A method for verifying gravity matching results based on carrier displacement

Abstract

This invention discloses a method for verifying gravity matching results based on carrier displacement. Based on the idea of ​​hypothesis testing, it utilizes the χ² method. 2 The verification method incorporates the characteristics of the gravity matching algorithm to design a verification algorithm that uses the difference between the observed displacement vector and the inertial navigation displacement vector in the gravity matching system to verify the correctness of the matching result. This method can meet the requirements for identifying incorrect matching results even when the initial position error of the inertial navigation is large, and its ability to identify incorrect matching results is significantly improved under the condition of inaccurate prior position information.

Description

Technical Field

[0001] This invention relates to the field of aircraft navigation, and more specifically to a method for verifying gravity matching results based on carrier displacement. Background Technology

[0002] Gravity matching navigation is a navigation method that uses gravity sensors to detect the characteristics of the gravity field at single or multiple points near the Earth. It then searches for points on a pre-made gravity field feature map that best match the detected features, determining the location of these points on the map and thus enabling vehicle positioning. Gravity matching navigation offers advantages such as stable navigation information sources, high stealth, and the elimination of the need to transmit or receive radio signals. Currently, it is used in submarines and ships, and with the miniaturization of equipment and improvements in measurement accuracy, it has broad application prospects in aircraft and near-space vehicles.

[0003] The Earth's gravitational field is highly complex, and gravity feature maps are generally multi-extremal and strongly nonlinear. Search algorithms may encounter local extrema during large-scale searches, leading to erroneous positioning results. Before using a gravity matching system to correct the inertial navigation system (INS), integrated navigation systems need to verify the navigation information provided by the gravity matching system to eliminate erroneous matching information. Utilizing the concept of fault detection in integrated navigation systems, this paper constructs detection quantities using the state variables of the integrated navigation system for hypothesis testing, calculates the rejection region using the state error variance, and judges the measurement information. Integrated navigation systems generally use INS position information to construct detection quantities to check the matching positioning results. However, this method cannot make effective judgments when the INS position is inaccurate. To accurately verify the correctness of the matching results under conditions of large INS position errors, this paper designs a matching result verification algorithm using the INS displacement vector as the detection quantity. This algorithm can maintain the requirement for accurate verification of positioning matching results even when the INS position is inaccurate and matching result detection based on the INS position is not possible. Summary of the Invention

[0004] To address the aforementioned shortcomings in the existing technology, this invention provides a method for verifying gravity matching results based on carrier displacement.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0006] A method for verifying gravity matching results based on carrier displacement includes the following steps:

[0007] S1. Use the gravity matching system to sample the gravity characteristic information of the current position of the aircraft and record the system time at the sampling moment;

[0008] S2. Use the particle swarm optimization algorithm to search for the best matching position of the sampling point on the map, perform two gravity matchings, output the positioning result and the system time corresponding to the aircraft passing through the sampling point, and read the navigation position information of the inertial navigation system at that moment.

[0009] S3, Construction χ 2 The detection quantity of the test is obtained by subtracting the two gravity matching results to obtain the carrier displacement vector observed by the gravity matching system, and by subtracting the two inertial navigation positions at the corresponding time to obtain the inertial navigation displacement vector.

[0010] S4. Calculate x 2 The rejection region of the test is based on the state error variance matrix P of the integrated navigation system. k Calculate the error variance of the inertial navigation displacement vector; based on the measurement noise variance R of the gravity matching system... k Calculate the error variance of the observed carrier displacement vector in the gravity matching system, based on χ. 2 The variance of the test sample and the algorithm accuracy are used to calculate the rejection region of the test.

[0011] S5. Construct statistics to perform hypothesis testing. Determine whether to accept the matching result based on whether there is a difference between the inertial navigation displacement vector and the carrier displacement vector observed by the gravity matching system.

[0012] Furthermore, the gravity feature information of the current position of the aircraft sampled in S1 is the sampling result of a single moment or multiple moments.

[0013] Furthermore, the specific method for performing two gravity matching operations in S2 using the particle swarm optimization algorithm to search for the optimal matching position of the sampling points on the map is as follows:

[0014]

[0015] In the formula, p PSO1 The position of the spacecraft, δp, is obtained for the first time through gravity matching calculation using the particle swarm optimization algorithm. PSO1 p represents the position error calculated using the particle swarm optimization algorithm in this iteration. PSO2 The spacecraft position, δp, is obtained from the second gravity matching calculation using the particle swarm optimization algorithm. PSO2 The position error is calculated by the particle swarm optimization algorithm at the current time; Δp is the navigation position information of the inertial navigation system read at the gravity matching moment. PSO This represents the displacement difference after two positioning operations in the particle swarm optimization algorithm.

[0016] Furthermore, the carrier displacement vector observed by the gravity matching system in S3 is expressed as:

[0017]

[0018] in, Δp is the displacement vector of the carrier observed by the gravity matching system, and Δp is the navigation position information of the inertial navigation system read at the moment of gravity matching.

[0019] Furthermore, the test metric in S3 is expressed as:

[0020]

[0021] Where, r k Let Δp be the displacement difference used as the test quantity. PSO Δp represents the displacement difference between two positioning operations performed by the particle swarm optimization algorithm. ins δp is the displacement vector of the carrier observed by the gravity matching system, Δp is the navigation position information of the inertial navigation system read at the gravity matching moment, and δv is the velocity error from the initial moment to the moment t0.

[0022] Furthermore, the rejection field in S4 is represented as follows:

[0023]

[0024] Among them, S k Let the displacement difference r be the rejection region. k The variance, r k Let Δp be the displacement difference used as the test quantity. PSO Δp represents the displacement difference between two positioning operations performed by the particle swarm optimization algorithm. ins σ is the displacement vector of the carrier observed by the gravity matching system, Δp is the navigation position information of the inertial navigation system read at the moment of gravity matching, and σ is the displacement vector of the carrier observed by the gravity matching system. PSO 2 P represents the variance of the localization error in the particle swarm optimization algorithm. k / k-1 For the state error variance matrix of the integrated navigation Kalman filter, H δv The expression is as follows:

[0025] H δv =[0 2×3 I 2×2 0 3×10 ].

[0026] Furthermore, S5 specifically includes the following steps:

[0027] S51. Construct a statistic and determine if the statistic matches the location correctly. If the statistic matches the location correctly, it follows the χ² pattern. 2 The distribution, when a matching error occurs, the statistic does not follow the χ² distribution. 2 distributed;

[0028] S52. Select the false alarm rate, based on χ². 2 Find the χ² function table of the distribution 2 The distribution corresponds to the critical value T of the false alarm rate.Di ;

[0029] S53. Determine the relationship between the statistic and the false alarm rate. If λ ik ≤T Di If both positioning results are correct, then the system proceeds to integrated navigation measurement update to correct the inertial navigation system position; if λ ik >T Di If the result of the PSO measurement is incorrect at least once, the process ends.

[0030] Furthermore, the S51 statistic is expressed as follows:

[0031]

[0032] Where, r k S is the test quantity. k For the rejected domain.

[0033] The present invention has the following beneficial effects:

[0034] This invention uses the inertial navigation displacement vector as the detection quantity and proposes a gravity matching result verification method based on the carrier displacement. It can meet the requirements for identifying incorrect matching results even when the initial position error of the inertial navigation is large, and the ability to identify incorrect matching results is significantly improved under the condition of inaccurate prior position information. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the gravity matching result verification method based on carrier displacement according to the present invention. Detailed Implementation

[0036] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0037] A method for verifying gravity matching results based on carrier displacement, such as... Figure 1 As shown, it includes the following steps:

[0038] S1. Use the gravity matching system to sample the gravity characteristic information of the current position of the aircraft and record the system time at the sampling moment;

[0039] The state equations and measurement equations of the integrated navigation system are as follows:

[0040]

[0041] Among them, X k X is the state vector at time k. k-1 W is the state vector at time k-1. k-1 Z is the process noise vector at time k-1. k H is the position measurement vector at time k. k Let V be the observation matrix at time k. k Let Φ be the measurement noise vector at time k. k / k-1 With Γ k / k-1 Discretization of the state equation and the noise driving matrix

[0042] Kalman filter time update to

[0043]

[0044] in, Let be the convergence value of the state vector at time k-1. Q is the one-step prediction value of the state. k-1 Let P be the covariance matrix of the system noise at time k-1. k-1 Estimate the mean square error matrix at time k-1.

[0045] Measurement updated to

[0046]

[0047] Among them, K k R is the filter gain matrix. k Let P be the covariance matrix of the noise measured at time k. k / k-1 The mean squared error matrix for one-step prediction has diagonal elements that are the variances of the state estimates, Q. k-1 Let P be the covariance matrix of the system noise at time k-1. k-1 To estimate the mean square error matrix at time k-1, P k Estimate the mean square error matrix at time k.

[0048] S2. Use the particle swarm optimization algorithm to search for the best matching position of the sampling point on the map, perform two gravity matchings, output the positioning result and the system time corresponding to the aircraft passing through the sampling point, and read the navigation position information of the inertial navigation system at that moment.

[0049] S3, Construction χ 2 The detection quantity of the test is obtained by subtracting the two gravity matching results to obtain the carrier displacement vector observed by the gravity matching system, and by subtracting the two inertial navigation positions at the corresponding time to obtain the inertial navigation displacement vector.

[0050] Based on the idea of ​​hypothesis testing, using χ² 2The verification method, which incorporates the characteristics of the gravity matching algorithm, designs a verification algorithm that uses the difference between the observed displacement vector and the inertial navigation displacement vector through the gravity matching system to verify the correctness of the matching results. The following is a derivation of the χ² method based on the displacement vector. 2 The formula for calculating the test method.

[0051] [t k t k+1 The inertial navigation displacement vector within a given time period is affected by the inertial navigation velocity error within that time period, as shown in the following formula:

[0052]

[0053] [t] k t k+1 The velocity error δv within the time period is considered a constant.

[0054]

[0055] Establish the equation:

[0056] δv k =H δv X k (5)

[0057] The variance of the velocity error is obtained by calculating the equation:

[0058] E(δv)=0

[0059]

[0060] Where P k / k-1 Given by (2).

[0061] The measurement information is obtained from each independent measurement. If both matches are correct, the measurement error follows a Gaussian distribution. The positions of the two gravity matches are p. PSO1 p PSO2 The expression is as follows:

[0062]

[0063] In the formula, p PSO1 The position of the spacecraft, δp, is obtained for the first time through gravity matching calculation using the particle swarm optimization algorithm. PSO1 p represents the position error calculated using the particle swarm optimization algorithm in this iteration. PSO2 The spacecraft position, δp, is obtained from the second gravity matching calculation using the particle swarm optimization algorithm. PSO2 The position error is calculated by the particle swarm optimization algorithm at the current time; Δp is the navigation position information of the inertial navigation system read at the gravity matching moment. PSO This represents the displacement difference after two positioning operations in the particle swarm optimization algorithm.

[0064] The mean and variance are the errors:

[0065]

[0066] Where, σ PSO 2 This represents the variance of the localization error in the matching algorithm.

[0067] When performing fault diagnosis, the PSO algorithm needs to perform two matching localizations, record the inertial navigation system (INS) position at the two localization times, and calculate the displacement vectors of the two PSO matching localizations. The INS position at the corresponding time is recorded, and the displacement vectors are calculated.

[0068] Displacement difference is

[0069]

[0070] Where, r k Let Δp be the displacement difference used as the test quantity. PSO Δp represents the displacement difference between two positioning operations performed by the particle swarm optimization algorithm. ins δp is the displacement vector of the carrier observed by the gravity matching system, Δp is the navigation position information of the inertial navigation system read at the gravity matching moment, and δv is the velocity error from the initial moment to the moment t0.

[0071] S4. Calculate χ 2 The rejection region of the test is based on the state error variance matrix P of the integrated navigation system. k Calculate the error variance of the inertial navigation displacement vector; based on the measurement noise variance R of the gravity matching system... k Calculate the error variance of the observed carrier displacement vector in the gravity matching system, based on χ. 2 The variance of the test sample and the algorithm accuracy are used to calculate the rejection region of the test.

[0072] S k Displacement difference r k The variance can be estimated using information from the integrated navigation system (including P). k / k -1 and R k )S k Equations (6) and (8) combined yield the following:

[0073]

[0074] S5. Construct statistics to perform hypothesis testing. Determine whether to accept the matching result based on whether there is a difference between the inertial navigation displacement vector and the carrier displacement vector observed by the gravity matching system.

[0075] Statistic λ ik It can be constructed using equation (11):

[0076]

[0077] Where, r k S is the test quantity. k For the rejected domain.

[0078] Statistic λ ik When the match is correct, it follows the χ² pattern. 2 Distribution, when a matching error occurs, the statistic λ ik Disobedience χ 2 distributed.

[0079] Next, select an appropriate false alarm rate P. FA Then according to χ 2 Find the χ² function table of the distribution 2 Distribution corresponding to P FA The critical value T Di T Di This refers to the threshold of the statistic, and the determination criteria are as follows:

[0080] If λ ik ≤T Di If both positioning results are correct, the system will proceed to integrated navigation measurement update and the position of the inertial navigation system will be corrected.

[0081] If λ ik >T Di If the result of the PSO measurement is incorrect at least once, the process ends.

[0082] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0083] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0084] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0085] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0086] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for checking the result of gravity matching based on carrier displacement, characterized in that, Includes the following steps: S1. Use the gravity matching system to sample the gravity characteristic information of the current position of the aircraft and record the system time at the sampling moment; S2. Using the particle swarm optimization algorithm, search for the optimal matching position of the sampling point on the map and perform two gravity matches. Output the positioning result and the system time corresponding to the aircraft passing through the sampling point. Read the navigation position information of the inertial navigation system at the time of gravity match. The specific method of using the particle swarm optimization algorithm to search for the optimal matching position of the sampling point on the map and perform two gravity matches is as follows: wherein, is the position of the vehicle calculated by the first time through the particle swarm algorithm for gravity matching, is the position error when the particle swarm algorithm is calculated this time; is the position of the vehicle calculated by the second time through the particle swarm algorithm for gravity matching, is the position error when the particle swarm algorithm is calculated this time; is the navigation position information of the inertial navigation system read at the gravity matching moment, is the displacement difference of the particle swarm algorithm after two times of positioning; S3, Construction The measured quantity for verification is obtained by subtracting the two gravity matching results to obtain the carrier displacement vector observed by the gravity matching system, and simultaneously by subtracting the two inertial navigation positions at the corresponding time to obtain the inertial navigation displacement vector. The detection volume is expressed as: in, The displacement difference is used as the measured quantity. This represents the displacement difference after two positioning operations in the particle swarm optimization algorithm. The displacement vector of the carrier observed by the gravity matching system. This refers to the navigation position information of the inertial navigation system read at the moment of gravity matching. From the initial time to t Velocity error at time 0; The displacement vector of the carrier observed by the gravity matching system is expressed as: in, The displacement vector of the carrier observed by the gravity matching system. The navigation position information of the inertial navigation system read at the moment of gravity matching; S4, Calculation The rejection region of the test is based on the state error variance matrix of the integrated navigation system. Calculate the error variance of the inertial navigation displacement vector; based on the measurement noise variance of the gravity matching system. Calculate the error variance of the observed carrier displacement vector in the gravity matching system, based on... The rejection region of the test is calculated from the variance of the test sample and the accuracy of the algorithm. The rejection region is expressed as: in, The displacement difference serves as the rejection region. variance The displacement difference is used as the test quantity. This represents the displacement difference after two positioning operations in the particle swarm optimization algorithm. The displacement vector of the carrier observed by the gravity matching system. This refers to the navigation position information of the inertial navigation system read at the moment of gravity matching. Let V be the variance of the localization error in the particle swarm optimization algorithm, where... The variance matrix of the state error of the integrated navigation Kalman filter. The expression is as follows: ； S5. Construct statistics to perform hypothesis testing. Determine whether to accept the matching result based on whether there is a difference between the inertial navigation displacement vector and the carrier displacement vector observed by the gravity matching system.

2. The gravity matching result verification method based on carrier displacement according to claim 1, characterized in that, The gravity feature information of the current position of the aircraft sampled in S1 is the sampling result at a single moment or multiple moments.

3. The gravity matching result verification method based on carrier displacement according to claim 1, characterized in that, S5 specifically includes the following steps: S51. Construct a statistic and determine whether the statistic matches the location correctly. If the statistic matches the location correctly, it follows the order of... The distribution, when a matching error occurs, the statistic does not follow a certain pattern. distributed; S52. Select the false alarm rate, based on... Find the function table of the distribution The distribution corresponds to the critical value of the false alarm rate. ; S53. Determine the relationship between the statistic and the false alarm rate. If both positioning results are correct, the system proceeds to integrated navigation measurement update to correct the inertial navigation system position; if... If the result of the PSO measurement is incorrect at least once, the process ends.

4. The gravity matching result verification method based on carrier displacement according to claim 3, characterized in that, The S51 statistic is expressed as follows: in, For testing purposes, For the rejected domain.

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