Collaborative navigation optimal measurement screening method for information joint evaluation

Abstract

The invention relates to a collaborative navigation optimal measurement screening method for information joint evaluation, which belongs to the technical field of collaborative navigation and comprises the following steps of: S1, evaluating the reduction degree of measurement on the uncertainty of state quantity to obtain measurement with high contribution degree and measurement with low contribution degree; s2, evaluating the external interference degree of measurement to obtain measurement with high credibility and measurement with low credibility; s3, screening measurements with high contribution degree and high credibility and measurements with low contribution degree and high credibility, and rejecting measurements with high contribution degree and low credibility and measurements with low contribution degree and low credibility; s4, if the measurement with low contribution degree and high credibility is reserved and the state quantity is considerable, and the measurement with low contribution degree and high credibility is rejected and the state quantity is not considerable, taking the measurement with high contribution degree and high credibility and the measurement with low contribution degree and high credibility as optimal measurement information; on the contrary, the measurement with the high contribution degree and the high credibility is used as the optimal measurement. The method ensures that the follower aircraft filter is efficient and robust.

Description

Technical Field

[0001] The present invention belongs to the technical field of cooperative navigation, and particularly relates to a method for screening optimal measurements of cooperative navigation with joint information evaluation. Background Art

[0002] In the process of cooperative navigation of a leader-follower aircraft cluster, the follower aircraft needs to use the navigation information of the leader aircraft as a reference and the relative measurement information as a constraint. By means of a cooperative navigation model, the positioning information, relative measurement information and its own navigation information of one or more leader aircraft are fused to obtain a higher-precision positioning information and suppress the divergence of positioning errors. Therefore, the relative measurement information between aircraft is the bridge to establish the association of aircraft navigation information. However, when the follower aircraft obtains a large amount of measurement information, the existing cooperative positioning algorithms have the problem of excessive computational complexity, and it is difficult to guarantee the optimal estimation of the cooperative navigation algorithm, and it is considered not to have the function of screening optimal measurements.

[0003] From the research results of existing cooperative strategies, the research focus of the existing technology is mostly on the research of cooperative navigation algorithms with optimal configurations. The essence of such algorithms is to improve the observability of state variables by means of configuration optimization on the premise of ensuring the observability of state variables, so as to achieve the optimal estimation of cooperative navigation algorithms. For example, considering the influence of dynamic changes in the formation topology on the accuracy of cooperative navigation algorithms, designing a cooperative navigation architecture for an aircraft cluster with an optimal formation configuration; an analysis method for cooperative positioning errors and optimal formation configurations of an aircraft cluster based on geometric interpretation; an optimal configuration design for cooperative navigation of an aircraft cluster based on various information analysis methods, etc.

[0004] However, due to factors such as external environmental interference, information occlusion and equipment failures, the positioning accuracy and ranging accuracy of the leader aircraft obtained by the follower aircraft vary greatly, resulting in inconsistent accuracy levels of the measurement information obtained by the follower aircraft. Therefore, in the cooperative positioning algorithm, it is not that the more the number of measurement information, the better the positioning accuracy of the filter for the follower aircraft. On the contrary, the measurement with a poor accuracy level is likely to cause the filtering estimation result to fall into a local optimum or even the problem of filter divergence after being sent into the filter, affecting the robustness of cooperative navigation. Therefore, how to formulate a cooperative navigation strategy to screen out the optimal measurements to improve the calculation efficiency and ensure the optimal estimation of the cooperative navigation algorithm is an application problem of the cooperative navigation algorithm for an aircraft cluster in the leader mode. Summary of the Invention

[0005] Aiming at the problem that the traditional cooperative positioning algorithm does not have the function of screening optimal measurements when the follower aircraft obtains sufficient measurement information, the purpose of the present invention is to provide a method for screening optimal measurements of cooperative navigation with joint information evaluation to solve or improve the defects existing in the prior art.

[0006] To achieve the above object, the present invention adopts the following technical solutions: A collaborative navigation optimal measurement screening method for information joint evaluation, comprising the following steps: S1. Evaluate the degree of reduction of the uncertainty of the estimated value of the position error state quantity by the measurement information, and obtain the measurement information with high contribution degree and the measurement information with low contribution degree; S2. Evaluate the degree of interference of the measurement information by external interference, and obtain the measurement information with high credibility and the measurement information with low credibility; S3. Screen the measurement information with high contribution degree and high credibility and the measurement information with low contribution degree and high credibility, and eliminate the measurement information with high contribution degree and low credibility and the measurement information with low contribution degree and low credibility; S4. If the measurement information with low contribution degree and high credibility is retained, the estimated value of the position error state quantity is observable, while if the measurement information with low contribution degree and high credibility is eliminated, the estimated value of the position error state quantity is unobservable, then the measurement information with high contribution degree and high credibility and the measurement information with low contribution degree and high credibility are used as the optimal measurement information; otherwise, the measurement information with high contribution degree and high credibility is used as the optimal measurement information.

[0007] Preferably, in step S1, the specific method for evaluating the degree of reduction of the uncertainty of the estimated value of the position error state quantity by the measurement information and obtaining the measurement information with high contribution degree and the measurement information with low contribution degree is as follows: S11. Construct a mutual information function of the state estimation before and after introducing the follower aircraft filter by the measurement information; S12. Calculate the mutual information of the measurement information, and evaluate the degree of reduction of the uncertainty of the estimated value of the position error state quantity according to the magnitude of the mutual information; if the mutual information is larger, the degree of reduction of the uncertainty of the estimated value of the position error state quantity by the measurement information is higher, that is, the contribution degree of the measurement information to the estimated value of the position error state quantity is higher; otherwise, it is the opposite; thus, the measurement information with high contribution degree and the measurement information with low contribution degree are obtained.

[0008] Preferably, in step S21, the specific method for constructing the mutual information of the state estimation before and after introducing the filter by the measurement information is as follows: According to Shannon's theorem, define the information entropy ι(χ) as: where f(χ i ) is the marginal probability density distribution function when the variable takes the value χ i , f(χ i ) ∈ [0, 1], lnf(χ i ) ∈ (-∞, 0]; The conditional entropy ι(χ|γ) is a function that measures the uncertainty of another variable χ given a variable γ, and its expression is: where f(γ i ) is the marginal probability density distribution function when the variable takes the value γ i , f(γ i ) ∈ [0, 1], lnf(γ i ) ∈ (-∞, 0]; ι(χ|γ = γ i ) represents the function that measures the uncertainty of the variable χ given that the variable γ = γ i , f(χ i , γ i ) is the joint probability distribution function when the variable takes the value χ i and the variable takes the value γ i , f(χ i |γ i ) is the conditional probability distribution function when the variable takes the value χ i given that the variable takes the value γ i ; According to the conditional entropy and the information entropy, the expression for the mutual information Δι(χ; γ) is: When χ is a one-dimensional random variable and its probability density distribution function follows a normal distribution, then there is the following expression: where f(χ) is the marginal probability density distribution function of the random event χ, μ represents the mean of the random event χ, and σ 2 represents the variance of the random event χ; Substituting the above formula into the formula for the information entropy ι(χ), the expression for the information entropy of a random variable following a normal distribution is obtained: If the variable in the above formula is extended from one dimension to n dimensions, that is, when χ is an n-dimensional vector and the covariance matrix between the elements in the vector is R, the specific expression for the information entropy of the n-dimensional random variable is: ι(χ) = 0.5ln(2πe) n det(R); Write the information entropy of the one-step prediction of the state quantity by the follower aircraft before the arrival of the new measurement information as: where X k,k-1 represents the one-step prediction of the state vector X k , which is the prior estimate of the state quantity X k , and x k,k-1 represents the state quantity Xk One-step prediction; When the one-step prediction X of the state vector k,k-1 has a normal distribution for its probability density function, the one-step prediction information entropy of the state quantity is rewritten as: ι(X k,k-1 ) = 0.5ln(2πe) n det(P k,k-1 ); where P k,k-1 is the one-step prediction mean square error matrix; After the measurement information is sent into the filter, the conditional entropy ι(X k |Z k ) of the posterior estimate of the state quantity is: where, represents the i-th measurement information obtained by the follower aircraft at time k; Combining the conditional entropy of the posterior estimate of the state quantity and the information entropy of the n-dimensional random variable, when the probability density function of the posterior estimate of the state quantity X k obeys a normal distribution, the conditional entropy of the posterior estimate of the state quantity is rewritten as: ι(X k |Z k ) = 0.5ln(2πe) n det(P k ); where P k represents the mean square error of the state estimate at time k; Then the mutual information Δι(X k ; Z k ) between the state estimates before and after the measurement information is introduced into the filter is: Δι(X k ; Z k ) = ι(X k,k-1 ) - ι(X k |Z k ); Substituting the rewritten one-step prediction information entropy formula of the state quantity and the rewritten conditional entropy formula of the posterior estimate of the state quantity into the mutual information formula of the state estimates before and after the measurement information is introduced into the filter, the rewritten mutual information of the state estimates before and after the measurement information is introduced into the filter is obtained as: The rewritten mutual information of the state estimates before and after the measurement information is introduced into the filter is further rewritten as: where I represents the identity matrix, K k represents the Kalman filter gain matrix, H kRepresents the measurement information matrix.

[0009] Preferably, in step S2, the specific method for evaluating the degree of external interference on the measurement information to obtain high-confidence measurement information and low-confidence measurement information is as follows: S21. Construct the Fisher information function of the measurement information; S22. Calculate the Fisher information of the measurement information, and evaluate the degree of external interference on the measurement information according to the magnitude of the Fisher information; if the Fisher information is larger, the degree of external interference on the measurement information is lower, that is, the confidence level of the measurement information is higher; otherwise, it is the opposite; thus, high-confidence measurement information and low-confidence measurement information are obtained.

[0010] Preferably, in step S21, the specific method for constructing the Fisher information function of the measurement information is as follows: Let the measurement information obtained by the follower aircraft Follow the conditional distribution probability density function f(Z|X), then construct the likelihood function S(Z k |X k ) as: Among them, Z k Represents the measurement information of the follower aircraft at time k, X k Represents the state vector of the follower aircraft at time k, Represents the i-th measurement information of the follower aircraft at time k; For the convenience of calculation, rewrite the likelihood function of the measurement information and the state quantity into the logarithmic form of the likelihood function as: Perform partial differentiation on both sides of the logarithmic form formula of the likelihood function to obtain the quality function V(Z k |X k ) as: Perform partial differentiation on the left and right sides of the quality function of the measurement information again to obtain the Fisher information J(X k ) as: Among them, the Fisher information J(X k ) represents the variance of the quality function of the measurement information; If the posterior estimate of the state quantity X k by the filtering algorithm is expressed as Then according to the Cramer-Rao lower bound theory, the posterior estimate The lower bound that the mean square error can reach is: where represents the variance of the estimator , and E represents the mathematical expectation; It can be seen from this that the lower bound of the mean square error of the posterior estimate is the reciprocal of the Fisher information; The estimation bias of the state quantity is: Since the estimation bias of the state quantity follows a normal distribution with a mean of 0, the formula for the lower bound that the mean square error of the posterior estimate can reach is rewritten in integral form as: Since the state quantity in the filter is a multi-dimensional vector, the Fisher information is rewritten in matrix form as: where J ij (X k ) represents the Fisher information matrix, and J ij represents the element in the i-th row and j-th column of the matrix J. J is a 3-order matrix, and represent the state quantity of the system; The Cramer-Rao lower bound corresponding to the matrix form of the Fisher information is: Ξ ≥ J -1 (X k ); where Ξ represents the covariance matrix of the unbiased estimate value of the state quantity; Rewrite the above formula as the following form: J(X k ) ≥ Ξ -1 .

[0011] Preferably, in step S3, the specific method for screening measurement information with high contribution and high credibility and measurement information with low contribution and high credibility, and eliminating measurement information with high contribution and low credibility and measurement information with low contribution and low credibility is: S31. Construct the optimization objective function and constraint conditions for measurement information screening; S32. Use the optimization objective function and constraint conditions to screen measurement information with high contribution and high credibility and measurement information with low contribution and high credibility, and eliminate measurement information with high contribution and low credibility and measurement information with low contribution and low credibility.

[0012] Preferably, in step S31, the specific method for constructing the optimization objective function and constraint conditions for measurement information screening is as follows: Based on mutual information and Fisher information, the optimization objective function for measurement information screening is constructed as: Among them, δp k represents the position error state quantity at time k, and J(δp k ) represents the Fisher information of the position error state quantity at time k. Ξ represents the covariance matrix of the unbiased estimated value of the state quantity. δp k,k-1 represents the estimated value of the position error state quantity from time k - 1 to time k. ι(δp k,k-1 ) represents the mutual information of the position error state quantity from time k - 1 to time k. Z k represents the measurement information at time k. ι(δp k |Z k ) represents the mutual information of the position error state quantity δp k under the condition of the measurement information Z k at time k. represents the feasible region; Let the unbiased estimated value of the optimal measurement information screened by the optimization objective function for the position error state quantity be while the unbiased estimate of the position error state quantity by other measurement information is All the unbiased estimated values construct a data set as Then the optimal measurement estimate value needs to satisfy the following conditions: Among them, represents the unbiased estimate of the position error state quantity by the i-th measurement information, represents the set of all unbiased estimated values, represents the unbiased estimated value of the optimal measurement information screened by the optimization objective function for the position error state quantity.

[0013] Compared with the prior art, the present invention has the following beneficial effects: The present invention jointly screens the optimal measurement information through two indicators of contribution degree and credibility, retains the measurement information with high contribution degree and high credibility, eliminates abnormal and / or low-quality measurement information, and supplements the measurement information with low contribution degree and high credibility when the measurement information with high contribution degree and high credibility is not sufficient to ensure the observability of the state quantity, ensuring the efficiency and robustness of the filter of the follower aircraft, solving the problem that the filtering estimation result falls into local optimality caused by abnormal and / or low-quality measurement information, and realizing the global optimal estimation of the multi-leader cooperative positioning algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] To more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0015] Figure 1 It is a principle block diagram of a collaborative navigation optimal measurement screening method for information joint evaluation according to an embodiment of the present invention.

[0016] Figure 2 It is a schematic flow chart of a collaborative navigation optimal measurement screening method for information joint evaluation according to an embodiment of the present invention.

[0017] Figure 3 It is a relationship diagram among information entropy, mutual information and conditional entropy. Specific embodiments

[0018] To make the objectives, technical solutions and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions in the present invention in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention. To make the above features and advantages of the present invention more obvious and understandable, specific embodiments are hereby given and detailed descriptions are made in conjunction with the drawings as follows.

[0019] Due to the influence of the relative position relationship, distance and external interference between the aircraft, there are differences in the two indicators of the contribution degree and credibility of the measurement information obtained between the follower aircraft and each leader aircraft. The lower the contribution degree of the measurement information, the lower the degree of estimation of the position error state quantity by the filter through the innovation. Conversely, the higher it is; the lower the credibility of the measurement information, the greater the estimation error of the innovation estimation for the state quantity. Therefore, the measurement information with a greater contribution degree and higher credibility should be the first choice of the filter. In addition, on the premise of ensuring the observability of the position error state quantity, eliminating the measurements with low contribution degree and low credibility, high contribution degree and low credibility, and low contribution degree and high credibility helps to improve the execution efficiency of the filter and prevent the filtering estimation result from falling into a local optimum.

[0020] The classification and sorting of the above four types of measurement information are shown in Table 1: Table 1 Sorting method of measurement information types

[0021] The measurement information ranked 3 and 4 in Table 1 can be called harmful measurements. Such measurements must be eliminated, otherwise it is easy to cause abnormal estimation of the position error state quantity by the filter, and even filter divergence. Although the measurements of the second type contribute little to the estimation of the position error state quantity, they will not cause filtering anomalies. On the premise that the first type of measurements ensure the observability of the position error state quantity, the second type of measurements should be eliminated to improve the calculation efficiency of the algorithm and the estimation accuracy of the position error state quantity. However, when the information of the first type of measurements is limited and cannot satisfy the observability of the position error state quantity, the second type of measurements should be retained to ensure the observability of the position error state quantity.

[0022] The navigation mode of the follower aircraft corresponding to the optimal measurement screening method is as follows: On the premise that the first type of measurements or the combined measurements of the first and second types can ensure the observability of the position error state quantity, the aircraft uses the cooperative positioning method to obtain positioning information. Otherwise, the aircraft relies on the autonomous navigation method to obtain positioning information. The specific implementation plan of the optimal measurement screening strategy is as attached Figure 1 shown.

[0023] Based on the above analysis, it can be seen that the indicators for measuring information screening are contribution degree and credibility. In order to effectively evaluate these two indicators, mutual information is used to evaluate the contribution degree of measurement information, and Fisher information is used to evaluate the credibility of measurement information. The information entropy is used to characterize the uncertainty of the state quantity X k before the innovation update. The mutual information represents the amount of information of the measurement. The greater the mutual information of the measurement, the richer the amount of information brought by the measurement to the filter (the greater the contribution degree), the better the measurement, the smaller the uncertainty of the state quantity estimated by this measurement, and the closer the filtering result of the cooperative positioning algorithm is to the global optimal estimation. Fisher information quantity is used to represent the expected value of the amount of information that a single observation value in the filter can provide for the state quantity, and is used to predict the accuracy of the filtering estimation result. The greater the Fisher observation information quantity, the greater the variance of the corresponding scoring function, reflecting that the observation information is richer, and the higher the accuracy of the filter's estimation of the state quantity.

[0024] The specific meanings of the contribution degree and credibility in the method of the present invention are as follows: Contribution degree: It refers to the degree to which the uncertainty of the estimated value of the position error state quantity is reduced after the measurement innovation is sent into the filter. In this method, this index is judged by the magnitude of the mutual information. Credibility: It refers to the degree to which the measurement information is interfered by external interference. The greater the external interference, the lower the credibility of the measurement information, and vice versa. In this method, this index is measured by the Fisher information quantity.

[0025] As Figure 2 shown, the embodiment of the present invention provides a cooperative navigation optimal measurement screening method for information joint evaluation, including the following steps: S1. Evaluate the degree of reduction of the uncertainty of the estimated value of the position error state quantity by the measurement information, and obtain the measurement information with high contribution degree and the measurement information with low contribution degree; S2. Evaluate the degree of interference of the measurement information by external interference, and obtain the measurement information with high credibility and the measurement information with low credibility; S3. Screen the measurement information with high contribution degree and high credibility and the measurement information with low contribution degree and high credibility, and eliminate the measurement information with high contribution degree and low credibility and the measurement information with low contribution degree and low credibility; S4. If the measurement information with low contribution degree and high credibility is retained, the estimated value of the position error state quantity is observable, and if the measurement information with low contribution degree and high credibility is eliminated, the estimated value of the position error state quantity is unobservable, then the measurement information with high contribution degree and high credibility and the measurement information with low contribution degree and high credibility are used as the optimal measurement information; otherwise, the measurement information with high contribution degree and high credibility is used as the optimal measurement information.

[0026] In this embodiment, in step S1, the specific method for evaluating the degree of reduction of the uncertainty of the estimated value of the position error state quantity by the measurement information and obtaining the measurement information with high contribution degree and the measurement information with low contribution degree is as follows: S11. Construct a mutual information function of the state estimation before and after introducing the follower aircraft filter by the measurement information; S12. Calculate the mutual information of the measurement information, and evaluate the degree of reduction of the uncertainty of the estimated value of the position error state quantity according to the size of the mutual information; if the mutual information is larger, the degree of reduction of the uncertainty of the estimated value of the position error state quantity by the measurement information is higher, that is, the contribution degree of the measurement information to the estimated value of the position error state quantity is higher; otherwise, it is the opposite; thus, the measurement information with high contribution degree and the measurement information with low contribution degree are obtained.

[0027] Information entropy is a concept proposed by Shannon for quantitatively evaluating information, mainly used to describe the uncertainty of the information source. The size of the information entropy can directly reflect the degree of uncertainty of the information source. The higher the uncertainty of the information source, the larger the information entropy. From a mathematical point of view, the information entropy represents the mathematical expectation of the uncertainty of a random variable.

[0028] In this embodiment, in step S21, the specific method for constructing the mutual information of the state estimation before and after introducing the filter by the measurement information is as follows: According to Shannon's theorem, define the information entropy ι(χ) as: where f(χ i ) is the marginal probability density distribution function when the variable takes the value of χ i , f(χ i ) ∈ [0, 1], lnf(χ i) ∈ (-∞, 0]; The conditional entropy ι(χ|γ) is a function that measures the uncertainty of another variable χ given a variable γ, and its expression is: where f(γ i ) is the marginal probability density distribution function when the variable takes the value γ i , f(γ i ) ∈ [0, 1], lnf(γ i ) ∈ (-∞, 0]; ι(χ|γ = γ i ) represents the function that measures the uncertainty of variable χ given that the variable γ = γ i , f(χ i , γ i ) is the joint probability distribution function when the variable takes the value χ i and the variable takes the value γ i , f(χ i |γ i ) is the conditional probability distribution function when the variable takes the value χ i when the variable takes the value γ i ; According to the conditional entropy and the information entropy, the expression for the mutual information Δι(χ; γ) is: When χ is a one-dimensional random variable and its probability density distribution function follows a normal distribution, then there is the following expression: where f(χ) is the marginal probability density distribution function of the random event χ, μ represents the mean of the random event χ, and σ 2 represents the variance of the random event χ; Substituting the above formula into the formula for the information entropy ι(χ), the expression for the information entropy of a random variable following a normal distribution is: From the above formula, it can be seen that the information entropy has nothing to do with the mean of the variable and is only related to its variance σ 2 ; If the variable in the above formula is extended from one dimension to n dimensions, that is, when χ is an n-dimensional vector and the covariance matrix between the elements in the vector is R, the specific expression for the information entropy of the n-dimensional random variable is: ι(χ) = 0.5ln(2πe) n det(R); The relationship among the conditional entropy, the information entropy, and the mutual information is as Figure 3 shown, from Figure 3It can be intuitively seen that mutual information is a function for measuring the correlation between two variables. The stronger the correlation between them, the greater the mutual information. In this embodiment, this characteristic of mutual information is utilized to evaluate the correlation between measurement information and state variables, that is, the greater the contribution degree of measurement information to the estimation of state variables, the greater the mutual information. From the perspective of information uncertainty, the greater the mutual information, the more the uncertainty of the state variable estimation value is reduced, that is, the more accurate the estimation value of the state variable. According to the above analysis, the information entropy of the one-step prediction of the state variable by the follower aircraft before the arrival of new measurement information is written as: where X k,k-1 represents the one-step prediction of the state vector X k , which is the prior estimation of the state variable X k , and x k,k-1 represents the one-step prediction of the state variable X k . [[ID=!8]]When the probability density function of the one-step prediction X k,k-1 of the state vector is a normal distribution, the information entropy of the one-step prediction of the state variable is rewritten as: ι(X k,k-1 ) = 0.5ln(2πe) n det(P k,k-1 ); where P k,k-1 is the one-step prediction mean square error matrix; After the measurement information is sent into the filter, the conditional entropy ι(X k |Z k ) of the posterior estimation of the state variable is: where represents the i-th measurement information obtained by the follower aircraft at time k; Combining the conditional entropy of the posterior estimation of the state variable and the information entropy of the n-dimensional random variable, when the probability density function of the posterior estimation of the state variable X k follows a normal distribution, the conditional entropy of the posterior estimation of the state variable is rewritten as: ι(X k |Z k ) = 0.5ln(2πe) n det(P k ); where P k represents the mean square error of the state estimation at time k; Then the mutual information Δι(X k ; Z k ) between the state estimations before and after the measurement information is introduced into the filter is: Δι(Xk ; Z k ) = ι(X k,k-1 ) - ι(X k |Z k ); Substitute the one-step prediction information entropy formula of the rewritten state quantity and the conditional entropy formula of the posterior estimation of the rewritten state quantity into the mutual information formula of the state estimation before and after introducing the measurement information into the filter, and the mutual information of the state estimation before and after introducing the rewritten measurement information into the filter is obtained as follows: As can be seen from the above formula, the physical meaning of Δι(X k ; Z k ) is the reduction of the uncertainty of the state estimation; The mutual information of the state estimation before and after introducing the rewritten measurement information into the filter is further rewritten as: where I represents the identity matrix, K k represents the Kalman filter gain matrix, and H k represents the measurement information matrix; As can be seen from the above formula, the mutual information Δι(X k ; Z k ) can measure the degree of correction of the measurement information to the prior state estimation.

[0029] In this embodiment, in step S2, the specific method for evaluating the degree of the measurement information being interfered by external interference and obtaining the measurement information with high credibility and the measurement information with low credibility is as follows: S21. Construct the Fisher information function of the measurement information; S22. Calculate the Fisher information of the measurement information, and evaluate the degree of the measurement information being interfered by external interference according to the magnitude of the Fisher information; if the Fisher information is larger, the degree of the measurement information being interfered by external interference is lower, that is, the credibility of the measurement information is higher; otherwise, it is the opposite; thus, the measurement information with high credibility and the measurement information with low credibility are obtained.

[0030] The Fisher information quantity is originally an index applicable to evaluating the information quantity of unknown parameters carried by random observation variables. Based on this property of the Fisher information quantity, it is used in this paper to evaluate the credibility of the measurement information obtained by the follower aircraft. The more sufficient the Fisher information quantity corresponding to the measurement information, the higher its credibility. The higher the credibility of the measurement information, the higher the proportion of useful information in the measurement information, and the lower the degree of influence of noise on the estimation accuracy of the state quantity. Therefore, in the process of optimal measurement screening, the priority of the credibility of the measurement information is higher than the contribution degree. Evaluating the credibility of the measurement information based on the Fisher information ensures the effectiveness and reliability of the measurement information.

[0031] According to the principle of the non - linear EKF, it is known that the essence of the filtering algorithm is to use the measurement information to achieve the prior estimation of the state quantity X k and correct it to obtain the posterior estimation process. In this process, the filtering algorithm itself cannot judge whether the measurement information is credible. Therefore, it cannot be judged whether the posterior estimation is the optimal estimation of the state quantity X either, nor can it be judged whether the estimated value is valid. In other words, the estimation result of the filtering algorithm is highly dependent on the measurement information, and it cannot identify and screen effective measurements by itself to ensure that the posterior estimation of the state quantity X k is the optimal estimation. The higher the credibility of the measurement information, the better the filtering estimation result, and vice versa. k is the optimal estimation, and the higher the credibility of the measurement information, the better the filtering estimation result, and vice versa. In this embodiment, in step S21, the specific method for constructing the Fisher information function of the measurement information is as follows:

[0032] Let the measurement information obtained by the follower aircraft follow the conditional distribution probability density function f(Z|X), then the likelihood function S(Z |X k |X k ) about the measurement information and the state quantity is constructed as: where Z k represents the measurement information of the follower aircraft at time k, X k represents the state vector of the follower aircraft at time k, represents the i - th measurement information of the follower aircraft at time k; For the convenience of calculation, the likelihood function about the measurement information and the state quantity is rewritten as the logarithmic form of the likelihood function: Taking the partial derivative of both sides of the logarithmic - form formula of the likelihood function simultaneously, the quality function V(Z k |X k ) about the measurement information is obtained as: Taking the partial derivative of both sides of the quality function about the measurement information again, the Fisher information J(X k ) is obtained as: where the Fisher information J(X k ) represents the variance of the quality function of the measurement information; If the posterior estimation of the filtering algorithm for the state quantity X k ​ According to the Cramer-Rao lower bound theory, the posterior estimate is obtained. The lower bound that the mean square error of can reach is: where, represents the variance of the estimator , and E represents the mathematical expectation; It can be seen from this that the lower bound of the mean square error of the posterior estimate is the reciprocal of the Fisher information; The estimation bias of the state quantity is: Since the estimation bias of the state quantity follows a normal distribution with a mean of 0, the formula for the lower bound that the mean square error of the posterior estimate can reach is rewritten in integral form as: Since the state quantity in the filter is a multi-dimensional vector, the Fisher information is rewritten in matrix form as: where, J ij (X k ) represents the Fisher information matrix, and J ij represents the element in the i-th row and j-th column of the matrix J. J is a 3-order matrix, and represent the state quantity of the system; The Cramer-Rao lower bound corresponding to the matrix form of the Fisher information is: Ξ ≥ J -1 (X k ); where, Ξ represents the covariance matrix of the unbiased estimate value of the state quantity; Rewrite the above formula as the following form: J(X k ) ≥ Ξ -1 ; It can be seen from the above formula that the larger the Fisher information J(X k ) of the measurement information is, the smaller the Cramer-Rao lower bound that the covariance Ξ of the unbiased estimate value of the state quantity can reach is, indicating that the smaller the interference received by the measurement information is, the higher the credibility of the measurement information is. Therefore, the Fisher information can be used to construct an optimization objective function to assist in screening out the optimal measurement.

[0033] In this embodiment, in step S3, the specific method for screening measurement information with high contribution degree and high credibility and measurement information with low contribution degree and high credibility, and eliminating measurement information with high contribution degree and low credibility and measurement information with low contribution degree and low credibility is as follows: S31. Construct an optimization objective function and constraint conditions for measurement information screening; S32. Use the optimization objective function and constraint conditions to screen measurement information with high contribution degree and high credibility and measurement information with low contribution degree and high credibility, and eliminate measurement information with high contribution degree and low credibility and measurement information with low contribution degree and low credibility.

[0034] During the collective flight of the aircraft cluster, the key of the cooperative positioning algorithm lies in correcting the position error of the follower aircraft. Since there are 3 state variables related to the position error in the state vector, other state variables do not need to be considered in the optimization objective function. In addition, according to the Cramer-Rao theory, the Cramer-Rao lower bound is the lowest variance that an unbiased estimate can achieve; according to the mutual information theory of information entropy, the greater the mutual information, the higher the contribution degree of the measurement information.

[0035] In this embodiment, in step S31, the specific method for constructing an optimization objective function and constraint conditions for measurement information screening is as follows: Based on mutual information and Fisher information, construct an optimization objective function for measurement information screening as: where, δp k represents the position error state variable at time k, J(δp k ) represents the Fisher information of the position error state variable at time k, Ξ represents the covariance matrix of the unbiased estimate value of the state variable, δp k,k-1 represents the estimated value of the position error state variable from time k-1 to time k, ι(δp k,k-1 ) represents the mutual information of the position error state variable from time k-1 to time k, Z k represents the measurement information at time k, ι(δp k |Z k ) represents the mutual information of the position error state variable δp k under the condition of the measurement information Z k at time k, represents the feasible region; Let the unbiased estimated value of the optimal measurement information screened by the optimization objective function for the position error state variable be while the unbiased estimate of the other measurement information for the position error state variable is All the unbiased estimated values construct a data set as Then the optimal measurement estimated value needs to meet the following conditions: Among them, represents the unbiased estimation of the \(i\)-th measurement information on the position error state quantity, represents the set of all unbiased estimation values, represents the unbiased estimation value of the optimal measurement information selected by the optimization objective function for the position error state quantity; It can be seen from the above formula that the essence of the optimal measurement information screening is to achieve the unbiased estimation of the position error state quantity, and the mean square error of the estimation value of the measurement information on the position state quantity is minimized, so as to achieve the global optimum of the filtering estimation result.

[0036] In this embodiment, an information entropy function of state estimation is established according to Shannon's theorem, and then a conditional entropy function under measurement constraints is established. The mutual information of measurement information evaluation is given by the way of taking the difference between the information entropy and the conditional entropy. In this embodiment, a likelihood function about the measurement information is constructed, and the Fisher information is obtained through two partial differentiations. Then, considering that the state quantity related to the position in the cooperative positioning algorithm is three-dimensional, the Fisher information is rewritten as an information matrix of partial differentiation with respect to the state quantity, and the lower bound of the covariance of the unbiased estimation of the state quantity is given. In this embodiment, an objective function for optimal measurement screening is constructed, and a constraint condition with the smallest equation is designed. Compared with the traditional method, the method of this embodiment solves the problem that the filtering estimation result falls into the local optimum caused by abnormal measurement through the optimal measurement screening strategy, and realizes the global optimum estimation of the multi-pilot cooperative positioning algorithm.

[0037] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A collaborative navigation optimal measurement screening method for joint information evaluation, characterized in that It includes the following steps: S1. Evaluate the degree of reduction of the uncertainty of the estimated value of the position error state quantity by the measurement information, and obtain the measurement information with high contribution degree and the measurement information with low contribution degree; S2. Evaluate the degree of interference of the measurement information by external interference, and obtain the measurement information with high credibility and the measurement information with low credibility; S3. Screen the measurement information with high contribution degree and high credibility and the measurement information with low contribution degree and high credibility, and eliminate the measurement information with high contribution degree and low credibility and the measurement information with low contribution degree and low credibility; S4. If the measurement information with low contribution degree and high credibility is retained, the estimated value of the position error state quantity is observable, and if the measurement information with low contribution degree and high credibility is eliminated, the estimated value of the position error state quantity is unobservable, then the measurement information with high contribution degree and high credibility and the measurement information with low contribution degree and high credibility are used as the optimal measurement information; On the contrary, the measurement information with high contribution degree and high credibility is used as the optimal measurement information.

2. The collaborative navigation optimal measurement screening method for information joint evaluation according to claim 1, wherein In step S1, the specific method for evaluating the degree of reduction of the uncertainty of the estimated value of the position error state quantity by the measurement information and obtaining the measurement information with high contribution degree and the measurement information with low contribution degree is as follows: S11. Construct the mutual information function of the state estimation before and after introducing the follower aircraft filter by the measurement information; S12. Calculate the mutual information of the measurement information, and evaluate the degree of reduction of the uncertainty of the estimated value of the position error state quantity according to the magnitude of the mutual information; If the mutual information is larger, the degree of reduction of the uncertainty of the estimated value of the position error state quantity by the measurement information is higher, that is, the contribution degree of the measurement information to the estimated value of the position error state quantity is higher; on the contrary, it is the opposite; thus, the measurement information with high contribution degree and the measurement information with low contribution degree are obtained.

3. The collaborative navigation optimal measurement screening method for information joint evaluation according to claim 2, wherein In step S21, the specific method for constructing the mutual information of the state estimation before and after introducing the filter by the measurement information is as follows: According to Shannon's theorem, the information entropy ι(χ) is defined as: Among them, f(χ i ) is the marginal probability density distribution function when the variable takes the value of χ i , f(χ i ) ∈ [0, 1], lnf(χ i ) ∈ (-∞, 0]; The conditional entropy ι(χ|γ) is a function for measuring the uncertainty of another variable χ when a variable γ is known, and its expression is: where f(γ i ) is the marginal probability density distribution function when the variable takes the value of γ i , f(γ i ) ∈ [0, 1], lnf(γ i ) ∈ (-∞, 0]; ι(χ|γ = γ i ) represents the function for measuring the uncertainty of the variable χ when the variable γ = γ i is known, f(χ i , γ i ) is the joint probability distribution function of the variable taking the value χ i and the variable taking the value γ i , f(χ i |γ i ) is the conditional probability distribution function when the variable takes the value γ i and the variable takes the value χ i ; According to the conditional entropy and the information entropy, the expression of the mutual information Δι(χ;γ) is obtained as: When χ is a one-dimensional random variable and its probability density distribution function follows a normal distribution, then there is the following expression: where f(χ) is the marginal probability density distribution function of the random event χ, μ represents the mean of the random event χ, and σ 2 represents the variance of the random event χ; Substitute the above formula into the formula of the information entropy ι(χ), and the expression of the information entropy of the random variable following a normal distribution is obtained: If the variable in the above formula is extended from one dimension to n dimensions, that is, when χ is an n-dimensional vector and the covariance matrix between the elements in the vector is R, the specific expression of the information entropy of the n-dimensional random variable is: ι(χ) = 0.5ln(2πe) n det(R); Write the information entropy of the one-step prediction of the state quantity by the follower aircraft before the arrival of the new measurement information as: Among them, X k,k-1 represents the one-step prediction of the state vector X k , which is the prior estimate of the state quantity X k , and x k,k-1 represents the one-step prediction of the state quantity X k ; When the probability density function of the one-step prediction \(X\) of the state vector k,k-1 is a normal distribution, the one-step prediction information entropy of the state quantity is rewritten as: ι(X k,k-1 ) = 0.5 ln(2πe) n det(P k,k-1 ) Among them, P k,k-1 is the one-step prediction mean square error matrix; After the measurement information is sent into the filter, the conditional entropy ι(X k |Z k ) is as follows: Among them, represents the i-th measurement information obtained by the follower aircraft at the k-th moment; Combined with the conditional entropy of the posterior estimate of the state quantity and the information entropy of the n-dimensional random variable, when the state quantity X k When the probability density function of the posterior estimate follows a normal distribution, the conditional entropy of the posterior estimate of the state quantity is rewritten as: ι(X k |Z k ) = 0.5 ln(2πe) n det(P k ); Among them, P k represents the mean square error of the state estimation at time k; Then the mutual information Δι(X k ; Z k ) before and after the measurement information is introduced into the filter is as follows: Δι(X k ; Z k ) = ι(X k,k-1 ) - ι(X k |Z k ); Substitute the rewritten formula of the information entropy of the one-step prediction of the state quantity and the rewritten formula of the conditional entropy of the posterior estimation of the state quantity into the mutual information formula of the state estimation before and after introducing the filter by the measurement information, and the rewritten mutual information of the state estimation before and after introducing the filter by the measurement information is obtained as: Further rewrite the rewritten mutual information of the state estimation before and after introducing the filter by the measurement information as: Among them, I represents the identity matrix, and K k represents the Kalman filter gain matrix, and H k represents the measurement information matrix.

4. The collaborative navigation optimal measurement screening method for information joint evaluation according to claim 1, wherein In step S2, the specific method for evaluating the degree of interference of the measurement information by external interference and obtaining the measurement information with high credibility and the measurement information with low credibility is as follows: S21. Construct the Fisher information function of the measurement information; S22. Calculate the Fisher information of the measurement information, and evaluate the degree of external interference on the measurement information according to the magnitude of the Fisher information; If the Fisher information is larger, the degree of external interference on the measurement information is lower, that is, the credibility of the measurement information is higher; otherwise, it is the opposite; thus, measurement information with high credibility and measurement information with low credibility are obtained.

5. A collaborative navigation optimal measurement screening method for information joint evaluation according to claim 4, characterized in that In step S21, the specific method for constructing the Fisher information function of the measurement information is as follows: Let the measurement information obtained by the follower aircraft follow the conditional distribution probability density function f(Z|X), then construct the likelihood function S(Z k |X k ) as follows: Among them, Z k represents the measurement information of the follower aircraft at time k, and X k represents the state vector of the follower aircraft at time k, represents the i-th measurement information of the follower aircraft at time k; For the convenience of calculation, rewrite the likelihood function about the measurement information and the state quantity into the logarithmic form of the likelihood function as: Taking the partial derivatives of both sides of the logarithmic form formula of the likelihood function simultaneously, the quality function V(Z k |X k ) with respect to the measurement information is obtained as follows: Taking the partial derivatives of both sides of the quality function with respect to the measurement information again, the Fisher information J(X k ) is as follows: Among them, the Fisher information J(X k ) represents the variance of the quality function of the measurement information; If the posterior estimate of the state quantity X k is expressed as then according to the Cramer-Rao lower bound theory, the lower bound that the mean square error of the posterior estimate can reach is: Among them, represents the variance of the estimator , and E represents the mathematical expectation; It can be seen from this that the lower bound of the mean square error of the posterior estimate is the reciprocal of the Fisher information; Estimation deviation of state quantity is as follows: Due to the estimation bias of the state variables obeys a normal distribution with a mean of 0. Therefore, the lower bound formula of the mean square error that the posterior estimation can achieve is rewritten in integral form as follows: Since the state quantity in the filter is a multi-dimensional vector, rewrite the Fisher information into matrix form as: Among them, J ij (X k ) represents the Fisher information matrix, and J ij represents the element in the i-th row and j-th column of matrix J. J is a 3-order matrix, and represent the state variables of the system; The Cramer-Rao lower bound corresponding to the matrix form of the Fisher information is: Ξ≥J -1 (X k ); where, Ξ represents the covariance matrix of the unbiased estimated value of the state quantity; Rewrite the above formula into the following form: J(X k )≥Ξ -1 。 6. A collaborative navigation optimal measurement screening method for information joint evaluation according to claim 1, characterized in that In step S3, the specific method for screening measurement information with high contribution and high credibility and measurement information with low contribution and high credibility, and eliminating measurement information with high contribution and low credibility and measurement information with low contribution and low credibility is as follows: S31. Construct the optimization objective function and constraint conditions for measurement information screening; S32. Use the optimization objective function and constraint conditions to screen measurement information with high contribution and high credibility and measurement information with low contribution and high credibility, and eliminate measurement information with high contribution and low credibility and measurement information with low contribution and low credibility.

7. A collaborative navigation optimal measurement screening method for information joint evaluation according to claim 6, characterized in that In step S31, the specific method for constructing the optimization objective function and constraint conditions for measurement information screening is as follows: Based on mutual information and Fisher information, construct the optimization objective function for measurement information screening as: Among them, δp k represents the position error state quantity at time k, J(δp k ) represents the Fisher information of the position error state quantity at time k, Ξ represents the covariance matrix of the unbiased estimated value of the state quantity, δp k,k-1 represents the estimated value of the position error state quantity from time k - 1 to time k, ι(δp k,k-1 ) represents the mutual information of the position error state quantity from time k - 1 to time k, Z k represents the measurement information at time k, ι(δp k |Z k ) represents the mutual information of the position error state quantity δp k under the condition of the measurement information Z k at time k, represents the feasible region; Let the unbiased estimated value of the optimal measurement information selected by the optimization objective function for the position error state quantity be while the unbiased estimate of the other measurement information for the position error state quantity is All the unbiased estimated values construct a data set as Then the optimal measurement estimated value needs to satisfy the following conditions: Among them, represents the unbiased estimation of the position error state quantity by the i-th measurement information, represents the set of all unbiased estimation values, represents the unbiased estimation value of the optimal measurement information for the position error state quantity screened by the optimization objective function.

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