Antenna direction correction method based on theoretical trajectory and improved genetic algorithm

Abstract

The invention discloses an antenna pointing correction method based on a theoretical trajectory and an improved genetic algorithm, and the method comprises the steps: constructing an antenna pointing error correction model, extracting correction parameters, carrying out the global optimization of the correction parameters through employing the improved genetic algorithm, and taking a residual matrix as a target value, taking error minimization between azimuth angle and pitch angle deviation predicted values output by the antenna pointing error correction model and a theoretical matrix as a fitness function, performing iterative solution through selection, intersection and mutation operation to obtain an optimal correction parameter group, and completing parameter calibration of the antenna pointing error model; the optimized parameters are fed back to the antenna pointing error correction model, and the antenna pointing error is corrected in real time. According to the method, the convergence speed of the algorithm is higher, a better solution can be found in a shorter time, the global search capability is enhanced, the pointing precision of the antenna is improved, and rapid tower-free calibration of the antenna is realized.

Description

Technical Field

[0001] This invention relates to the field of antenna servo control and precision measurement technology, specifically to an antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm. Background Technology

[0002] Antennas are core equipment in fields such as radio astronomy, satellite communication, deep space exploration, and remote sensing reception. Pointing accuracy is a crucial technical indicator for evaluating antenna performance. Studies show that when an antenna's pointing deviates from 1 / 10 of its half-power beamwidth at the operating frequency, the antenna efficiency drops by approximately 2.7%; when it deviates from 1 / 5 of the half-power beamwidth, the efficiency loss can reach as high as 10.5%. Therefore, in engineering, it is generally required that the pointing accuracy of an antenna must be better than 1 / 5 of its half-power beamwidth at the operating frequency.

[0003] Antenna pointing error refers to the deviation between the actual pointing direction of an antenna and its theoretically calculated direction. Antenna pointing accuracy is affected by various error factors, such as random errors like antenna temperature deformation, wind load, mechanical deviation of the shaft gears, and deformation of the antenna rails, as well as systematic errors like shaft system errors, gravity deformation, encoder errors, and atmospheric refraction. Currently, antenna pointing error correction is mainly divided into two categories: hardware correction and software correction. Hardware correction is primarily implemented during the manufacturing and installation stages, employing methods such as shaft system calibration, feed position correction, and shaft angle encoder eccentricity correction. After the antenna is installed and debugged, software correction becomes the core means to ensure its accuracy.

[0004] The current mainstream software calibration method is the "radio star method." This method observes radio stars at known precise locations, collects antenna pointing error samples, establishes a mathematical model describing the pointing error, and finally uses traditional mathematical optimization algorithms such as the least squares method to fit the coefficients in the model, thereby compensating for the servo commands and correcting the pointing error. However, this method has two inherent bottlenecks. First, the optimization algorithm has limitations. The least squares method, as a local search algorithm, is prone to getting trapped in local optima when dealing with the strong nonlinearity and multi-peak error response surfaces widely present in antenna systems, making it impossible to find the globally optimal model parameters, fundamentally limiting further improvements in calibration accuracy. Second, the radio star method is affected by weather conditions and cannot meet all-weather application requirements. In addition, due to the limitations of radio star flux density, this method is only suitable for large-aperture antennas, severely restricting its timeliness and applicability.

[0005] Therefore, the industry urgently needs a novel antenna pointing error correction method that can break away from reliance on traditional calibration sources and possess powerful global optimization capabilities. Genetic algorithms, as a global optimization stochastic search algorithm that simulates the natural evolutionary process, offer a new approach to solving this problem due to their powerful global search capabilities, robustness, and low dependence on model form. However, standard genetic algorithms themselves suffer from premature convergence and slow convergence speed in later stages, making their direct application to antenna pointing correction with high real-time requirements still unsatisfactory.

[0006] In summary, under the current technological background, developing an antenna pointing error correction method based on an "improved genetic algorithm" that does not rely on radio star observations and can effectively overcome the shortcomings of standard genetic algorithms is of great significance for improving the pointing accuracy and engineering applicability of antennas under complex operating conditions. Summary of the Invention

[0007] This invention aims to solve the technical problem of insufficient antenna pointing accuracy in high real-time scenarios. The purpose is to provide an antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm. By globally optimizing the correction parameters through the improved genetic algorithm, and by improving the selection, crossover, mutation operators and parameter settings, the algorithm converges faster, finds a better solution in a shorter time, enhances global search capabilities, improves antenna pointing accuracy, and realizes rapid towerless antenna calibration.

[0008] This invention is achieved through the following technical solution:

[0009] The first aspect of this invention provides an antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm, comprising the following specific steps:

[0010] Construct an antenna pointing error correction model and extract correction parameters;

[0011] The measured azimuth and elevation sequences are obtained by sampling every second during one orbit of the satellite self-tracking antenna. The corresponding theoretical azimuth and elevation sequences are calculated by combining the satellite's theoretical ballistic data. Four two-dimensional data matrices are calculated and constructed to store the theoretical pointing, measured pointing, residual, and model predicted pointing.

[0012] An improved genetic algorithm is used to globally optimize the correction parameters. The residual matrix is ​​used as the objective value, and the fitness function is to minimize the error between the predicted azimuth and elevation angle deviations output by the antenna pointing error correction model and the theoretical pointing matrix. The optimal set of correction parameters is obtained by iteratively solving through selection, crossover, and mutation operations, thus completing the parameter calibration of the antenna pointing error model.

[0013] The optimized parameters are fed back to the antenna pointing error correction model to correct the antenna pointing error in real time.

[0014] Furthermore, the construction of the antenna pointing error correction model specifically includes:

[0015] The antenna pointing error correction model takes the antenna azimuth and elevation angles as input variables, and uses the azimuth encoder zero-point deviation, elevation encoder zero-point deviation, first-order term of electrical axis gravity deformation error, elevation axis and azimuth axis non-orthogonality error, electrical axis and elevation axis non-orthogonality error, azimuth axis east-west tilt error, azimuth axis north-south tilt error, and atmospheric refraction residual as correction parameters to be solved. It outputs the predicted values ​​of azimuth and elevation angle deviations.

[0016] Furthermore, the two-dimensional matrix includes:

[0017] The TH matrix is ​​used to store theoretical azimuth and elevation angle data of the antenna;

[0018] The MT matrix is ​​used to store the azimuth and elevation angle data of the antenna during actual tracking.

[0019] The ER matrix is ​​used to store the pointing errors of the antenna azimuth and elevation angles;

[0020] The PR matrix is ​​used to store the predicted azimuth and elevation angle data based on the antenna's current actual tracking position and pointing error.

[0021] Furthermore, the step of using an improved genetic algorithm to globally optimize the correction parameters specifically includes:

[0022] The population is initialized by encoding individuals in the solution space using real-number encoding to form the first generation population;

[0023] The fitness of each individual in the current population is evaluated, and a fitness function is constructed.

[0024] Determine whether the current evolutionary process meets the preset termination criteria;

[0025] If the conditions are met, output the optimal individual steps directly; otherwise:

[0026] Then, a hybrid selection operator, which combines random selection with tournament selection and no-replay remainder selection, is used to select individuals in the current population to form the parent population.

[0027] Perform simulated binary crossover on individuals in the parent population according to a preset crossover probability to generate intermediate offspring individuals;

[0028] The intermediate offspring individuals are subjected to a mixed mutation operation that combines Gaussian mutation and uniform mutation according to a preset mutation probability to obtain a new generation population, and it is determined whether the current evolutionary process meets the preset termination criterion.

[0029] Output the optimal individual step, and output the individual with the best fitness obtained during the evolution process as the data processing result.

[0030] Furthermore, the encoding of individuals in the solution space using real-number encoding specifically includes:

[0031] Get correction parameters to The value range is [-1, 1];

[0032] The modified parameters are encoded using a real-number encoding method, where the gene encoding value of each parameter is obtained through a formula. generate;

[0033] in, Represents a random number between 0 and 2;

[0034] The encoded parameter combinations are used as individuals to construct the initial population.

[0035] Furthermore, the construction of the fitness function specifically includes:

[0036] Introduce a perturbation amount to each individual i in the population and And generate individual prediction pointer values. and ;

[0037] The disturbances are summed up as the total population error pointing to the antenna azimuth and elevation angles;

[0038] Based on the MT matrix of the azimuth and elevation data of the antenna during the actual tracking process, and the ER matrix of the antenna azimuth and elevation pointing errors, the PR matrix of the antenna prediction azimuth and elevation data is determined, where PR = MT + ER.

[0039] A threshold is set based on the TH matrix of the theoretical azimuth and elevation data of the antenna. The objective function is constructed with the goal of minimizing the deviation |PR−TH| between the predicted azimuth and elevation data and the theoretical azimuth and elevation data of the antenna.

[0040] The system-level output PR is calculated based on PR = MT + ER, and the optimization objective is to minimize |PR − TH|.

[0041] Iteratively adjust the disturbance amount and The process continues until the total population error in the antenna azimuth and elevation angles reaches a set threshold, causing PR to approximate TH, and finally outputting the actual value of the individual to construct the fitness function.

[0042] Furthermore, the random selection of the no-replay remainder specifically includes:

[0043] A hybrid selection operator, combining no-replay remainder random selection and tournament selection, is used to select individuals in the current population. Specifically, this includes:

[0044] Based on the fitness function, calculate the expected number of selections for each individual i in the next generation of the population;

[0045] Decompose the expected number of choices for each individual i into an integer part and a fractional part;

[0046] The number of selectable individuals is determined based on the integer part.

[0047] Sort all individuals in the population in descending order of their fractional parts, remove individuals already selected during the integer selection process, and then select the top individuals from the sorted population in order. Individuals, among which This represents the proportion of operations that use random selection with no replay remainder.

[0048] Furthermore, the tournament selection specifically includes:

[0049] From the set of individuals not selected in the no-replacement random selection operation, two different individuals are randomly selected without replacement. The one with the higher fitness is selected to enter the next generation population pool and removed from the pool of remaining individuals.

[0050] Repeat execution Repeat the above operations until the selection operation for all remaining populations is completed, where N is the population size.

[0051] Furthermore, the simulated binary crossover operation specifically includes:

[0052] Randomly sort the parent population individuals and select two parent individuals in sequence;

[0053] Based on the current population's maximum fitness value, average fitness value, and the larger fitness value among the two selected parent individuals, the crossover probability is dynamically calculated using a cosine mapping.

[0054] Generate a first random number. If the random number is less than or equal to the dynamic crossover probability, then perform the crossover operation; otherwise, directly copy the two parent individuals into child individuals.

[0055] When performing a crossover operation, the distribution index in the expansion factor calculation formula is preset, and a second random number is generated to calculate the expansion factor according to the distribution index.

[0056] Using the expansion factor, perform arithmetic crossover on the two parent individuals to obtain two offspring individuals;

[0057] The crossover is completed by replacing the corresponding positions in the original population with offspring individuals.

[0058] Furthermore, the mixed mutation operation, which combines Gaussian mutation and uniform mutation, specifically includes:

[0059] Initialize the standard deviation, and based on the simulated annealing exponential cooling strategy, dynamically calculate the standard deviation corresponding to the variable length of generation t according to the ratio of the current generation to the maximum generation.

[0060] The standard deviation corresponding to the variation length of generation t is used as the standard deviation of uniform variation, and perturbation is applied to each gene locus of the selected individuals.

[0061] Based on the current population's maximum fitness value, average fitness value, and the fitness value of the individual to be mutated, the probability of this mutation is dynamically calculated using a cosine mapping.

[0062] Generate a random number. If the random number is less than or equal to the dynamic mutation probability, perform a uniform mutation operation on the individual. Otherwise, retain the original individual and return the mutated or retained individual to the population.

[0063] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0064] By improving the selection, crossover, and mutation operators in the genetic algorithm and optimizing parameter settings, the global search capability of the algorithm is significantly enhanced, avoiding the algorithm from getting trapped in local optima, improving the convergence speed of the algorithm, ensuring that a better global solution is found in a shorter time, significantly improving the pointing accuracy of the antenna, and realizing rapid towerless calibration of the antenna. Attached Figure Description

[0065] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0066] Figure 1 This describes the operational flow of satellite-based theoretical ballistic data and the improved genetic algorithm in this embodiment of the invention.

[0067] Figure 2 This is the operation flow of the improved genetic algorithm in the embodiments of the present invention. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this invention are only for explaining this invention and are not intended to limit this invention.

[0069] As one possible implementation method, such as Figure 1 As shown, this embodiment provides an antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm, including the following specific steps:

[0070] Step 1: Construct an antenna pointing error correction model;

[0071]

[0072]

[0073] in The antenna azimuth angle. The antenna elevation angle, This is the azimuth deviation. For pitch angle deviation, This is the azimuth random error term. For pitch angle random error term, to The model correction parameters are the solution terms of the method described in this patent. The meaning of each correction parameter is shown in Table 1.

[0074]

[0075] Step 2: Acquire the azimuth and elevation data sampled per second during one orbit of the satellite tracked by the antenna, along with the satellite's theoretical trajectory data. Combine the theoretical trajectory data to calculate the corresponding theoretical azimuth and elevation sequences. Calculate and construct four two-dimensional data matrices to store the theoretical pointing, measured pointing, residual, and model-predicted pointing. Assuming the antenna tracks the satellite for one orbit in T minutes, and assuming one azimuth and elevation position per second, there are a total of 2*60T angular position data points. The two-dimensional matrix includes:

[0076] The TH matrix, used to store theoretical azimuth and elevation angle data of the antenna, is denoted as... ;

[0077] The MT matrix, used to store the azimuth and elevation angle data of the antenna during actual tracking, is denoted as... ;

[0078] The ER matrix, used to store the pointing errors of the antenna azimuth and elevation angles, is denoted as... ;

[0079] The PR matrix used to store the predicted azimuth and elevation angles based on the antenna's current actual tracking position and pointing error is denoted as... .

[0080] Step 3: The improved genetic algorithm is used to globally optimize the correction parameters. The residual matrix is ​​used as the objective value, and the fitness function is to minimize the error between the predicted azimuth and elevation angle deviations output by the antenna pointing error correction model and the theoretical pointing matrix. The optimal correction parameter set is obtained through selection, crossover, and mutation operations, and the parameter calibration of the antenna pointing error model is completed. The optimized parameters are fed back to the antenna pointing error correction model to correct the antenna pointing error in real time.

[0081] like Figure 2 As shown, an improved genetic algorithm is used to globally optimize the corrected parameters, specifically including:

[0082] The population is initialized by encoding individuals in the solution space using real-number encoding to form the first generation population;

[0083] The fitness of each individual in the current population is evaluated, and a fitness function is constructed.

[0084] Determine whether the current evolutionary process meets the preset termination criteria;

[0085] If the conditions are met, output the optimal individual steps directly; otherwise:

[0086] Then, a hybrid selection operator, which combines random selection with tournament selection and no-replay remainder selection, is used to select individuals in the current population to form the parent population.

[0087] Perform simulated binary crossover on individuals in the parent population according to a preset crossover probability to generate intermediate offspring individuals;

[0088] The intermediate offspring individuals are subjected to a mixed mutation operation that combines Gaussian mutation and uniform mutation according to a preset mutation probability to obtain a new generation population, and it is determined whether the current evolutionary process meets the preset termination criterion.

[0089] Output the optimal individual step, and output the individual with the best fitness obtained during the evolution process as the data processing result.

[0090] 1. Determine the population size;

[0091] The population size directly affects the final result of genetic optimization and the execution efficiency of the genetic algorithm. For the 8-parameter optimization problem of the antenna pointing error correction model, the population size is determined to be 1000.

[0092] 2. Determine the parameter encoding method;

[0093] Genetic coding transforms optimization variables into a combined representation of genes. For the antenna-direction correction error model, where the eight parameters are continuous numerical optimization problems, this embodiment employs real-number coding to encode individuals in the solution space, specifically including:

[0094] Get correction parameters to The value range is [-1, 1];

[0095] The modified parameters are encoded using a real-number encoding method, where the gene encoding value of each parameter is obtained through a formula. generate;

[0096] in, Represents a random number between 0 and 2;

[0097] The encoded parameter combinations are used as individuals to construct the initial population.

[0098] 3. Determine the population fitness function;

[0099] Introduce a perturbation amount to each individual i in the population and And generate individual prediction pointer values. and ;

[0100] The disturbances are summed up as the total population error pointing to the antenna azimuth and elevation angles;

[0101] Based on the MT matrix of the azimuth and elevation data of the antenna during the actual tracking process, and the ER matrix of the antenna azimuth and elevation pointing errors, the PR matrix of the antenna prediction azimuth and elevation data is determined, where PR = MT + ER.

[0102] A threshold is set based on the TH matrix of the theoretical azimuth and elevation data of the antenna. The objective function is constructed with the goal of minimizing the deviation |PR−TH| between the predicted azimuth and elevation data and the theoretical azimuth and elevation data of the antenna.

[0103] The system-level output PR is calculated based on PR = MT + ER, and the optimization objective is to minimize |PR − TH|.

[0104] For individual i within the population, and Thus, the disturbance amount is iteratively adjusted. and The process continues until the total population error in the antenna azimuth and elevation angles reaches a set threshold, causing PR to approximate TH. The final actual value of each individual is then output, and the initial fitness function for individual i is constructed. , making Minimum.

[0105]

[0106] Constructing the final fitness function of individual i in the improved genetic algorithm , making Maximum, that is .

[0107] 4. A hybrid selection operator combining no-replay remainder random selection and tournament selection is adopted;

[0108] The selection operator selects some superior individuals from the nth generation population P(n) according to certain rules based on the fitness of the individuals and passes them on to the next generation population P(n+1). For the 8-parameter optimization problem, this invention creatively proposes a hybrid combination operator of random selection operator without replay remainder and tournament selection operator, which can effectively maintain population diversity and avoid premature convergence of the algorithm.

[0109] To balance convergence reliability and population diversity, while also considering convergence speed, and taking into account the best balancing strategy that the golden ratio can provide in optimization design problems, it is determined that 70% of the individuals in the population will perform random selection with no replay remainder, and 30% of the individuals will perform tournament selection.

[0110] The remainder is randomly selected without replay, specifically including:

[0111] A hybrid selection operator, combining no-replay remainder random selection and tournament selection, is used to select individuals in the current population. Specifically, this includes:

[0112] Based on the fitness function, calculate the expected number of selections for each individual i in the next generation of the population. ;

[0113]

[0114] Decompose the expected number of choices for each individual i into an integer part and a fractional part;

[0115] use The integer part of the number of times each individual i is selected in the next generation determines the total number of selections that can be generated. Individuals, among which Representative Integer part.

[0116] All individuals in the population are divided into Sort the fractional parts in descending order, remove individuals already selected during the integer selection process, and then select the top-ranked individuals from the sorted list in order. Each individual can only be selected once during the selection process, thus completing the selection operation with no replay remainder for 70% of the population.

[0117] Tournament selections, specifically including:

[0118] From the remaining individuals pool, i.e. the set of individuals not selected in the random selection operation without replay, two different individuals are randomly selected without replacement. The one with the higher fitness is selected to enter the next generation population pool and removed from the remaining individuals pool.

[0119] Repeat execution Repeat the above operations until the selection of all remaining 30% of the population is completed, where N is the population size.

[0120] 5. Simulate binary crossover operator;

[0121] The crossover operator randomly pairs selected individuals from a population and exchanges parts of their chromosomes with a certain crossover probability to form new individuals, thus significantly improving the search capability of the algorithm. For the 8-parameter optimization problem, this invention proposes using a simulated binary crossover operator, which is particularly suitable for parameter optimization problems with real-number encoding, and also utilizes a controllable distribution exponent. This allows for precise control over the entire search process.

[0122] Randomly sort the parent population individuals, and select two parent individuals in sequence, denoted as... and ;

[0123] Based on the current population's maximum fitness value, average fitness value, and the larger fitness value among the two selected parent individuals, the crossover probability is dynamically calculated using a cosine mapping.

[0124] Generate the first random number If the random number is less than or equal to the dynamic crossover probability ( If the condition is met, then perform the crossover operation; otherwise, directly copy the two parent individuals into child individuals.

[0125] When performing the crossover operation, the distribution index in the expansion factor calculation formula is preset, and a second random number is generated. The expansion factor is calculated according to the distribution index. The expansion factor is used to perform arithmetic crossover on two parent individuals to obtain two offspring individuals. The offspring individuals replace the corresponding positions in the original population to complete this crossover.

[0126] The cross operation includes:

[0127]

[0128] in , random numbers, The value is 2 in the early exploration stage of the algorithm to enable the algorithm to search a wide range of solutions in the entire set, and 4 in the later fine search stage to enable the algorithm to finely adjust near the best solution.

[0129] To effectively overcome the rigid strategies of fixed crossover probability in improved genetic algorithms, such as insufficient early-stage exploration, excessive late-stage exploitation, and lack of problem adaptability, this invention creatively proposes an adaptive cosine crossover probability algorithm. This algorithm can dynamically adjust the balance between global search and local exploration, significantly improving the robustness of the algorithm. The operators of this algorithm are as follows:

[0130]

[0131] in and These represent the upper and lower bounds of the crossover probability, for an 8-parameter optimization problem. The value is 0.9. The value is 0.4;

[0132] This represents the maximum fitness value in the population;

[0133] This represents the average fitness value of the population.

[0134] This represents the larger population fitness value among the two individuals participating in the crossover.

[0135] 6. Mixed mutation operation, which combines Gaussian mutation and uniform mutation;

[0136] Mutation operators change the gene value at a specific locus to another allele value for each individual in the population with a certain mutation probability. This is an auxiliary search operation in genetic algorithms and also a means of maintaining population diversity. For the 8-parameter optimization problem, this embodiment creatively proposes a hybrid mutation operator combining Gaussian mutation and uniform mutation, which can effectively balance local fine-grained search and global exploration capabilities, improving the robustness of the improved genetic algorithm.

[0137] This embodiment suggests that the mutation operator for the 8-parameter optimization problem should primarily employ local fine-grained search, supplemented by global search. To balance convergence speed and efficiency, and considering the partial coupling effect between parameters, it is determined that 90% of the mutation events will use the Gaussian mutation operator, and 10% will use the uniform mutation operator.

[0138] The steps for Gaussian mutation are as follows:

[0139] ,in For the contemporary population, For the next generation population after the mutation operation, With a mean of 0 and a standard deviation of Gaussian distributed random numbers.

[0140] Furthermore, for values ​​that exceed the boundary after the mutation operation, the absorption method is used to handle such values, that is, they are directly set as the nearest boundary value.

[0141] Initialize the standard deviation, and based on the simulated annealing linear cooling strategy, dynamically calculate the standard deviation corresponding to the variable asynchronous length in generation t according to the ratio of the current generation to the maximum generation: the variable asynchronous length is determined by the standard deviation. The control parameter C has a step size ranging from 1% to 10%. For an 8-parameter optimization problem, the value of C ranges from [-1, 1], therefore the standard deviation... The value ranges from 0.02 to 0.2. If If the value is too large, the mutation operator degenerates into a random search algorithm. If the standard deviation is too small, the algorithm may stagnate and fail to converge. Therefore, this invention creatively proposes a standard deviation based on simulated annealing. The approach is adjusted to allow for extensive exploration in the early stages to avoid premature convergence, followed by refined searches in the later stages to improve accuracy, thereby effectively balancing exploration and development.

[0142]

[0143] in The standard deviation of the population when it reaches generation t;

[0144] The initial standard deviation is 0.2.

[0145] The final standard deviation is 0.02.

[0146] The current generation of the population;

[0147] This represents the maximum number of evolutionary iterations for the population.

[0148] The steps for uniform variation are as follows:

[0149] , For the next generation population after the mutation operation, It is a value that is uniformly and randomly selected within the range [min, max].

[0150] Furthermore, to effectively overcome the problems of fixed mutation probability in numerical exploration and convergence accuracy in improved genetic algorithms, this invention creatively proposes an adaptive cosine mutation probability algorithm. This algorithm can dynamically adjust the balance between early numerical exploration and later precise search. The operator of this algorithm is as follows:

[0151]

[0152] in and These represent the upper and lower limits of the mutation probability, for an 8-parameter optimization problem. The value is 0.1. The value is 0.001;

[0153] This represents the maximum fitness value in the population;

[0154] This represents the average fitness value of the population.

[0155] This represents the fitness value of the mutated individual in the population.

[0156] 7. Determine the termination generation

[0157] The termination generation of genetic operations is a parameter of the algorithm's termination condition. For the antenna direction correction error model, where the eight parameters are continuous numerical optimization problems, this invention determines the termination generation to be 1000.

[0158] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm, characterized in that, The specific steps include the following: Construct an antenna pointing error correction model and extract correction parameters; The measured azimuth and elevation sequences are obtained by sampling every second during one orbit of the satellite self-tracking antenna. The corresponding theoretical azimuth and elevation sequences are calculated by combining the satellite's theoretical ballistic data. Four two-dimensional data matrices are calculated and constructed to store the theoretical pointing, measured pointing, residual, and model predicted pointing. An improved genetic algorithm is used to globally optimize the correction parameters. The residual matrix is ​​used as the objective value, and the fitness function is to minimize the error between the predicted azimuth and elevation angle deviations output by the antenna pointing error correction model and the theoretical pointing matrix. The optimal set of correction parameters is obtained by iteratively solving through selection, crossover, and mutation operations, thus completing the parameter calibration of the antenna pointing error model. The optimized parameters are fed back to the antenna pointing error correction model to correct the antenna pointing error in real time.

2. The antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm according to claim 1, characterized in that, The construction of the antenna pointing error correction model specifically includes: The antenna pointing error correction model takes the antenna azimuth and elevation angles as input variables, and uses the azimuth encoder zero-point deviation, elevation encoder zero-point deviation, first-order term of electrical axis gravity deformation error, elevation axis and azimuth axis non-orthogonality error, electrical axis and elevation axis non-orthogonality error, azimuth axis east-west tilt error, azimuth axis north-south tilt error, and atmospheric refraction residual as correction parameters to be solved. It outputs the predicted values ​​of azimuth and elevation angle deviations.

3. The antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm according to claim 1, characterized in that, The two-dimensional matrix includes: The TH matrix is ​​used to store theoretical azimuth and elevation angle data of the antenna; The MT matrix is ​​used to store the azimuth and elevation angle data of the antenna during actual tracking. The ER matrix is ​​used to store the pointing errors of the antenna azimuth and elevation angles; The PR matrix is ​​used to store the predicted azimuth and elevation angle data based on the antenna's current actual tracking position and pointing error.

4. The antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm according to claim 1, characterized in that, The step of using an improved genetic algorithm to globally optimize the corrected parameters specifically includes: The population is initialized by encoding individuals in the solution space using real-number encoding to form the first generation population; The fitness of each individual in the current population is evaluated, and a fitness function is constructed. Determine whether the current evolutionary process meets the preset termination criteria; If the conditions are met, output the optimal individual steps directly; otherwise: Then, a hybrid selection operator, which combines random selection with tournament selection and no-replay remainder selection, is used to select individuals in the current population to form the parent population. Perform simulated binary crossover on individuals in the parent population according to a preset crossover probability to generate intermediate offspring individuals; The intermediate offspring individuals are subjected to a mixed mutation operation that combines Gaussian mutation and uniform mutation according to a preset mutation probability to obtain a new generation population, and it is determined whether the current evolutionary process meets the preset termination criterion. Output the optimal individual step, and output the individual with the best fitness obtained during the evolution process as the data processing result.

5. The antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm according to claim 4, characterized in that, The method of encoding individuals in the solution space using real number encoding specifically includes: Get correction parameters to The value range is [-1, 1]; The modified parameters are encoded using a real-number encoding method, where the gene encoding value of each parameter is obtained through a formula. generate; in, Represents a random number between 0 and 2; The encoded parameter combinations are used as individuals to construct the initial population.

6. The antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm according to claim 4, characterized in that, The construction of the fitness function specifically includes: Introduce a perturbation amount to each individual i in the population and And generate individual prediction pointer values. and ; The disturbances are summed up as the total population error pointing to the antenna azimuth and elevation angles; Based on the MT matrix of the azimuth and elevation data of the antenna during the actual tracking process, and the ER matrix of the antenna azimuth and elevation pointing errors, the PR matrix of the antenna prediction azimuth and elevation data is determined, PR = MT + ER. A threshold is set based on the TH matrix of the theoretical azimuth and elevation data of the antenna. The objective function is constructed with the goal of minimizing the deviation |PR−TH| between the predicted azimuth and elevation data and the theoretical azimuth and elevation data of the antenna. The system-level output PR is calculated based on PR = MT + ER, and the optimization objective is to minimize |PR − TH|. Iteratively adjust the disturbance amount and The process continues until the total population error in the antenna azimuth and elevation angles reaches a set threshold, causing PR to approximate TH, and finally outputting the actual value of the individual to construct the fitness function.

7. The antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm according to claim 4, characterized in that, The random selection of the no-replay remainder specifically includes: A hybrid selection operator, combining no-replay remainder random selection and tournament selection, is used to select individuals in the current population. Specifically, this includes: Based on the fitness function, calculate the expected number of selections for each individual i in the next generation of the population; Decompose the expected number of choices for each individual i into an integer part and a fractional part; The number of selectable individuals is determined based on the integer part. Sort all individuals in the population in descending order of their fractional parts, remove individuals already selected during the integer selection process, and then select the top individuals from the sorted population in order. Individuals, among which This represents the proportion of operations that use random selection with no replay remainder.

8. The antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm according to claim 4, characterized in that, The tournament selection specifically includes: From the set of individuals not selected in the no-replacement random selection operation, two different individuals are randomly selected without replacement. The one with the higher fitness is selected to enter the next generation population pool and removed from the pool of remaining individuals. Repeat execution Repeat the above operations until the selection operation for all remaining populations is completed, where N is the population size.

9. The antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm according to claim 4, characterized in that, The simulated binary interleaving operation specifically includes: Randomly sort the parent population individuals and select two parent individuals in sequence; Based on the current population's maximum fitness value, average fitness value, and the larger fitness value among the two selected parent individuals, the crossover probability is dynamically calculated using a cosine mapping. Generate a first random number. If the random number is less than or equal to the dynamic crossover probability, then perform the crossover operation; otherwise, directly copy the two parent individuals into child individuals. When performing a crossover operation, the distribution index in the expansion factor calculation formula is preset, and a second random number is generated to calculate the expansion factor according to the distribution index. Using the expansion factor, perform arithmetic crossover on the two parent individuals to obtain two offspring individuals; The crossover is completed by replacing the corresponding positions in the original population with offspring individuals.

10. The antenna pointing correction method based on theoretical ballistics and an improved genetic algorithm according to claim 4, characterized in that, The hybrid mutation operation, which combines Gaussian and uniform mutations, specifically includes: Initialize the standard deviation, and based on the simulated annealing exponential cooling strategy, dynamically calculate the standard deviation corresponding to the variable length of generation t according to the ratio of the current generation to the maximum generation. The standard deviation corresponding to the variation length of generation t is used as the standard deviation of uniform variation, and perturbation is applied to each gene locus of the selected individuals. Based on the current population's maximum fitness value, average fitness value, and the fitness value of the individual to be mutated, the probability of this mutation is dynamically calculated using a cosine mapping. Generate a random number. If the random number is less than or equal to the dynamic mutation probability, perform a uniform mutation operation on the individual. Otherwise, retain the original individual and return the mutated or retained individual to the population.

Images