of 3, a maximum number of iterations of 100, and L=1. In each generation, the top 20% of sparrows by fitness value are discoverers, 10% of sparrows are randomly selected as watchers, and the rest are followers.

[0105] The three-dimensional results of integer ambiguity are as follows Figures 3 to 8 As shown. In Figure 3 In the process, the GA algorithm ultimately obtained three local optima, failing to find the correct solution; Figure 4 In this context, the AGA algorithm can find the correct solution, but local optima still exist within the solution; Figure 5 In this context, the SSA algorithm's search results are distributed around the global optimum, forming multiple solutions; Figures 6 to 8 In this study, the method of this invention, the LAMBDA and MLAMBDA algorithms can all search for the correct integer ambiguity, and the population can converge completely to a point.

[0106] To verify the accuracy and reliability of the algorithm, this embodiment repeated the experiment 100 times. The performance analysis results of the 3D IAR experiment are shown in Table 1:

[0107] Table 1 Performance Analysis Results

[0108] algorithm Results of the whole week Number of iterations Average solution time ( / s) Success rate (%) GA Unstable Local Optimum ------- ------- AGA 5,3,4 28 0.2531 95 SSA Unstable Non-convergence ------- ------- LAMBDA 5,3,4 ------ 0.0621 100 MLAMBDA 5,3,4 ------ 0.0314 100 Method of the present invention 5,3,4 7 0.0309 100

[0109] As shown in Table 1, the GA algorithm gets stuck in a local optimum, the SSA algorithm fails to converge, and the results are unstable. The CY_SRSA, AGA, LAMBDA, and MLAMBDA algorithms can all solve integer ambiguities, but the overall performance of the method in this invention is better than that of the AGA, LAMBDA, and MLAMBDA algorithms, as can be seen from the number of iterations, average solution time, and success rate.

[0110] Simulation Example 2: Multidimensional IAR Experiment

[0111] Experiments on 6D and 12D ambiguity resolution were added to the CY_SRSA, LAMBDA, and MLAMBDA algorithms. The true values ​​of the 6D and 12D floating-point solutions and integer ambiguities are as follows:

[0112]

[0113] N 6(truth) =[-28506 65833 38880 5008 29210 -257] T

[0114]

[0115] N 12(truth) =[-28451 65749 38814 5025 -29195 -278 -22170 51233 30245 3916-22725 -144] T

[0116] The results of the multidimensional IAR experimental performance analysis are shown in Table 2:

[0117] Table 2 Performance Analysis Results

[0118]

[0119] As shown in Table 2, all three algorithms can solve integer ambiguity in both three-dimensional and multi-dimensional cases. However, the method of this invention has a shorter average solution time, a higher success rate, and better overall performance than the LAMBDA and MLAMBDA algorithms.

[0120] Simulation Example 3: Real Data Experiment

[0121] The method of this invention was applied to an RTK experiment. In the experiment, an MTX906 receiver was used to collect 700 data points. The baseline length was known to be 2.1m, and a total of 10 GPS and BDS satellites were received, with PRNs G07, G08, G09, G27, C06, C09, C12, C24, C26, and C33. The experimental results are as follows... Figure 4-6 As shown.

[0122] Figure 9 The graph shows the baseline calculation results. As can be seen from the graph, the baseline fluctuates between 2.11m and 2.12m, with an amplitude of about 1 cm. Figure 10 The positioning errors of SSA, LAMBDA, and the method of this invention during RTK are described. Due to the poor convergence of the SSA algorithm, floating-point solutions appear in the ambiguity, affecting the positioning accuracy. The LAMBDA algorithm has some floating-point solutions in the first 40 periods, resulting in an initial error of meter level. However, after the ambiguity is fixed in the later period, the accuracy can reach centimeter level. The output coordinate errors of the method of this invention are ±1cm, ±2cm, and ±1cm in the east, north, and upward directions, respectively, with corresponding standard deviations of 0.35cm, 0.63cm, and 0.37cm, respectively. Therefore, the accuracy of the method of this invention can reach centimeter level. Figure 11 The cumulative distribution curve of the positioning error is shown in the figure. It can be seen that the LAMBDA algorithm has a faster growth rate of cumulative positioning error in the first 30 periods. This is because there are a large number of floating-point solutions during these periods, with a solution error of approximately 1m, resulting in a larger initial cumulative error. After the ambiguity is fixed, the growth rate of the cumulative positioning error is close to that of the CY_SRSAS algorithm. The growth rate of the cumulative positioning error of the SSA algorithm is consistently greater than that of the CY_SRSAS algorithm. Therefore, compared with the other two algorithms, the cumulative error rate of the method in this invention grows the slowest. The RTK experimental performance analysis results are shown in Table 3.

[0123] Table 3. RTK Performance Analysis Results

[0124] algorithm Time ( / s) Fixed rate Standard deviation (E) Standard deviation (N) Standard deviation (U) Method of the present invention 19.15s 100％ 0.35cm 0.63cm 0.37cm SSA 20.18s 93.42％ 15.75cm 50.15cm 35.58cm LAMBDA 21.06s 95.57％ 14.68cm 6.84cm 21.36cm

[0125] As shown in Table 3, the method of this invention achieves a 100% fixation rate and requires only 19.15 seconds of runtime. Compared with the other two methods, this method reduces runtime by 1.03 seconds and 1.91 seconds, respectively, and improves fixation rates by 6.58% and 4.43%, respectively. Furthermore, the standard deviations in the three directions indicate that the method of this invention has the highest positioning accuracy. Therefore, the method of this invention exhibits a good integer ambiguity repair rate in practical applications and can meet the requirements of real-time calculation.

[0126] The results of the three-dimensional and multi-dimensional experiments show that the proposed method outperforms the other five IAR methods in terms of real-time performance, effectiveness, and accuracy. Experiments in real-world environments also verify the applicability, stability, and reliability of the algorithm, making it suitable for engineering applications.

[0127] In summary, compared with the prior art, the present invention has the following advantages and beneficial effects:

[0128] (1) Chaotic mapping is used to initialize the sparrow population to ensure species diversity; the exploration and development performance of the search space is improved by optimizing the follower strategy and the vigilant strategy; population density monitoring strategy is used to maintain population diversity and overcome the problem of getting trapped in local optima; a memory regression model for sparrow foraging is proposed to enhance convergence ability.

[0129] (2) Baseline constraints are introduced based on the coherence characteristics of the carrier to narrow the search space and ensure that the search space contains the correct solution.

[0130] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A carrier phase positioning method based on chaotic mapping sparrow search, characterized in that, The method comprises the following steps: Step 1: system initialization, initializing the number of individuals in the population, individual dimension, iteration number, early warning value, and search space range; Step 2: population initialization; Step 3: calculating the initial population fitness value and sorting, recording the optimal position and the worst position of the individual; Step 4: classifying the sparrows according to the fitness value, and updating the positions of the corresponding role sparrows; Step 5: calculating the population density and completing individual migration; Step 6: repeatedly executing Step 3, updating and recording the optimal fitness value, average fitness value and worst fitness value of the population; Step 7: judging whether the optimal fitness value, worst fitness value and average fitness value of the population converge to a point, if yes, performing whole-week ambiguity resolution; Otherwise, continue iteration; Step 8: judging whether the iteration number reaches the total iteration number, if yes, terminating iteration and outputting the whole-week ambiguity; Otherwise, returning to Step 4; In the process of population initialization, the initial population is generated by piecewise linear chaotic mapping, and the initial position is uniformly distributed; The expression of the piecewise linear chaotic mapping is: wherein is a control parameter, and by assigning an initial value to an initial value, a random sequence with good statistical properties can be generated after iteration.

2. The carrier phase positioning method based on chaotic mapping sparrow regression search according to claim 1, wherein The fitness function for calculating the initial population fitness value is to fit the fixed solution with the ambiguity floating point solution by using the least square method, so that the floating point solution reaches the integer optimum, and the cost function is: The fitness function is: where is the double-difference ambiguity float solution, is the double-difference ambiguity fixed solution, is the inverse of the corresponding covariance matrix, and b is a sufficiently large number such that the fitness function is always positive.

3. The carrier phase positioning method based on chaotic mapping sparrow regression search according to claim 2, wherein The process of classifying the sparrows according to the fitness value and updating the positions of the corresponding role sparrows comprises the following steps: Updating the position of the discoverer; Updating the position of the follower; Updating the position of the alarm.

4. The carrier phase positioning method based on chaotic mapping sparrow regression search according to claim 3, wherein In the process of updating and recording the optimal fitness value, average fitness value and worst fitness value of the population, the fitness value of the new position of the sparrow is calculated and sorted, the new position of each sparrow is compared with the optimal position in memory, the optimal value is selected and the global optimal position and the corresponding fitness value are updated.

5. The carrier phase positioning method based on chaotic mapping sparrow regression search according to claim 4, wherein In the process of selecting the optimal value and updating the global optimal position, the regression foraging behavior is introduced, and the strategy formula is as follows: wherein is the best fitness value, is the current fitness value, is the memorized best position, is the current position; by introducing the regressive foraging behavior, the best foraging position in the search process is memorized.

6. The carrier phase positioning method based on chaotic mapping sparrow regression search according to claim 5, wherein When performing whole-week ambiguity resolution search, the baseline constraint is introduced, and the constraint of double-difference whole-week ambiguity obtained by following the carrier attitude measurement principle of global positioning system interferometer is followed.

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