A Pseudo-Satellite Indoor Positioning Optimization Method Based on Ergodic Robust Kalman Filtering

Abstract

This invention discloses a pseudo-satellite indoor positioning optimization method based on ergonomic robust Kalman filtering, comprising the following steps: obtaining the initial positions of all positioning base stations; setting the verification information parameters in the ergonomic robust Kalman filter model; obtaining positioning route data passing through the initial positions of all positioning base stations; inputting the positioning route data into the ergonomic robust Kalman filter model for processing to obtain the optimized positions of the positioning base stations; obtaining the optimal verification information value by comparing the optimized positions with the initial positions; setting the optimal verification information value as the model verification information for this positioning, and starting the positioning process. This invention combines the idea of ​​the ergonomic algorithm with the robust Kalman filter algorithm, thereby effectively solving the problem of ensuring the optimality of verification information in the robust Kalman filter algorithm model during actual positioning, thus further improving the accuracy of the algorithm and obtaining a better filtering effect.

Description

Technical Field

[0001] This invention relates to the field of pseudosatellite system positioning technology, and more specifically, to a pseudosatellite indoor positioning optimization method based on ergodic robust Kalman filtering. Background Technology

[0002] In recent years, with the development of wireless communication technology and the continuous enhancement of mobile terminal device performance, users have increasingly higher demands for location-based services (LBS). However, due to multipath effects, signal blockage, and other reasons, the Global Navigation Satellite System (GNSS) cannot provide stable and high-precision positioning services in indoor environments.

[0003] A pseudosatellite (PL) is a positioning device installed on the ground that generates and transmits navigation signals similar to GNSS. Because it does not have ionospheric and tropospheric errors when performing indoor positioning, a pseudosatellite can be used as a supplement to GNSS to solve the problem of low positioning accuracy of GNSS in enclosed indoor environments.

[0004] Pseudo-satellites offer advantages such as flexible placement, convenient maintenance, and low cost. However, in indoor measurements, due to the close proximity of the pseudo-satellite to the receiver, pseudo-satellite positioning suffers from more severe multipath effects than outdoors, accompanied by significant noise. Therefore, reducing the errors in indoor pseudo-satellite positioning has become a hot topic in the positioning and navigation field in recent years.

[0005] Therefore, this invention proposes a pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering. Summary of the Invention

[0006] To address the problems in related technologies, this invention proposes a pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering, in order to overcome the aforementioned technical problems existing in the existing related technologies.

[0007] Therefore, the specific technical solution adopted by the present invention is as follows:

[0008] A pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering includes the following steps:

[0009] S1. Obtain the initial positions of all positioning base stations using measurement techniques;

[0010] S2. Set the verification information parameters in the robust Kalman filter model;

[0011] S3. Obtain the positioning route data that passes through the initial positions of all positioning base stations;

[0012] S4. Input the positioning route data into the traversal robust Kalman filter model for processing to obtain the optimized location of the positioning base station;

[0013] S5. The optimal verification information value is obtained by comparing the optimized position with the initial position using the positioning base station;

[0014] S6. Set the optimal verification information value as the model verification information for this positioning and start positioning.

[0015] Furthermore, the verification information parameters include the overall range of the verification information and the step size of each update of the robust Kalman filter model.

[0016] Furthermore, obtaining positioning route data passing through the initial positions of all positioning base stations also includes the following steps: determining the state equation and observation equation based on the observation data.

[0017] Furthermore, the state equation is:

[0018] x k =Ax k-1 +ω k

[0019] In the formula, ω k Let A represent the state noise vector, and let A be an n×n dimensional state transition matrix. k Indicates the current state, x k-1 Indicates the state at the previous moment;

[0020] Let the state noise vector ω k Satisfy p(ω) k )~(0 ω ,Q), where p(ω) k ) represents the state noise vector ω k The probability distribution, 0 ω For ω k The expectation, Q is ω k The covariance matrix, where E represents the identity matrix and T represents the transpose, is:

[0021] Q = E[ω] k ω k T ].

[0022] Furthermore, the observation equation Z k for:

[0023] z k =Hx k +v k

[0024] In the formula, v k H represents the observation noise vector, and H represents the coefficient matrix of the observation equation at time k.

[0025] Let the state noise vector v k Satisfy p(ν) k )~(0 v ,R), where p(ν) k ) represents the observation noise vector v k The probability distribution, 0 v For v k The expectation, R is v k The covariance matrix, i.e.:

[0026] R = E[ν k ν k T ].

[0027] Furthermore, the location route data is input into a robust Kalman filter model for processing, which includes two steps: prediction and updating.

[0028] Furthermore, the prediction formula is as follows:

[0029]

[0030] P k - =AP k-1 A T +Q

[0031] In the formula, This represents the predicted value for the next step in state k. P represents the optimal estimate in state k-1. k - P represents the covariance matrix corresponding to state k. k-1 Let represent the verified covariance matrix in state k-1.

[0032] Furthermore, the updated formula is:

[0033] K k =P k - H T HP k - H T +R) -1

[0034]

[0035] P k = (1-K) k H)P k -

[0036] In the formula, K k This represents the Kalman filter gain matrix. Let y represent the optimal estimate. k P represents the measurement value at time k. k This represents the corrected covariance matrix.

[0037] Furthermore, the process of inputting the location route data into the traversal robust Kalman filter model for processing also includes the following steps:

[0038] Calculate the observation weight factor residual u of the observation noise vector residual. k ,in, Covariance matrix φ = HP k - H T ;

[0039] Let the verification information △u k =u k T φ -1 u k And calculate the equivalent weight, where the formula for calculating the equivalent weight is:

[0040]

[0041] In the formula, a represents the equivalent weight, and c represents a constant with a value of 1.5;

[0042] Replace v in the Kalman filter with R / a k The covariance matrix R.

[0043] Furthermore, obtaining the optimal verification information value by comparing the optimized location with the initial location using the positioning base station includes the following steps:

[0044] S51. Compare the optimized position of the positioning base station with the initial position of the positioning base station;

[0045] S52. Using the standard deviation on the XY plane as the evaluation criterion, calculate the error between the optimized position and the initial position;

[0046] S52. The verification information value with the smallest error is taken as the optimal verification information value.

[0047] This invention compares the positioning data when the route passes a base station with the corresponding initial coordinates of the base station to determine the accuracy of different verification information. The basis for determining the accuracy is the absolute value of the difference between the positioning data and the initial coordinates in the X-axis and Y-axis directions.

[0048] The beneficial effects of this invention are as follows:

[0049] 1) By measuring the initial coordinates of all positioning base stations and setting a route that passes through all positioning base stations, the positioning data when passing through the base stations is compared with the corresponding initial coordinates of the base stations. The verification information value with the smallest error value is obtained and set as the verification information for this positioning. This can improve the accuracy of the initial position, improve the longitude of the pseudo-satellite indoor positioning, and thus provide a more accurate pseudo-satellite positioning position, obtain more accurate positioning data, and improve the indoor positioning accuracy.

[0050] 2) This invention combines the idea of ​​traversal algorithm with robust Kalman filter algorithm, which can effectively solve the problem of difficulty in ensuring the optimality of test information in robust Kalman filter algorithm model in actual positioning process, thereby further improving the accuracy of algorithm and obtaining better filtering effect. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a flowchart of a pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to an embodiment of the present invention;

[0053] Figure 2 This is a motion trajectory diagram on the XY plane obtained in a pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to an embodiment of the present invention;

[0054] Figure 3 This is a comparison chart of standard deviations on the XY plane obtained in a pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to an embodiment of the present invention. Detailed Implementation

[0055] To further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. These drawings are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementation methods and the advantages of the present invention. The components in the drawings are not drawn to scale, and similar component symbols are generally used to represent similar components.

[0056] According to an embodiment of the present invention, a pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering is provided.

[0057] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figures 1-3 As shown, according to an embodiment of the present invention, a pseudo-satellite indoor positioning optimization algorithm based on ergodic robust Kalman filtering includes the following steps:

[0058] S1. Obtain the initial positions of all positioning base stations using measurement techniques;

[0059] Specifically, before positioning begins, the initial positions of all positioning base stations are obtained through measurement technology.

[0060] S2. Set the verification information parameters in the robust Kalman filter model;

[0061] The verification information parameters include the overall range of the verification information and the step size of each update of the robust Kalman filter model.

[0062] S3. Obtain the positioning route data that passes through the initial positions of all positioning base stations;

[0063] Specifically, a set of location route data is obtained, and the route must pass through the initial positions of all base stations in order to facilitate the later selection of the optimal verification information.

[0064] In addition, obtaining positioning route data that passes through the initial positions of all positioning base stations also includes the following steps: determining the state equation and observation equation based on the positioning route data.

[0065] Specifically, the state equation is:

[0066] x k =Ax k-1 +ω k

[0067] In the formula, ω k Let A represent the state noise vector, and let A be an n×n dimensional state transition matrix. k Indicates the current state, x k-1 Indicates the state at the previous moment;

[0068] Let the state noise vector ω k Satisfy p(ω) k )~(0 ω ,Q), where p(ω) k ) represents the state noise vector ω k The probability distribution, 0 ω For ω k The expectation, Q is ω k The covariance matrix, where E represents the identity matrix and T represents the transpose, is:

[0069] Q = E[ω] k ω kT ].

[0070] Observation equation Z k for:

[0071] z k =Hx k +v k

[0072] In the formula, v k H represents the observation noise vector, and H represents the coefficient matrix of the observation equation at time k.

[0073] Let the state noise vector v k Satisfy p(ν) k )~(0 v ,R), where p(ν) k ) represents the observation noise vector v k The probability distribution, 0 v For v k The expectation, R is v k The covariance matrix, i.e.:

[0074] R = E[ν k ν k T ].

[0075] S4. Input the positioning route data into the traversal robust Kalman filter model for processing to obtain the optimized location of the positioning base station;

[0076] The process of inputting the location route data into a robust Kalman filter model for processing includes two steps: prediction and updating.

[0077] Specifically, the prediction steps are as follows:

[0078]

[0079] P k - =AP k-1 A T +Q

[0080] In the formula, This represents the predicted value for the next step in state k. P represents the optimal estimate in state k-1. k - Let P represent the covariance matrix corresponding to state k. k-1 Let represent the verified covariance matrix in state k-1.

[0081] The update steps are as follows:

[0082] K k =P k- H T HP k - H T +R) -1

[0083]

[0084] P k = (1-K) k H)P k -

[0085] In the formula, K k This represents the Kalman filter gain matrix. Let y represent the optimal estimate. k P represents the measurement value at time k. k This represents the corrected covariance matrix.

[0086] For the observation equation z k =Hx k +v k Let be the observation noise vector. It is generally assumed that the observations are independent and of equal precision, and their weight matrix is ​​set to the identity matrix. However, this is not the case in actual observations; the actual observations are not of equal precision and may be affected by field errors. To control these effects, the weight factor residuals u of the observations can be calculated from the residuals of the observation noise vector. k ,in, Covariance matrix φ = HP k - H T ;

[0087] Let the verification information △u k =u k T φ -1 u k And calculate the equivalent weight, where the formula for calculating the equivalent weight is:

[0088]

[0089] In the formula, a represents the equivalent weight, and c represents a constant, which should be determined according to the specific problem. In this embodiment, it is taken as 1.5.

[0090] Replace v in the Kalman filter with R / a k The covariance matrix R.

[0091] S5. The optimal verification information value is obtained by comparing the optimized position with the initial position using the positioning base station;

[0092] The process of obtaining the optimal verification information value by comparing the optimized location with the initial location using the positioning base station includes the following steps:

[0093] S51. Compare the optimized position of the positioning base station with the initial position of the positioning base station;

[0094] S52. Using the standard deviation on the XY plane as the evaluation criterion, calculate the error between the optimized position and the initial position;

[0095] S52. The verification information value with the smallest error is taken as the optimal verification information value.

[0096] S6. Set the optimal verification information value as the model verification information for this positioning and start positioning.

[0097] In this embodiment, the positioning data is fed into the algorithm model. Based on the step size, the optimized position of the positioning base station is obtained after optimization through various verification information. Each optimized position is compared with the measured initial position. The standard deviation on the XY plane is used as the evaluation standard. The optimal verification information value is obtained through comparison and set as the model verification information for this positioning.

[0098] The algorithm proposed in this invention was simulated and tested using Matlab software. The initial position of the receiver was set to (0, 0). Relevant code was written to obtain the motion trajectory data of the receiver (which was used as the true positioning value), and several data points were randomly selected as the true position of the positioning base station. A certain amount of error was artificially added, and the data after adding the error was recorded as the measured value. The measured value was substituted into the algorithm model, and the optimized value obtained after optimization through various verification information was obtained according to the step size. The true position of the receiver was compared with its corresponding optimized position, and the standard deviation on the XY plane was used as the evaluation standard. The optimal verification information value was obtained by comparison and set as the model verification information for this positioning. Finally, the positioning began.

[0099] In summary, by utilizing the above-mentioned technical solution of the present invention, the initial coordinates of all positioning base stations are obtained by measurement, and a route is set to pass through all positioning base stations. The positioning data when passing through the base stations is compared with the corresponding initial coordinates of the base stations to obtain the verification information value with the smallest error value. This value is then set as the verification information for this positioning, thereby improving the accuracy of the initial position, increasing the longitude of the pseudo-satellite indoor positioning, and thus providing a more accurate pseudo-satellite positioning position, obtaining more accurate positioning data, and improving indoor positioning accuracy.

[0100] Furthermore, by combining the idea of ​​traversal algorithm with robust Kalman filter algorithm, this invention can effectively solve the problem of difficulty in ensuring the optimality of test information in robust Kalman filter algorithm model during actual positioning process, thereby further improving the accuracy of the algorithm and obtaining better filtering effect.

[0101] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering, characterized in that, The pseudo-satellite indoor positioning optimization method includes the following steps: S1. Obtain the initial positions of all positioning base stations using measurement techniques; S2. Set the verification information parameters in the robust Kalman filter model; S3. Obtain the positioning route data that passes through the initial positions of all positioning base stations; S4. Input the positioning route data into a robust Kalman filter model for processing to obtain the optimized location of the positioning base station; S5. The optimal verification information value is obtained by comparing the optimized position with the initial position using the positioning base station; S6. Set the optimal verification information value as the model verification information for this positioning and start positioning.

2. The pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to claim 1, characterized in that, The verification information parameters include the overall range of the verification information and the step size of each update of the robust Kalman filter model.

3. The pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to claim 1, characterized in that, The method of obtaining positioning route data passing through the initial positions of all positioning base stations also includes the following steps: determining the state equation and observation equation based on the observation data.

4. The pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to claim 3, characterized in that, The state equation is: x k =Ax k-1 +ω k In the formula, ω k Let A represent the state noise vector, and let A be an n×n dimensional state transition matrix. k Indicates the current state, x k-1 Indicates the state at the previous moment; Let the state noise vector ω k Satisfy p(ω) k )~(0 ω ,Q), where p(ω) k ) represents the state noise vector ω k The probability distribution, 0 ω For ω k The expectation, Q is ω k The covariance matrix, where E represents the identity matrix and T represents the transpose, is: Q=E[ω k oh k T ]。 5. The pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to claim 4, characterized in that, The observation equation Z k for: z k =Hx k +v k In the formula, v k H represents the observation noise vector, and H represents the coefficient matrix of the observation equation at time k. Let the state noise vector v k Satisfy p(ν) k )~(0 v ,R), where p(ν) k ) represents the observation noise vector v k The probability distribution, 0 v For v k The expectation, R is v k The covariance matrix, i.e.: R=E[ν k n k T ]。 6. The pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to claim 5, characterized in that, The process of inputting the positioning route data into a robust Kalman filter model includes two steps: prediction and updating.

7. The pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to claim 6, characterized in that, The formula for prediction is: In the formula, This represents the predicted value at time k. P represents the optimal estimate at time k-1. k - Let P represent the covariance matrix at time k. k-1 Let represent the post-calibration covariance matrix at time k-1.

8. The pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to claim 7, characterized in that, The updated formula is: K k =P k - H T (HP k - H T +R) -1 In the formula, K k This represents the Kalman filter gain matrix. Let y represent the optimal estimate. k P represents the measurement value at time k. k This represents the corrected covariance matrix.

9. A pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to claim 8, characterized in that, The step of inputting the positioning route data into a robust Kalman filter model for processing also includes the following steps: Calculate the observation weight factor residual u of the observation noise vector residual. k ,in, Covariance matrix φ = HP k - H T ; Let the verification information △u k =u k T φ -1 u k And calculate the equivalent weight, where the formula for calculating the equivalent weight is: In the formula, a represents the equivalent weight, and c represents a constant with a value of 1.5; Replace v in the Kalman filter with R / a k The covariance matrix R.

10. The pseudo-satellite indoor positioning optimization method based on ergodic robust Kalman filtering according to claim 1, characterized in that, The process of obtaining the optimal verification information value by comparing the optimized location with the initial location using the positioning base station includes the following steps: S51. Compare the optimized position of the positioning base station with the initial position of the positioning base station; S52. Using the standard deviation on the XY plane as the evaluation criterion, calculate the error between the optimized position and the initial position; S52. The verification information value with the smallest error is taken as the optimal verification information value.

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