CN107607972A - A kind of integer ambiguity fast acquiring method based on materialized view maintenance - Google Patents
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Abstract
The invention discloses a kind of integer ambiguity fast acquiring method based on materialized view maintenance, step are as follows：S1, data are observed by carrier phase, establish double-differential carrier phase observational equation；S2, after observational equation is linearized, the float-solution of integer ambiguity and corresponding covariance matrix are obtained using Kalman filtering；S3, by the use of known base line length as constraints, determine the hunting zone of integer ambiguity；S4, drop relevant treatment is carried out to above-mentioned float-solution and covariance matrix using improving Cholesky decomposition methods；S5, fitness function determined according to object function, determine each operational factor in IAGA algorithms, problem is subjected to real coding, finally obtains the optimal solution of integer ambiguity using IAGA algorithm search.The invention can not only non-linearly be adjusted corresponding cross and variation probability by individual adaptation degree, moreover it is possible to solved the problems, such as Hamming steep cliff using real coding, improved the resolving efficiency of integer ambiguity.
Description
Technical Field
The invention relates to the technical field of solving carrier phase integer ambiguity by using an optimization algorithm, in particular to a real number coding self-adaptive genetic algorithm-based integer ambiguity fast acquisition method.
Background
With the development of satellite navigation technology, the applications in various global fields not only have higher dependence on the satellite navigation technology, but also have higher requirements on positioning accuracy and timeliness. Since the original observation of the satellite carrier phase contains the integer ambiguity, the distance between the satellite and the receiver determined directly from the observation is not equal to the true distance. However, once the integer ambiguity is accurately calculated, the distance between the satellite and the receiver can be obtained with the accuracy of cm or even mm, so that the positioning of cm or even mm can be carried out. Therefore, the integer ambiguity fixing is a key problem of high-precision positioning and is always a hotspot problem in the field of satellite navigation. Since Counselman proposed high-precision positioning by using carrier phase observation values in 1981, numerous scholars at home and abroad have been studying the problem of integer ambiguity resolution in the carrier phase positioning technology, and numerous integer ambiguity resolution methods have been proposed successively.
The solution method of the integer ambiguity is generally classified into a Non-Search (Non-Search) based solution method and a Search-based solution method according to different processing modes. The non-search based solution method mainly includes a Motion-based (Motion-based) method and a method based on a special operation. The motion-based ambiguity resolution method makes full use of effective information brought by the movement of observation equipment and the change of an observation satellite, so that the method has strong dependence on the geometric relationship between the satellite and a receiver, and the search-based ambiguity resolution method does not depend on the geometric relationship between the satellite and the receiver, so that the method can carry out fast integer ambiguity resolution. The search-based ambiguity resolution method is further classified into an ambiguity search method in a coordinate domain, an ambiguity search method in an observation domain, and an ambiguity search method in an ambiguity domain. The search method in the ambiguity domain can be further classified into a Bayesian estimation method and a Non-Bayesian estimation method according to the type of the solution result. The specific classification of the ambiguity resolution method is shown in table 1.
TABLE 1 ambiguity resolution method Classification Table
At present, the most widely applied method is an LAMBDA (Least-squares AMBiguy correlation evaluation) method which is proposed by Teunissen and utilizes integer Gaussian transformation to transform an AMBiguity variance matrix, the variance matrix is transformed, an AMBiguity search space is reduced, the correlation among AMBiguity components is reduced, meanwhile, the conditional Least square Adjustment is utilized to carry out gradual recursion, and finally, the AMBiguity of the whole circle is obtained through search.
The genetic algorithm is proposed by professor J Holland in the United states and has the characteristics of intrinsic parallelism, global optimization and robustness. Because the cross probability and the mutation probability of the operation parameters of the simple genetic algorithm are constant, the initially set cross probability and the initially set mutation probability can not meet the initial and later searches of the operation easily, and the speed and the efficiency of the search are influenced. The IAGA Algorithm (Improved Adaptive Genetic Algorithm, shortly called IAGA) is an Improved Algorithm proposed on the basis of Simple Genetic Algorithm (Simple Genetic Algorithm). The cross probability and the variation probability of the operation parameters in the IAGA algorithm can be automatically changed along with the fitness, and can be subjected to nonlinear adjustment along with a sigmoid curve between the average fitness and the maximum fitness, when most individuals in a population have similar fitness and the average fitness is close to the maximum fitness, the cross rate and the variation rate of most individuals are improved, and the improvement amplitude is higher than the cross rate and the variation rate which are changed according to a cosine function; meanwhile, the modes of individuals near the maximum fitness are reserved as much as possible, the cross rate and the variation rate of the modes are reduced, the probability that the individuals of the modes participate in cross pairing is increased, and the algorithm strives to jump out local convergence. For many optimization problems, under the condition that population individuals are equivalent, most individuals close to the periphery of the average fitness are pulled apart to drive the evolution to advance, and the method has positive significance for getting rid of local convergence and preventing the algorithm from being stopped.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a real number coding-based adaptive genetic algorithm whole-cycle ambiguity rapid acquisition method.
The purpose of the invention can be achieved by adopting the following technical scheme:
a real number coding adaptive genetic algorithm-based integer ambiguity fast acquisition method comprises the following steps:
s1, establishing a carrier phase double-difference observation equation according to carrier phase observation data;
and if two receivers k and i observe two satellites j and o at the time t, the carrier phase double-difference observation equation is as follows:
in the formulaFor a double-difference carrier-phase observation,is double difference integer ambiguity, lambda is carrier wavelength, R (t) is distance from satellite to receiver, V (t) is residual vector;
s2, linearizing the carrier phase double-difference observation equation, and acquiring a floating point solution of integer ambiguity and a corresponding covariance matrix by using Kalman filtering;
establishing a Kalman filter under a constant acceleration model, wherein a state equation and a measurement equation of the Kalman filter are respectively as follows:
X k ＝Φ k,k-1 X k-1 +Γ k-1 W k-1 (2)
Z k ＝H k X k +V k (3)
in the formula, X K For a state vector containing receiver position parameters and double-difference ambiguities, phi k,k-1 Being a state transition matrix, r K Is a system noise matrix, Z K Is a vector of observations in double difference mode, H K For measuring the matrix, V k To observe noise;
when there are t epochs j +1 satellites, the covariance matrix of the estimated parameters is:
Q＝σ 2 (H T M -1 H) -1 (4)
wherein, σ is the mean square error of unit weight of the estimated parameter, and M is the weight matrix of the carrier phase double-difference observed quantity;
float solution in found ambiguitiesOn the basis of (1), a fixed solution N of the integer ambiguity is found by searching for the minimum objective function:
s3, determining a searching range of the integer ambiguity by using the known base length as a constraint condition;
for a baseline of length L, the range of values for each double-difference integer ambiguity Nn (n =1,2.. Once, j) is within the range of the L meter baseline centered on the floating-point solution, i.e.:
-L/λ≤N n ≤L/λ (6)
wherein λ is the L1 carrier wavelength;
s4, performing decorrelation processing on the floating solution and the covariance matrix obtained in the step S2 by using an improved Cholesky decomposition method;
the aim of continuous correlation reduction is realized by continuously executing improved upper triangle Cholesky decomposition and lower triangle Cholesky decomposition for multiple times, before Cholesky decomposition, diagonal elements of a ambiguity covariance matrix are sequenced, and a transformed ambiguity covariance matrix Q can be obtained through a final conversion matrix Z Z Sum ambiguity float solution
(7)
The objective function formula (8) after decorrelation can be obtained from the formula (5) and the formula (7):
and S5, determining a fitness function according to the target function, determining each operating parameter in the IAGA algorithm, performing real number coding on the problem, and finally searching by using the IAGA algorithm to obtain an optimal solution of the integer ambiguity.
Further, the step S5 specifically includes:
s501, real number coding is carried out;
s502, selecting a fitness function and introducing a penalty function;
for the objective function equation (8), the IAGA algorithm chooses the following as the fitness function:
f(N)＝b-lg(G(N)) (9)
wherein b is a positive number large enough to ensure that f (N) >0;
introducing a penalty function, reducing the fitness of the individual violating the constraint condition, reducing the probability of the individual being inherited to the next generation population, and introducing the penalty function in the formula (9) to obtain the following formula:
in the formula: f' (N) is a new fitness function, and a is a penalty coefficient;
s503, presetting operation parameters of an IAGA algorithm, wherein the operation parameters of the IAGA algorithm comprise: seed of a plantGroup size M, termination evolution algebra T of genetic algorithm, and cross probability P C Probability of mutation P m ；
And S504, applying the IAGA algorithm to the fast resolving of the integer ambiguity, and searching for the optimal solution of the integer ambiguity.
Further, the cross probability P C And the mutation probability P m Is automatically changed along with the fitness of individuals in the population, and can carry out nonlinear adjustment along with a sigmoid curve between the average fitness and the maximum fitness according to the fitness of the individuals, P C And P m The adaptive adjustment is performed by equations (11), (12) shown below:
in the formula (f) max As maximum fitness in the population of each generation, f avg The average fitness value of each generation of population, f' is the greater fitness value of the two individuals to be crossed, and f is the fitness of the individual to be mutated.
Further, the wavelength λ of the L1 carrier in step S3 is 19cm.
Further, the penalty coefficient a in step S5 is 0.4.
Further, the population size M in step S5 is 20.
Further, the evolutionary algebra T is terminated 200 in step S5.
Compared with the prior art, the invention has the following advantages and effects:
(1) The method adopts Kalman filtering to solve the floating solution of integer ambiguity and has higher initial solution precision;
(2) The improved Cholesky decomposition is adopted to perform the decorrelation processing on the integral ambiguity covariance matrix, so that the decomposition effect of the matrix is improved, the correlation among the integral ambiguity components is effectively reduced, and the ambiguity discrete search efficiency and quality are improved;
(3) The invention introduces the IAGA algorithm into the search of the integer ambiguity, avoids the complex calculation amount in the solution process of the Lambda algorithm, and has stronger convergence capability compared with the simple genetic algorithm;
(4) The IAGA algorithm coding adopts real number coding, avoids the inherent Hamming cliff problem of binary coding, and simplifies the required parameters.
Drawings
FIG. 1 is a flowchart illustrating the steps of a real number encoding-based adaptive genetic algorithm fast integer ambiguity resolution method disclosed in the present invention;
FIG. 2 is a graph showing the variation of the crossover probability in the IAGA algorithm;
fig. 3 is a graph showing variation probability in the IAGA algorithm.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Examples
As shown in fig. 2 and fig. 3, in the IAGA algorithm, the mutation probability and the cross probability are automatically changed according to the fitness of individuals in the population, and can be non-linearly adjusted according to the fitness of the individuals between the average fitness and the maximum fitness along a sigmoid curve. When most individuals in the population have similar fitness and the average fitness is close to the maximum fitness, the crossing rate and the variation rate of most individuals are improved, and the improved amplitude is higher than the crossing rate and the variation rate which change according to a cosine function; meanwhile, the modes of individuals near the maximum fitness are reserved as much as possible, the cross rate and the variation rate of the modes are reduced, the probability that the individuals of the modes participate in cross pairing is increased, and the algorithm strives to jump out of local convergence. The IAGA algorithm has average fitness which is closer to the optimal fitness than a cosine improved algorithm, and shows that the IAGA population has more excellent solutions and shows stronger self-adaptive performance.
In FIGS. 2 and 3, f max Is the maximum fitness in each generation of population; f. of avg Is the mean fitness value of each generation population; f' is the greater fitness value of the two individuals to be crossed; f is the fitness of the individual to be mutated; p cmax ＝0.9，P cmin ＝0.6，P mmax ＝0.1，P mmin ＝0.001，A＝9.903438。
The embodiment specifically discloses a real number coding adaptive genetic algorithm-based integer ambiguity fast acquisition method, and a flow chart is shown in fig. 1, and includes the following steps:
s1, establishing a carrier phase double-difference observation equation according to carrier phase observation data;
in order to eliminate most errors such as an ionosphere error, a troposphere error, a satellite clock error, a receiver clock error and the like in a carrier phase, a carrier phase double-difference observation value is often adopted for processing in satellite precision positioning. And if the two receivers k and i observe two satellites j and o at the time t, the carrier phase double-difference observation equation is as follows:
in the formulaFor a double-difference carrier-phase observation,for double-difference integer ambiguity, λ is the carrier wavelength, R (t) is the satellite-to-receiver distance, and V (t) is the residual vector.
Step S2, after the observation equation obtained in the step S1 is linearized, a floating point solution of integer ambiguity and a corresponding covariance matrix are obtained by Kalman filtering;
in order to facilitate computer modeling and simulation, the observation equation in the step S1 is linearized, and a Kalman filter under a constant acceleration model is established. The state equation and the measurement equation are respectively as follows:
X k ＝Φ k,k-1 X k-1 +Γ k-1 W k-1 (2)
Z k ＝H k X k +V k (3)
in the formula, X K For a state vector containing receiver position parameters and double-difference ambiguities, phi k,k-1 Being a state transition matrix, r K Is a system noise matrix; z is a linear or branched member K Is a vector of observations in double difference mode, H K For measuring the matrix, V k To observe the noise. According to the adjustment measurement principle, when there are t epochs j +1 satellites, the covariance matrix of the estimated parameters is as follows:
Q＝σ 2 (H T M -1 H) -1 (4)
where σ is the unit weight mean square error of the estimated parameter, and M is the weight matrix of the carrier-phase double-difference observed quantity.
Because the constraint condition that the integer ambiguity is an integer is not added, the integer ambiguity obtained by the Kalman equation is a real number, namely a floating solution of the ambiguity without integer constraintOn the basis of the found ambiguity floating solution, finding a fixed solution N for the integer ambiguity by searching for the minimum objective function:
where N is a vector of j double-differenced integer ambiguities.
S3, determining a searching range of the integer ambiguity by using the known base length as a constraint condition;
for a baseline of length L, the range of values for each double-difference integer ambiguity Nn (n =1,2.. Once, j) is within the range of the L meter baseline centered on the floating-point solution, i.e.:
-L/λ≤N n ≤L/λ (6)
wherein λ =19.03cm is L of GPS 1 And (4) carrying waves.
S4, performing decorrelation processing on the floating point solution and the covariance matrix obtained in the step S2 by using an improved Cholesky decomposition method;
in order to ensure that the good mode of each chromosome in the genetic algorithm is not damaged, before searching and solving, the floating point solution and the covariance matrix thereof are subjected to decorrelation processing. Aiming at the defects that the numerical calculation is unstable and the operation amount is twice of that of the Cholesky decomposition in the Gaussian decomposition decorrelation, the improved Cholesky decomposition method is adopted. Improved upper triangle Cholesky (UDU) by multiple successive executions T ) Breakdown and lower triangle Cholesky (LDL) T ) Decomposition achieves the purpose of continuously reducing correlation. Before Cholesky decomposition, the diagonal elements of the ambiguity covariance matrix are sorted (ascending or descending) to reduce the condition number of the matrix, effectively improve the decomposition effect of the matrix, and improve the ambiguity discrete search efficiency and quality Z Sum ambiguity float solution
(7)
The objective function formula (8) after decorrelation can be obtained from the formula (5) and the formula (7):
s5, determining a fitness function according to the target function, determining each operating parameter in an IAGA algorithm, performing real number coding on the problem, and finally searching by using the IAGA algorithm to obtain an optimal solution of the integer ambiguity;
the real number coded IAGA algorithm is an efficient, steady and parallel global search algorithm, can simplify the required parameters, and adaptively adjusts the cross probability and the variation probability of a genetic algorithm in the search process to obtain a global optimal solution. On the basis of solving the integer ambiguity floating solution and the search space of the formula (6), the objective function of the formula (8) is searched and optimized by designing the IAGA algorithm of the text, including coding, setting fitness function, genetic operator and other operations.
Step S501, encoding;
the encoding of genetic algorithms is a transformation method that transforms the feasible solution of a problem from its solution space to a search space that the genetic algorithm can handle. The coding mode is mainly binary coding, and integer ambiguity searching is to find an integer optimal solution and a nonlinear optimization problem, so real number coding can reflect inherent structural characteristics of the problem better, the individual length is short, the occupied memory of a computer is small, and the Hamming cliff problem in the binary coding does not exist. After obtaining the floating point solution of integer ambiguity and its precision, according to the experiment, the searching range of integer ambiguity is + -10 weeks, the real number coding of integer ambiguity is directly coded by j integer ambiguities, each integer ambiguity N n The real number of (n =1,2, …, j) is encoded as one code, and the length of the encoded string of the integer ambiguity is j bits. ByForming an initial population, wherein m is the size of the population.
Step S502, fitness function;
for the objective function of equation (8), the IAGA algorithm chooses the following as the fitness function:
f(N)＝b-lg(G(N)) (9)
in the formula, b is a positive number large enough to ensure that f (N) >0, and the logarithm of the target function is used for reducing the difference between the whole-cycle combinations, so that the early maturing of the genetic algorithm is avoided, and the local optimum is trapped.
Since the integer ambiguity search is an integer optimization problem, there is a case that an individual violates a constraint condition in the encoding process, that is, there is no individual with a corresponding feasible solution in the solution space, considering the case that individuals in this group violate the constraint condition, a penalty function is introduced to reduce the fitness of the individual violating the constraint condition, so that the probability that the individual is inherited to the next generation group is reduced, and the penalty function is introduced in the formula (9) to obtain the following formula:
in the formula: f' (N) is the new fitness function; and a is a penalty coefficient, and the invention takes a =0.4.
Step S503, operating parameters of an IAGA algorithm;
the IAGA algorithm has 4 operation parameters needing to be preset, namely, the population size M, the termination evolution algebra T of the genetic algorithm and the cross probability P C Probability of variation P m ；
(1) A population size M;
the population size M, i.e., the number of individuals contained in the population. If a larger population size is selected, more extreme points can be obtained, the global optimal solution is easier to find, but the searching efficiency is reduced. Therefore, the present invention takes the population size M as 20.
(2) Terminating the evolution algebra T;
the final evolution algebra T of the genetic algorithm is selected according to actual conditions, and is not suitable to be too small or too large, when the T is too small, the global optimal solution cannot be searched, and when the T is too large, the search time is increased, and the search efficiency is reduced. Therefore, the present invention takes T =200.
(3) Cross probability P C And the mutation probability P m ；
The cross probability and the mutation probability in the parameters of the genetic algorithm directly influence the convergence and the search efficiency of the algorithm. Cross probability P c The larger the size, the faster the new individual will be produced in the offspring. When P is present c If the population is too large, the probability that the good mode in the population is damaged is higher; when P is c If the time is too short, the rate of new individuals in the offspring will be reduced and the search process will be slowed. The mutation operation itself is a random search algorithm that determines the local search capability of the genetic algorithm, when P is m When the size is too large, the genetic algorithm becomes a pure random search algorithm, and when P is too large m When the time is too small, the local search capability is reduced, and premature convergence is likely to occur.
In the IAGA algorithm adopted by the invention, the variation probability and the cross probability are automatically changed along with the fitness of individuals in a population, and nonlinear adjustment can be carried out between the average fitness and the maximum fitness according to the fitness of the individuals, wherein P in the IAGA algorithm C And P m The following equations (11) and (12) and fig. 2 and 3 are used for adaptive adjustment:
in the formula (f) max As the maximum fitness in each generation population, f avg Is the mean fitness value of each generation population, f' is the greater fitness value of the two individuals to be crossed, f is the fitness of the individual to be mutated, P cmax ＝0.9，P cmin ＝0.6，P mmax ＝0.1，P mmin ＝0.001，A＝9.903438。
After the self-adaptive adjusting method is adopted, the mutation probability and the cross probability are automatically changed along with the individual fitness in the population, and the cross rate and the mutation rate can be subjected to non-linear adjustment along with a sigmoid curve between the average fitness and the maximum fitness according to the individual fitness. When most individuals in the population have similar fitness and the average fitness is close to the maximum fitness, the crossing rate and the variation rate of most individuals are improved, and the improved amplitude is higher than the crossing rate and the variation rate which change according to a cosine function; meanwhile, the modes of individuals near the maximum fitness are reserved as much as possible, the cross rate and the variation rate of the modes are reduced, the probability that the individuals of the modes participate in cross pairing is increased, and the algorithm strives to jump out local convergence. The IAGA algorithm has the average fitness which is closer to the optimal fitness than a cosine improved algorithm, so that the IAGA population has more excellent solutions and shows stronger self-adaptive performance. For many optimization problems, under the condition that population individuals are equivalent, most individuals close to the periphery of the average fitness are pulled apart to drive the evolution to advance, and the method has positive significance for getting rid of local convergence and preventing the algorithm from being stopped.
And step S504, the IAGA algorithm is applied to the rapid resolving of the integer ambiguity, and the optimal solution of the integer ambiguity is searched.
In summary, the Lambda algorithm is the most complete theoretical system and the most widely applied in the current method for solving the integer ambiguity. But in practical application, the problems of large search space, relatively complex calculation and the like exist; the genetic algorithm is proposed by professor J Holland in the United states and has the characteristics of intrinsic parallelism, global optimization and robustness, but in the actual searching process, the algorithm is easy to fall into local optimization because the cross probability and the variation probability of the genetic algorithm are kept unchanged. The whole-cycle ambiguity fast resolving method based on the real number coding self-adaptive genetic algorithm provided by the embodiment well solves the problems. The method uses Kalman filtering to obtain a floating solution with higher initial precision, uses Cholesky decomposition based on sequencing to perform decorrelation on ambiguity space, and finally applies an IAGA adaptive algorithm to search and solution of integer ambiguity based on real number coding.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (7)
1. A real number coding adaptive genetic algorithm-based integer ambiguity fast acquisition method is characterized by comprising the following steps:
s1, establishing a carrier phase double-difference observation equation according to carrier phase observation data;
and if the two receivers k and i observe two satellites j and o at the time t, the carrier phase double-difference observation equation is as follows:
in the formulaFor a double-difference carrier-phase observation,is double difference integer ambiguity, lambda is carrier wavelength, R (t) is distance from satellite to receiver, V (t) is residual vector;
s2, linearizing the carrier phase double-difference observation equation, and acquiring a floating point solution of integer ambiguity and a corresponding covariance matrix by using Kalman filtering;
establishing a Kalman filter under a constant acceleration model, wherein a state equation and a measurement equation of the Kalman filter are respectively as follows:
X k ＝Φ k,k-1 X k-1 +Γ k-1 W k-1 (2)
Z k ＝H k X k +V k (3)
in the formula, X K For state vectors containing receiver position parameters and double-difference ambiguities, phi k,k-1 Being a state transition matrix, r K Is a system noise matrix, Z K Is a vector of observations in double difference mode, H K For measuring the matrix, V k To observe noise;
when there are t epochs j +1 satellites, the covariance matrix of the estimated parameters is:
Q＝σ 2 (H T M -1 H) -1 (4)
wherein, σ is the unit weight mean square error of the estimation parameter, and M is the weight matrix of the carrier phase double-difference observed quantity;
float solution in found ambiguitiesOn the basis of (1), a fixed solution N of the integer ambiguity is found by searching for the minimum objective function:
s3, determining a searching range of the integer ambiguity by using the known base length as a constraint condition;
for a baseline of length L, the range of values for each double-difference integer ambiguity Nn (n =1,2.. Once, j) is within the range of the L meter baseline centered on the floating-point solution, i.e.:
-L/λ≤N n ≤L/λ (6)
wherein λ is the L1 carrier wavelength;
s4, performing decorrelation processing on the floating point solution and the covariance matrix obtained in the step S2 by using an improved Cholesky decomposition method;
the purpose of continuous correlation reduction is realized by continuously executing improved upper triangle Cholesky decomposition and lower triangle Cholesky decomposition for multiple times, before Cholesky decomposition, diagonal elements of a ambiguity covariance matrix are sequenced, and a transformed ambiguity covariance matrix Q can be obtained through a final conversion matrix Z Z Sum ambiguity float solution
The objective function formula (8) after decorrelation can be obtained from the formula (5) and the formula (7):
and S5, determining a fitness function according to the target function, determining each operating parameter in the IAGA algorithm, performing real number coding on the problem, and finally searching by using the IAGA algorithm to obtain an optimal solution of the integer ambiguity.
2. The method according to claim 1, wherein the step S5 specifically comprises:
s501, real number coding is carried out;
s502, selecting a fitness function and introducing a penalty function;
for the objective function equation (8), the IAGA algorithm chooses the following as the fitness function:
f(N)＝b-lg(G(N)) (9)
wherein b is a positive number large enough to ensure that f (N) >0;
introducing a penalty function, reducing the fitness of the individual violating the constraint condition, reducing the probability of the individual being inherited to the next generation population, and introducing the penalty function in the formula (9) to obtain the following formula:
in the formula: f' (N) is a new fitness function, and a is a penalty coefficient;
s503, presetting operation parameters of an IAGA algorithm, wherein the operation parameters of the IAGA algorithm comprise: population size M, termination evolution algebra T of genetic algorithm and cross probability P C Probability of mutation P m ；
S504, the IAGA algorithm is applied to the rapid resolving of the integer ambiguity, and the optimal solution of the integer ambiguity is searched.
3. The method of claim 1, wherein the cross probability P is a real number coding adaptive genetic algorithm-based integer ambiguity resolution C And the mutation probability P m Is automatically changed along with the fitness of individuals in the population, and can carry out nonlinear adjustment along with a sigmoid curve between the average fitness and the maximum fitness according to the fitness of the individuals, P C And P m The adaptive adjustment is performed by equations (11), (12) shown below:
in the formula (f) max As the maximum fitness in each generation population, f avg The average fitness value of each generation of population, f' is the greater fitness value of the two individuals to be crossed, and f is the fitness of the individual to be mutated.
4. The method for fast acquiring integer ambiguity based on real number encoding adaptive genetic algorithm as claimed in any one of claims 1 to 3, wherein the L1 carrier wavelength λ in step S3 is 19cm.
5. The method for fast acquiring integer ambiguity based on real number encoding adaptive genetic algorithm as claimed in claim 2 or 3, wherein the penalty factor a in step S5 is 0.4.
6. The method according to claim 2 or 3, wherein the population size M in step S5 is 20.
7. The method as claimed in claim 2 or 3, wherein the evolution algebra T of step S5 is terminated to obtain 200.
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| CN111487657A (en) * | 2020-03-21 | 2020-08-04 | 哈尔滨工程大学 | Beidou real-time precise orbit determination method based on satellite perturbation |
| CN111487657B (en) * | 2020-03-21 | 2022-07-15 | 哈尔滨工程大学 | Beidou real-time precise orbit determination method based on satellite perturbation |
| CN112904385A (en) * | 2021-01-26 | 2021-06-04 | 桂林电子科技大学 | Novel double-difference integer ambiguity resolution method |
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