Baseline constraint type real-time direction finding method optimized by AGWO algorithm

Abstract

The invention discloses a baseline constraint type real-time direction finding method based on AGWO algorithm optimization, and relates to the field of global satellite navigation, and the baseline constraint type real-time direction finding method based on AGWO algorithm optimization is mainly divided into two parts. One method is an optimized rapid satellite selection method based on the eagle-grey wolf algorithm, the AGWO heuristic algorithm is introduced into the satellite navigation field to achieve the optimal satellite selection strategy, satellite ephemeris data for direction finding are selected, the search range of the integer ambiguity in the subsequent direction finding step is limited, the calculation complexity is greatly reduced, and the optimal satellite selection strategy is achieved. Therefore, the purpose of real-time direction finding is achieved. The first method is a baseline constraint type five-step real-time direction finding method, the second method is a baseline constraint type five-step real-time direction finding method, baseline information between double antennas is fully utilized in an observed quantity domain, an ambiguity domain and a direction finding domain, meanwhile, baseline ambiguity factors are fully considered, and it is ensured that high-precision and high-reliability direction finding can be achieved in a dynamic environment under the limitation of low-cost GNSS equipment.

Description

Technical Field

[0001] The present invention relates to the field of Global Navigation Satellite System (GNSS), involving GNSS direction finding and artificial intelligence technologies, and particularly focuses on the dual-antenna low-cost GNSS direction finding technology driven by a heuristic optimization algorithm in a dynamic environment. Specifically, it relates to a baseline constraint type real-time direction finding method optimized by an AGWO algorithm. Background Art

[0002] Heading measurement is an essential core technology in fields such as aerospace, navigation, and land transportation navigation, and has great significance in practical applications. With the rapid development of GNSS carrier phase differential technology, the heading measurement technology based on it has gradually emerged and has great development prospects. By reasonably arranging two or more antennas, an independent multi-antenna GNSS attitude measurement system can be formed. Taking the carrier phase as the observation value, differential operations are performed to obtain the baseline vector, and further calculations can be used to obtain the attitude information of the baseline vector in the geographic coordinate system.

[0003] Currently, the research and development direction of GNSS direction finding devices is gradually tending towards low cost and miniaturization. However, at the hardware level, low-cost GNSS receiver boards are weaker than high-performance GNSS receiver boards in terms of clock accuracy, number of signal channels, available signal frequencies, and signal processing fineness. As a result, low-cost GNSS receivers have fewer available observables, larger observable noise, and difficulties in aspects such as observable quality and model strength. Therefore, research on achieving high-precision and highly reliable low-cost GNSS direction finding by upgrading and improving direction finding algorithms under low-cost GNSS hardware conditions is advanced and urgent. With the rapid development of satellite navigation technologies in various countries, various attitude solution methods based on baseline constraints and real-time dynamic solution methods for integer ambiguity have provided the possibility for the realization of low-cost and high-precision GNSS attitude measurement devices. Currently, there are mainly three methods for integer ambiguity resolution using baseline constraints: Method 1 is to use a fixed baseline length to construct a function equation related to the baseline estimator, introduce and strengthen the model strength. However, this method requires a relatively long fixed baseline length. Otherwise, the ignored linearization error may introduce model bias, which will instead cause the model estimation to be biased and weaken the direction finding accuracy. Usually restricted by the carrier installation, the fixed baseline length of a dual-antenna generally does not exceed 10m, which makes it difficult to exert the advantages of this method.

[0004] Method 2 uses the baseline length constraint information as the basis for verifying the correctness of the integer ambiguity, ensuring the correctness of the solution, and thus indirectly ensuring the direction finding accuracy and reliability. However, the floating-point solution obtained using low-cost devices has relatively low accuracy, and sometimes the correct integer ambiguity cannot be solved due to the simplification of the rules, resulting in relatively small improvement.

[0005] Method 3 uses the known fixed baseline length constraint information to reconstruct the minimum cost function and adjust the integer ambiguity search criterion. A typical method is the Least-squares Ambiguity Decorrelation Adjustment (LAMBDA) algorithm with baseline length constraint. Since this method adjusts the search criterion, the success rate of integer ambiguity solution is greatly improved, but at the same time, it also increases the complexity of the search, making it difficult to play a role when the device computing power is limited and the real-time requirement is high.

[0006] Method 4 screens the optimal satellite combination through a hierarchical satellite selection strategy based on elevation angle and azimuth angle, constructs a geometric model by combining pseudorange and carrier phase observations, and finally uses the LAMBDA algorithm for ambiguity resolution and baseline length residual verification. Although this method simplifies the satellite selection process and reduces the search range to a certain extent, the hierarchical strategy lacks the ability of global search optimization and is difficult to dynamically adapt to changes in satellite geometry distribution. Especially in a large-signal environment fluctuation or dynamic scenario, it may not be able to select the truly geometrically optimal satellite combination, thus making it difficult to ensure the accuracy requirements. In addition, the baseline ambiguity is not fully considered in this method, so it is impossible to ensure sufficient direction finding accuracy in a high-dynamic or low-cost restricted device environment, thus affecting the stability and reliability of the solution result.

[0007] By comprehensively comparing the above methods, using the known fixed baseline length to solve the integer ambiguity is a relatively effective method to ensure the direction finding accuracy and reliability of GNSS. However, there are still many problems to be solved in the current various methods. Especially in the face of the limitations of low-cost GNSS direction finding devices, how to achieve the goal of real-time direction finding in a dynamic environment while ensuring high direction finding accuracy and high reliability. Summary of the Invention

[0008] An embodiment of the present invention provides an AGWO algorithm-optimized baseline constraint-based real-time direction finding method. Under the condition of low-cost GNSS hardware, the success rate of integer ambiguity resolution is improved by optimizing the direction finding algorithm, so as to achieve high-precision, high-reliability, and good real-time low-cost dual-antenna GNSS direction finding in a dynamic real environment.

[0009] In the first aspect, the present invention provides an AGWO algorithm-optimized baseline constraint-based real-time direction finding method, including: Obtain all visible satellites with elevation angles greater than the altitude cutoff angle at the current epoch and the observation information of each visible satellite; Construct an observation matrix from the observation information of each visible satellite, and perform optimal satellite selection through the AGWO algorithm based on the observation matrix to obtain the optimal satellite combination; Calculate the double-difference observables of the optimal satellite combination, and construct virtual observables based on the baseline length in the observable domain to enhance the model strength at the observable domain level; When the sum of the number of observables and virtual observables at this epoch is greater than a preset value, introduce baseline ambiguity constraints in the LAMBDA algorithm to perform ambiguity resolution; Use the prior baseline length as the standard to judge whether the ambiguity resolution result is correct, reconstruct the discrimination criterion, and screen out the correct integer ambiguity; When an integer ambiguity that meets the discrimination criterion is found, obtain the baseline vector according to the correct integer ambiguity, and thus complete the direction finding according to the geometric relationship; If an integer ambiguity that meets the discrimination criterion is not found, then limit and expand the subsequent search range according to the optimal satellite combination obtained by AGWO optimal satellite selection, form a new ambiguity search space, re-solve the alternative ambiguity set in the new ambiguity search space, and use the prior baseline length discrimination criterion to perform ambiguity resolution until the integer ambiguity is successfully fixed or the ambiguity resolution is all completed.

[0010] In some examples, the construction of the observation matrix from the observation information of each visible satellite and the performance of optimal satellite selection through the AGWO algorithm based on the observation matrix to obtain the optimal satellite combination include: For any number of visible satellites, its observation vector is , represents the altitude angle of the visible satellite, represents the azimuth angle of the visible satellite, and the observation vectors of all visible satellites will form a complete observation matrix , and construct a fitness function from the observation matrix; Use the update of the eagle population to obtain the global optimal position of the current round , and use this to guide the update of the optimal position of the gray wolf population, where the individuals in the eagle population and the gray wolf population both represent a satellite combination; Find the optimal satellite combination by continuously iteratively updating the positions of the population individuals to minimize the fitness function value.

[0011] In some examples, the update of for the optimal position of the gray wolf population, where is the control parameter, is the optimal position of the updated gray wolf population.

[0012] In some instances, from the fitness function is obtained, where .

[0013] In some instances, from the virtual observation equation is obtained, where is the geometric baseline vector, is the approximation of the baseline vector, is the length of the baseline vector, is the linearized residual.

[0014] In some instances, introducing baseline ambiguity constraints in the LAMBDA algorithm for ambiguity resolution includes: From the initial ambiguity solution is obtained , where is the ambiguity design matrix, is the ambiguity covariance matrix, is the observation information; Introducing baseline ambiguity constraints in the LAMBDA algorithm, the initial ambiguity solution is optimized and solved to search for n groups of alternative ambiguity solutions.

[0015] In some instances, from the optimization objective of the LAMBDA algorithm is obtained, is the ambiguity function of the baseline length, is the initial estimate of the baseline length, is the standard deviation of the baseline length, λ is the trade-off coefficient, is the covariance matrix of the ambiguity parameters, is the ambiguity parameter vector, that is, the integer ambiguity to be solved.

[0016] In some instances, using the prior baseline length as the criterion for judging the correctness of the ambiguity solution result, reconstructing the discrimination criterion, and screening out the correct integer ambiguity includes: Screening out the integer ambiguity combinations less than the preset threshold in the ambiguity alternative set composed of n groups of alternative ambiguities, where is the least squares residual of the double-difference observation, represents the weight matrix of the double-difference observables; Calculating the baseline length of the screened integer ambiguity combinations, taking the difference between the calculated baseline length of the integer ambiguity combinations and the known baseline length, and taking the group of integer ambiguities corresponding to the smallest difference as the correct integer ambiguity.

[0017] In some instances, the optimal satellite combination obtained based on the AGWO most optimal star is used to limit and expand the subsequent search range, including: To satisfy the condition that the weighted sum of squares of the least squares residuals is minimized, that is The integer ambiguity group is used as the search space. Taking each ambiguity in the search space as a benchmark, ±m weeks are successively added to it to form a new ambiguity search space , which contains ambiguity combinations, where k is the number of satellites in the optimal combination after star selection by AGWO.

[0018] In some instances, from the baseline vector is obtained according to the correct integer ambiguity , where is the ambiguity transformation matrix, is the integer ambiguity solved by the improved LAMBDA algorithm, is the remaining floating-point solution of the carrier phase observation value.

[0019] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the following beneficial effects can be achieved: (1) Optimized the most optimal star selection strategy The present invention adopts the Eagle - Grey Wolf heuristic optimization algorithm (AGWO) to implement a star selection strategy that combines global search and local optimization, greatly reducing the complex calculation amount and significantly improving the real-time performance. At the same time, compared with the traditional hierarchical star selection strategy based on elevation angle and azimuth angle, this method can ensure quickly finding an approximately optimal satellite combination in a dynamic environment, minimizing the geometric dilution of precision (GDOP), and ensuring the accuracy of subsequent direction finding. (2) Enhanced the robustness and accuracy of the direction finding system The present invention designs a baseline constraint type five-step direction finding method, which fully utilizes the baseline information in the observation domain, ambiguity domain and direction finding domain. In particular, by resetting the ambiguity resolution method and expanding the limited ambiguity search space to improve the LAMBDA algorithm, and introducing the baseline ambiguity into it, the rationality of the baseline length is ensured, effectively solving the problem of unstable observation data of low-cost direction finding devices under noise interference and in a dynamic environment, significantly improving the accuracy of integer ambiguity resolution, and ensuring the stability and accuracy of the low-cost direction finding system under complex conditions. (3) Broadened the application field of low-cost direction finding devices The proposed real-time direction finding method based on the AGWO algorithm optimization with baseline constraints ensures high-precision direction finding results while effectively limiting the computational complexity of satellite selection and solution. This enables low-cost GNSS devices to adapt to complex dynamic environments under limited resource conditions and continuously provide stable and reliable direction finding results comparable to high-cost devices, thus significantly expanding the application scenarios and market prospects of low-cost direction finding devices. Brief Description of the Drawings

[0020] To more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present application and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0021] Figure 1 It is a schematic flowchart of the real-time direction finding method based on the AGWO algorithm optimization with baseline constraints provided by the embodiments of the present invention; Figure 2 It is a schematic diagram of direction finding solution provided by the embodiments of the present invention. Detailed Embodiments

[0022] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present invention.

[0023] In the following description, specific embodiments of the present invention will be described with reference to the steps and symbols executed by one or more computers, unless otherwise specified. Therefore, these steps and operations will be mentioned several times as being executed by a computer. The computer execution referred to herein includes the operations of a computer processing unit that represents electronic signals in a structured form of data. This operation transforms the data or maintains it at a position in the computer's memory system, which can be reconfigured or otherwise changed in a manner well known to those skilled in the art. The data structure maintained by the data is the physical location of the memory, which has specific characteristics defined by the data format. However, the principles of the present invention are described in the above text, which does not represent a limitation. Those skilled in the art will understand that the following various steps and operations can also be implemented in hardware.

[0024] As used herein, the terms "module" or "unit" may be regarded as software objects executed on the computing system. Different components, modules, engines, and services herein may be regarded as implementation objects on the computing system. The devices and methods herein are preferably implemented in software, but may also be implemented in hardware, all within the scope of protection of the present invention.

[0025] Those skilled in the art of the present technology can understand that, unless specifically stated otherwise, the singular forms "a", "an", and "the" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the specification of the present invention means the presence of features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or their groups. It should be understood that when we say an element is "connected" or "coupled" to another element, it can be directly connected or coupled to other elements, or there may also be intermediate elements. In addition, the "connection" or "coupling" used herein may include wireless connection or wireless coupling. The phrase "and / or" used herein includes all or any unit and all combinations of one or more related listed items.

[0026] The baseline constraint-based real-time direction finding method optimized by the AGWO algorithm is mainly divided into two parts. One is the optimized fast satellite selection method based on the Adaptive Grey Wolf Optimization Algorithm (AGWO). This method introduces the AGWO heuristic algorithm into the satellite navigation field to implement the optimal satellite selection strategy, selects the satellite ephemeris data for direction finding, and restricts the search range of the integer ambiguity in the subsequent direction finding steps, greatly reducing the computational complexity, thereby achieving the purpose of real-time direction finding. The other is the baseline constraint-based five-step real-time direction finding method. This method makes full use of the baseline information between the two antennas in the observation domain, ambiguity domain, and direction finding domain, and fully considers the baseline ambiguity factor to ensure high-precision and high-reliability direction finding in a dynamic environment under the limitation of low-cost GNSS devices.

[0027] (1) Optimized fast satellite selection method based on the Adaptive Grey Wolf Optimization Algorithm (AGWO) Step 1: Initialize satellite data First, all satellites with elevation angles greater than the altitude cut-off angle at the current epoch need to be obtained from the navigation message file, the number of all visible satellites at this epoch is counted, and all visible satellites at the current epoch are sorted in ascending order by the Pseudo-Random Noise (PRN) number, and then they are numbered in sequence from to make the serial number correspond to the visible satellites at this epoch.

[0028] Meanwhile, obtain the observation data of the currently visible satellites from the GNSS system. Assume that there are N visible satellites currently, and for each satellite the observation data includes the elevation angle and the azimuth angle , forming the following matrix:

[0029] These data will be used in the process of calculating the Geometric Dilution Precision (GDOP) of each satellite combination in the subsequent steps.

[0030] Step 2: Initialize the population Based on the obtained satellite data, initialize the population. The AGWO algorithm contains two populations: the eagle population and the gray wolf population, which are used for global search and local optimization respectively. Let the population size be , and each individual represents a combination of satellites randomly selected from satellites, where , otherwise directly select the only satellite for subsequent ambiguity search. Therefore, the size of the eagle population is , denoted as , and each is a satellite combination; the size of the gray wolf population is , denoted as , and each is also a satellite combination.

[0031] The initial position of each individual is randomly generated, and the specific initialization formula is:

[0032] Among them, and represent the minimum and maximum boundaries of the satellite combination respectively, is a random number used for random generation to ensure population diversity.

[0033] Step 3: Construction of the geometric observation matrix The construction of the geometric observation matrix H depends on the satellite observation matrix S obtained in Step 1, and each row of it represents the geometric relationship between a satellite and the receiver. For each satellite , its geometric observation vector can be expressed as:

[0034] Therefore, the geometric observation matrix H of the selected k satellites can be expressed as:

[0035] Each row of this matrix describes the geometric relationship between the satellite and the receiver, especially the projection of the satellite in three-dimensional space, which will be used in subsequent steps to calculate the Geometric Dilution of Precision (GDOP) for each satellite combination, so as to obtain the optimal satellite combination.

[0036] Step 4: Construct the fitness function The Geometric Dilution of Precision (GDOP) is a value that can directly reflect the impact of the satellite geometric distribution on the positioning accuracy. The more reasonable the geometric distribution, the smaller the GDOP value and the higher the positioning accuracy. Therefore, in the AGWO algorithm search, it can be used as the fitness function to evaluate the quality of the geometric distribution of each satellite combination and search for the optimal combination.

[0037] The GDOP value of the geometric distribution factor is calculated based on the geometric observation matrix H and is used to measure the impact of the satellite geometric structure on the positioning accuracy. Its specific calculation formula is:

[0038] where is the covariance matrix of the observation matrix, and the trace function is used to extract the sum of the diagonal elements of the matrix to obtain the GDOP value. The smaller the GDOP value, the better the geometric distribution of the satellite combination. To score each satellite combination in the population, the fitness function is defined as the reciprocal of the GDOP value:

[0039] Therefore, the smaller the GDOP value, the larger the fitness value, indicating that the geometric distribution of this satellite combination is more reasonable and the positioning accuracy is higher. The fitness function is used to select the satellite combination with the best geometric distribution, so as to guide the subsequent global search and local optimization. Step 5: Aquila global search stage The Aquila population is responsible for performing the global search, and the goal is to explore the entire satellite combination space as much as possible. Each Aquila individual will update its position in each iteration, and the formula is as follows:

[0040] where is the optimal solution in the current round of the Aquila population, is the average position of the Aquila population, is a constant, t is the current iteration number, and T is the maximum iteration number.

[0041] Through the global search of the Aquila population, the algorithm can explore a wider solution space and avoid falling into local optima.

[0042] Step 6: Local Optimization Stage of Grey Wolf Guided by Tianying Population The grey wolf population is used for local optimization. Each grey wolf individual gradually optimizes its position by referring to the global exploration results of Tianying. Three main individuals in the grey wolf group represent the optimal, sub-optimal, and third satellite combination optimal solutions in the current population respectively. In each iteration, the optimal solution of the grey wolf will be adjusted according to the optimal solution found by Tianying and affect the position of the optimal solution of the next generation of the wolf pack. This is achieved by introducing a control parameter which can adjust the grey wolf individual to approach the Tianying optimal solution. The formula is as follows:

[0043] And the position update formula of the grey wolf individual is:

[0044] Where is a dynamic parameter that controls the step size of the grey wolf population searching for the optimal solution. Its control step size gradually decreases as the search progresses to quickly approach the optimal satellite combination solution. The specific expression is as follows:

[0045] Where is an initial value that gradually decreases from 2 to 0 during the iteration process, is a random number, and .

[0046] And is the distance vector, which represents the relative distance between the current grey wolf individual and the optimal individual . Its role is to determine how the grey wolf approaches the optimal solution in the next iteration. The specific definition is as follows:

[0047] Where is the attraction coefficient, which controls the attraction of the grey wolf individual to the optimal solution, helps the grey wolf population maintain sufficient search ability during the iteration process, and ensures that it will not fall into a local optimal solution. The specific calculation is as follows:

[0048] At the end of each iteration, the global search of Tianying and the local optimization of the grey wolf will generate a local optimal solution, which is represented by the optimal individual of the grey wolf population. This solution is the optimal solution obtained through local adjustment under the influence of the Tianying global search. In this process, the Tianying optimal solution Only as a guide, but the final result is determined by the local optimization of the grey wolves.

[0049] This optimal solution will be used as the initial solution for the next generation. Based on this, the eagle population and the grey wolf population will continue to search and optimize, gradually finding a satellite combination with a smaller GDOP value.

[0050] Step 7: Iteration and termination of the satellite selection optimization of eagle - grey wolf In each iteration, the searches of the eagles and grey wolves will cycle according to Step 5 and Step 6 until the iteration count reaches the set maximum iteration count or the GDOP value of the optimal satellite combination obtained in this round of search is less than the preset ideal threshold. Then the iteration terminates, indicating that the current satellite combination has reached an approximately optimal geometric structure. The specific conditions are as follows:

[0051] Among them, is the preset search iteration count, is the GDOP threshold corresponding to the ideal satellite combination geometric structure. When either of the above conditions is met, the final solution output is the local optimal solution obtained by the grey wolf population under the guidance of the eagles. The satellite geometric structure corresponding to this solution is an approximately optimal structure, and the GDOP value reaches an approximately minimum value, ensuring the optimization of the positioning accuracy of the GNSS system.

[0052] (2) Five - step real - time direction - finding method with baseline constraint Step 1: Construct virtual observables in the observable domain In a dynamic environment, due to large model errors, few observation information, and poor observation quality, it is usually difficult for the dynamic positioning of low - cost receivers to search for the correct integer ambiguity within a single epoch. Therefore, it is necessary to use baseline length constraints to correct existing algorithms, improving both the solution success rate and the algorithm effectiveness.

[0053] When performing dual - antenna GNSS direction - finding, a relatively accurate virtual observable can be formed by the accurately measured baseline length in advance, enhancing the model strength at the observable domain level. The baseline constraint can be expressed as:

[0054] Among them, is the geometric baseline vector. The above formula is a non - linear equation. If it is to be used as a virtual observable, it needs to be linearized at the approximate value of the baseline vector. Specifically, it can be expressed as:

[0055] Expanding it gives:

[0056] Among them, is the linearized residual error, which is the noise of the virtual observable baseline length constraint. This equation can be transformed and combined to obtain the virtual observation equation as:

[0057] It can be seen from the above process that increasing the baseline length constraint is equivalent to increasing a GNSS observable, thereby enhancing the strength of the observation model in the observation domain, improving the system redundancy, and theoretically improving the accuracy of the float solution of the ambiguity.

[0058] Step 2: Improve the ambiguity candidate solution in the LAMBDA algorithm After enhancing the model strength in the observable domain, if the number of observables obtained is greater than 4, the ambiguity can be resolved in the ambiguity domain, and the resolution of the ambiguity is a key link to ensure accurate direction finding. When the traditional LAMBDA algorithm resolves the integer ambiguity, the initial ambiguity solution is mainly obtained through the least squares estimation of the float solution, which is specifically expressed as:

[0059] Among them, is the ambiguity design matrix, is the ambiguity covariance matrix, is the observation data.

[0060] However, there are often large deviations in the float solution. Especially in the case of dynamic environments and low-cost devices, it is easily affected by noise. Therefore, to improve the reliability of the solution, the LAMBDA algorithm needs to be improved, and the baseline ambiguity constraint is introduced into this algorithm. The baseline ambiguity helps to improve the solution accuracy by restricting the baseline length to keep it within a reasonable range. The ambiguity function of the baseline length is defined as:

[0061] Among them, is the initial estimate of the baseline length, is the standard deviation of the baseline length. Introducing the baseline ambiguity into the optimization objective of the LAMBDA algorithm and combining the influence of the geometric dilution of precision (GDOP), the final optimization objective function is:

[0062] Among them, the first term is the minimization of the ambiguity covariance matrix, representing the optimization of the float solution of the integer ambiguity; the second term is the constraint of the baseline ambiguity, and λ is the trade-off coefficient used to adjust the influence of the baseline ambiguity on the solution process.

[0063] Through this optimization process, the improved LAMBDA algorithm can integerize the ambiguity while ensuring the rationality of the baseline length. This not only helps to improve the success rate of ambiguity resolution, but also enhances the robustness and stability of the resolution, making it more suitable for direction-finding tasks in low-cost devices and dynamic environments.

[0064] In addition, the traditional LAMBDA method usually defaults to only taking the optimal solution as the judgment object. If it passes the test, the optimal solution is accepted; if it fails the test, the fixation is determined to be a failure. In fact, due to the poor quality of the observations of low-cost GNSS receivers, there is a problem of poor discrimination between the optimal solution and the sub-optimal solution when using the LAMBDA method, resulting in an easy occurrence of the "false acceptance" situation during the Ratio test, thus causing the failure of integer ambiguity fixation, which to a certain extent disrupts the continuity of GNSS direction finding. Therefore, the improved LAMBDA algorithm for searching alternative solutions of integer ambiguities is also different from the traditional method that only determines two groups of solutions, namely the optimal and the sub-optimal. This algorithm searches for n groups of alternative ambiguity solutions to form an alternative ambiguity set. The value of n is related to the quality of the observations and is usually between 5 and 100. The probability of including the correct integer ambiguity solution in these alternative sets is:

[0065] In the formula, represents is the probability of the correct integer ambiguity, where is the th alternative solution. From the above formula, it can be seen that determining the fixed solution among more alternative solutions can effectively increase the probability of obtaining the correct integer ambiguity.

[0066] Step 3: Verification of baseline length residuals and ambiguity fixation After the ambiguity resolution is completed, the prior baseline length needs to be used as the criterion for judging whether the ambiguity resolution result is correct, and the correct integer ambiguity is selected. Among the ambiguity alternative sets composed of n groups of ambiguities, select the integer ambiguity combinations with less than a certain threshold, calculate the baseline lengths of these ambiguity combinations, and use the known accurately measured baseline length as the best condition. The group of ambiguities corresponding to the smallest difference is the correct integer ambiguity. The specific formula is as follows:

[0067] Among them, is the least squares residual of the double-difference observations, and represents the weight matrix of the double-difference observations.

[0068] If the correct integer ambiguity has been found in the first three steps, the ambiguity fixing is successful. Step five can be directly carried out. The baseline vector can be obtained according to the fixed solution of the integer ambiguity, and then the heading angle and pitch angle can be calculated to complete the direction finding. Otherwise, go to step four.

[0069] Step four: Limited expansion of the ambiguity search range If the integer ambiguity fixing fails after the search in the first three steps, the subsequent search range can be limited and expanded according to the results of the AGWO optimal satellite selection strategy, so as to improve the success rate of the ambiguity resolution algorithm on the premise of fully ensuring the real-time performance of dynamic direction finding.

[0070] First, to improve the success rate of the ambiguity search, the integer ambiguity group in the search in the third step is used as the basis for the search in the fourth step. The search space is further expanded. Each ambiguity in this space is used as a benchmark, and ±m weeks are added to it in turn to form a new ambiguity search space which contains ambiguity combinations, where k is the number of satellites. Specifically, it is as follows:

[0071] Then, step three is carried out again using the expanded new set of alternative ambiguities until the integer ambiguity fixing is successful or the ambiguity resolution is completely completed. As can be seen from the above formula, the larger m and k are, the more alternative ambiguity combinations are included in the new ambiguity search space and the corresponding success rate of the ambiguity resolution is also improved. However, since the search range is expanded, the ambiguity search efficiency decreases. Therefore, to improve the resolution efficiency, the AGWO optimal satellite selection strategy can be adjusted according to the dynamic environment conditions to constrain the power function value k, so as to limit the expanded search range. In this way, the resolution accuracy can be maximally improved on the premise of ensuring the real-time performance of direction finding.

[0072] Step five: Calculation of the baseline vector and direction finding angle for the integer ambiguity solution in the direction finding domain After the integer ambiguity resolution is completed, first, the baseline vector needs to be calculated using the solved integer ambiguity. The baseline vector represents the relative displacement between two receivers and is the basis for subsequent calculation of the heading angle and pitch angle. The calculation formula of the baseline vector is as follows:

[0073] where, is the ambiguity transformation matrix, is the integer ambiguity obtained through the optimized search algorithm in the first four steps, It is the remaining floating-point solution of the carrier phase observation value. Based on this, combined with the observation data, the accurate baseline vector can be calculated by correcting the observation value.

[0074] Furthermore, based on this baseline vector, the heading angle and pitch angle can be further calculated. The heading angle represents the azimuth angle of the projection of the baseline vector on the horizontal plane, reflecting the angle between the eastward and northward directions of the baseline in the northeast celestial coordinate system. Its calculation formula is:

[0075] where and are the eastward and northward components of the baseline vector in the ENU coordinate system respectively. If , then the result needs to be added with π to ensure that the heading angle is in the range of [0, 2π].

[0076] The pitch angle describes the elevation angle of the baseline vector relative to the horizontal plane, and its calculation formula is:

[0077] where is the component of the baseline vector in the vertical direction, is the projection length of the baseline vector on the horizontal plane.

[0078] Through the above baseline-constrained five-step real-time direction-finding process, the direction information of the device or vehicle can be calculated in each epoch, providing accurate angle data for the direction-finding task. With the continuous reception of new epoch data, repeating these steps can achieve real-time direction-finding in a dynamic environment, ensuring that the device can continuously obtain accurate direction positioning.

[0079] In a dynamic environment, the implementation process of real-time direction-finding based on the AGWO algorithm optimization with a low-cost direction-finding device is as Figure 1 shown. The process Figure 1 shows how to complete direction-finding according to the satellite ephemeris data received by the low-cost GNSS device, optimized by the AGWO heuristic algorithm, combined with baseline constraint information and the five-step real-time direction-finding method, improving the direction-finding accuracy and real-time performance of the low-cost GNSS system at the algorithm level.

[0080] First, it is necessary to obtain the satellite ephemeris data of the current epoch from the navigation message file as input. The satellite ephemeris data contains the three-dimensional position coordinates of each satellite . Through preliminary screening, only the visible satellites with elevation angles greater than a certain threshold are retained. Next, based on the screened satellite information, an observation matrix is constructed. For each satellite, its observation vector It depends on the geometric relationship between the satellite and the receiver, and the specific formula is:

[0081] After screening, the observation vectors of all satellites will form a complete observation matrix , and it will be used as the input to enter the next stage of optimal satellite selection for optimization.

[0082] In the process of optimal satellite selection, the system designs the Eagle-Grey Wolf Optimization Satellite Selection Algorithm (AGWO), introduces the heuristic algorithm into the satellite selection process, combines the advantages of global search and local optimization, and uses the update of the eagle population to obtain the global optimal position in the current round , so as to guide the update of the optimal position of the grey wolf population . The individuals in the eagle population and the grey wolf population both represent a satellite combination, and the specific formula is as follows:

[0083] Among them, a control parameter is introduced to adjust the optimization iteration process of the algorithm. In addition, since the Geometric Dilution of Precision (GDOP) is used to evaluate the influence of the geometric distribution of satellites on the positioning accuracy, it can be used as the fitness function of the AGWO satellite selection algorithm, so that the algorithm can minimize this value by continuously iterating and updating the positions of the population individuals to quickly find the optimal satellite combination. The calculation formula of GDOP is:

[0084] After optimization by AGWO, the optimal satellite selection combination and its number of satellites k are obtained. The geometric distribution of these satellites can effectively improve the accuracy of subsequent direction finding, and at the same time can also impose certain constraints on the subsequent ambiguity search range.

[0085] After the satellite selection is completed, the system can calculate the double-difference observable in this epoch for subsequent integer ambiguity resolution. In addition, since low-cost devices are vulnerable to noise interference in a dynamic environment and affect the observation data, virtual observables can be constructed in the observable domain to enhance the redundancy and geometric distribution of the system. The virtual observable ensures that the baseline length meets the rationality constraint, and the specific formula is:

[0086] Performing linearization processing and merging on it can obtain the following virtual observation equation:

[0087] This virtual observation equation enhances the redundancy in the observation data. Especially when there are few observables in a dynamic environment, this method can enhance the robustness and stability of the model by increasing the number of observations, providing a more stable physical constraint basis for the subsequent integer ambiguity resolution and improving the solution accuracy.

[0088] Furthermore, it is necessary to judge the number of observables. When the sum of the number of observables and virtual observables at this epoch is greater than 4, the system can enter the ambiguity domain for ambiguity resolution.

[0089] In the ambiguity domain, first, the initial ambiguity solution can be obtained through least squares estimation , and the calculation formula is:

[0090] where the ambiguity design matrix is constructed according to the linear relationship between the observation geometry and the double-difference observation data, specifically reflecting the change of the satellite signal path through the observation equation. The ambiguity covariance matrix is calculated from the covariance information of the observation data, which reflects the influence of observation noise and errors on the ambiguity resolution result.

[0091] For the problem that the floating-point solution is vulnerable to influence in the case of dynamic environment and low-cost devices, it is necessary to introduce baseline ambiguity constraints to improve the traditional LAMBDA algorithm. The baseline ambiguity restricts the baseline length to keep it within a reasonable range, helping to improve the solution accuracy. The ambiguity function of the baseline length is defined as:

[0092] where is the initial estimate of the baseline length, is the standard deviation of the baseline length. Introducing the baseline ambiguity into the optimization objective of the LAMBDA algorithm and combining the influence of the geometric dilution of precision (GDOP), the final optimization objective function is:

[0093] where the first term is the minimization of the ambiguity covariance matrix, representing the optimization of the floating-point solution of the integer ambiguity; the second term is the constraint of the baseline ambiguity, and λ is a trade-off coefficient used to adjust the influence of the baseline ambiguity on the solution process.

[0094] Through this optimization process, the improved LAMBDA algorithm can ensure the rationality of the baseline length while integerizing the ambiguity, which not only helps to improve the success rate of ambiguity resolution but also enhances the robustness and stability of the solution, making it more suitable for the direction-finding tasks in low-cost devices and dynamic environments.

[0095] In addition, the traditional LAMBDA method usually defaults to only taking the optimal solution as the judgment object. If it passes the test, the optimal solution is accepted; if it fails the test, it is determined to be fixed as a failure. In fact, due to the poor quality of observations of low-cost GNSS receivers, when using the LAMBDA method, there is a problem of poor discrimination between the optimal solution and the sub-optimal solution, resulting in an easy occurrence of the "false acceptance" situation during the Ratio test, thus causing the failure of integer ambiguity fixation, which to a certain extent disrupts the continuity of GNSS direction finding. Therefore, the improved LAMBDA algorithm for searching alternative solutions of integer ambiguity also differs from the traditional method in that it only determines two groups of solutions, namely the optimal and the sub-optimal. This algorithm searches for n groups of alternative ambiguity solutions to form an alternative ambiguity set. The value of n is related to the quality of observations and is usually between 5 and 100. Due to the low floating-point solution accuracy of low-cost GNSS devices, the value of n can be appropriately increased, such as 50. The probability of including the correct integer ambiguity solution in these alternative sets is as follows:

[0096] In the formula, denotes is the probability of the correct integer ambiguity, where is the th alternative solution. From the above formula, it can be seen that determining the fixed solution among more alternative solutions can effectively increase the probability of obtaining the correct integer ambiguity.

[0097] Furthermore, after the ambiguity resolution is completed, the prior baseline length can be used as the criterion for judging whether the ambiguity resolution result is correct, reconstructing the discrimination criterion to screen out the correct integer ambiguity. Specifically, among the ambiguity alternative sets composed of n groups of ambiguities, screen out the integer ambiguity combinations less than a certain threshold, calculate the baseline lengths of these ambiguity combinations, take the known accurately measured baseline length as the best condition, and the group of ambiguities corresponding to the smallest difference is the correct integer ambiguity. The specific formula is as follows:

[0098] Wherein, is the least squares residual of the double-difference observations, represents the weight matrix of the double-difference observations.

[0099] In the above formula, when takes too large a value, there may be misjudgment; when it is too small, there may be missed judgment. Since low-cost receivers generally use short baselines, if the ambiguity resolution is correct, the baseline calculated using the carrier phase observations is at the millimeter level. Usually, the carrier phase error is considered to be 3 mm. According to the 3 principle, 1 cm is taken.

[0100] At this time, when the integer ambiguity that meets the discrimination criterion is found, it indicates that the ambiguity resolution is successful, and the baseline vector can be directly calculated to complete the direction finding according to the geometric relationship. However, if the integer ambiguity that meets the discrimination criterion is not found, it is necessary to limit and expand the subsequent search range according to the results of the AGWO optimal satellite selection strategy, and improve the success rate of the algorithm's ambiguity resolution on the premise of fully ensuring the real-time performance of dynamic direction finding.

[0101] Specifically, first, it is necessary to use the integer ambiguity group obtained in the previous search process as the basis for further search to expand the search space. Each ambiguity in this space is used as a benchmark, and ±m weeks are successively added to it to form a new ambiguity search space , which contains ambiguity combinations, where k is the number of satellites. Specifically as follows:

[0102] Then, the alternative ambiguity set in this ambiguity space is re-solved and the prior baseline length discrimination criterion is used for ambiguity resolution until the integer ambiguity is successfully fixed or the ambiguity resolution is all completed. Theoretically, the larger the expanded search range, the higher the success rate of ambiguity resolution. However, the larger the number of weeks m and the number of satellites k, the lower the ambiguity search efficiency. Therefore, the AGWO optimal satellite selection strategy can be adjusted according to the dynamic environment to constrain the power function value k. Generally, when using low-cost equipment for direction finding in a dynamic environment, the value of the number of satellites k in the optimal satellite combination obtained by algorithm optimization can be set to 10, and the expanded number of weeks is set to 1, so as to balance the relationship between the integer ambiguity resolution efficiency and the success rate.

[0103] Furthermore, after the integer ambiguity resolution is completed, the baseline vector can be calculated using the solved integer ambiguity . The specific calculation formula is as follows: .

[0104] Finally, based on this baseline vector, the heading angle and pitch angle can be further calculated using the mathematical geometric projection relationship. Specifically as Figure 2 shown, the schematic Figure 2 shows the geometric projection relationship between the heading angle and pitch angle calculation in the east-north-up (ENU) coordinate system and the baseline vector .

[0105] The above has introduced in detail a baseline constraint-based real-time direction finding method optimized by the AGWO algorithm. In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A baseline-constrained real-time direction finding method optimized by AGWO algorithm, characterized in that: include: Obtain the observation information of all visible satellites and each visible satellite whose elevation angle is greater than the altitude cutoff angle in the current epoch; The observation matrix is ​​constructed from the observation information of each visible satellite, and the optimal satellite combination is obtained by optimizing the satellites based on the observation matrix through the AGWO algorithm; Calculate the double-difference observations of the optimal satellite combination, and construct virtual observations based on the baseline length in the observation domain to enhance the model strength at the level of the observation domain; When the sum of the observed and virtual observed quantities at this epoch is greater than the preset value, a baseline ambiguity constraint is introduced into the LAMBDA algorithm to resolve the ambiguity; The prior baseline length is used as the criterion for judging whether the ambiguity resolution result is correct or not, and the judgment criterion is reconstructed to screen out the correct integer ambiguity. When the integer ambiguity that meets the judgment criteria is searched, the baseline vector is obtained according to the correct integer ambiguity, so that the direction finding is completed according to the geometric relationship; If the integer ambiguity that meets the judgment criteria is not found, the subsequent search range is limited and expanded according to the optimal satellite combination obtained by the AGWO optimal satellite selection to form a new ambiguity search space. The alternative ambiguity set in the new ambiguity search space is re-solved and the ambiguity is resolved using the prior baseline length judgment criterion until the integer ambiguity is successfully fixed or the ambiguity resolution is completed.

2. The method according to claim 1, characterized in that The step of constructing an observation matrix from the observation information of each visible satellite and performing optimal satellite selection by using the AGWO algorithm based on the observation matrix to obtain an optimal satellite combination includes: For any visible satellite, its observation vector for , represents the altitude angle of the visible satellite, Represents the azimuth of the visible satellite. The observation vectors of all visible satellites will form a complete observation matrix , construct the fitness function from the observation matrix; Use the update of the Eagle population to obtain the global optimal position of the current round , in order to guide the gray wolf population to its optimal position Update, in which individuals in both the Sky Eagle population and the Gray Wolf population represent a satellite assemblage; The optimal satellite combination is found by continuously iteratively updating the individual positions of the population to minimize the fitness function value.

3. The method according to claim 2, characterized in that Depend on Optimal location for gray wolf populations Update, where To control the parameters, is the updated optimal position of the gray wolf population.

4. The method according to claim 3, characterized in that Depend on Get the fitness function, where .

5. The method according to claim 4, characterized in that Depend on The virtual observation equation is obtained, where is the geometric baseline vector, is the approximate value of the baseline vector, is the length of the baseline vector, is the linearization residual.

6. The method according to claim 5, characterized in that The baseline fuzziness constraint is introduced into the LAMBDA algorithm to resolve the fuzziness, including: Depend on Get the initial ambiguity solution ,in, Design matrix for fuzziness, is the ambiguity covariance matrix, For observation information; The baseline ambiguity constraint is introduced into the LAMBDA algorithm, the initial ambiguity solution is optimized and solved, and n groups of alternative ambiguity solutions are searched out.

7. The method according to claim 6, characterized in that Depend on Get the optimization goal of the LAMBDA algorithm, is the fuzziness function of the baseline length, is an initial estimate of the baseline length, is the standard deviation of the baseline length, λ is the trade-off coefficient, is the covariance matrix of the ambiguity parameters, is the ambiguity parameter vector, i.e. the integer ambiguity to be resolved.

8. The method according to claim 7, characterized in that The prior baseline length is used as a criterion for determining whether the ambiguity resolution result is correct or not, and the determination criterion is reconstructed to select the correct integer ambiguity, including: Select from the fuzzy candidate set composed of n groups of candidate fuzzy combinations The integer ambiguity combination that is smaller than the preset threshold, where: is the least squares residual of the double-differenced observations, represents the double difference observation weight matrix; The baseline length of the screened integer ambiguity combination is calculated, and the baseline length of the calculated integer ambiguity combination is subtracted from the known baseline length. The set of integer ambiguities corresponding to the minimum difference is taken as the correct integer ambiguity.

9. The method according to claim 8, characterized in that The optimal satellite combination obtained according to the AGWO most preferred satellites limits and expands the subsequent search range, including: To meet the minimum condition of the least squares residual weighted sum of squares, that is The integer ambiguity group As the search space, take each ambiguity in the search space as a benchmark, and build up a new ambiguity search space by ±m cycles on it. , which contains ambiguity combinations, and k is the number of satellites in the optimal combination after AGWO selection.

10. The method according to claim 9, characterized in that Depend on Get the baseline vector based on the correct integer ambiguity ,in, is the ambiguity transformation matrix, is the integer ambiguity resolved by the improved LAMBDA algorithm, is the residual floating-point solution for the carrier phase observations.

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