GNSS adaptive positioning method based on sliding window self-tuning

Abstract

The invention belongs to the technical field of adaptive positioning, and discloses an adaptive positioning method based on GNSS sliding window self-tuning. The method comprises the following steps: firstly, acquiring a GNSS positioning result coordinate as a data input source of GNSS adaptive positioning based on sliding window self-tuning; then, a sliding window with a fixed size is arranged in front of a current epoch of real-time Kalman filtering, and GNSS positioning results in the window are divided into a test set and a verification set to serve as observation values of self-tuning Kalman smoothing; an automatic tuning Kalman smoothing problem is converted into a constrained least square problem, and a non-convex optimization algorithm is adopted for solving; and finally, iteratively solving hyper-parameters by adopting a near-end gradient descent method, and transmitting an optimal solution to real-time Kalman filtering to obtain an optimal positioning result estimated value. According to the method, the problem that the statistical characteristics of the process noise variance matrix and the observation noise variance matrix in Kalman filtering are difficult to determine is solved, and the positioning precision can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of adaptive positioning technology, and in particular to an adaptive positioning method of a global navigation satellite system based on sliding window self-tuning. Background Art

[0002] Adaptive navigation and positioning is a technical means to obtain and process data from carrier sensors and receivers, accurately identify the carrier's position and navigation. It estimates and predicts the displacement of the carrier, triggers an early warning signal when a serious deviation occurs, and provides a basis and guidance for carrier movement route planning and real-time navigation.

[0003] In recent decades, GNSS has become one of the main means of adaptive navigation and positioning. With the popularization of GNSS, adaptive dynamic navigation and positioning can achieve real-time positioning, navigation and path planning. The advantages of GNSS-based adaptive dynamic navigation and positioning include high accuracy, no weather influence, strong real-time performance, strong anti-interference ability, etc. There have been many studies on how to use GNSS observation data to estimate the dynamic displacement of the carrier. Compared with traditional navigation and positioning methods, GNSS-based dynamic navigation and positioning can meet the needs of real-time navigation, dynamic path planning, etc.

[0004] At present, most GNSS-based adaptive positioning algorithms are based on Kalman filtering and its variants. However, when GNSS signals encounter multipath effects, signal obstruction, and changes in the application scenarios and the surrounding environment of the carrier, both process noise and observation noise will change. How to accurately describe the statistical characteristics of process noise and observation noise remains an urgent problem to be solved. Summary of the invention

[0005] The present invention provides a GNSS adaptive positioning method based on sliding window self-tuning, thereby realizing adaptive estimation of process noise and observation noise and improving the positioning accuracy of GNSS.

[0006] The present invention provides a GNSS adaptive positioning method based on sliding window self-tuning, comprising the following steps:

[0007] Step 1: Obtain the coordinates of the GNSS positioning results and obtain the observation values ​​that meet the filter model as the data input source of the real-time Kalman filter;

[0008] Step 2: Set a sliding window of fixed size before the current epoch of the Kalman filter, and divide the GNSS positioning results in the window into a test set and a validation set as observation values ​​for the self-tuning Kalman smoothing;

[0009] Step 3: Use self-tuning Kalman smoothing to convert the self-tuning problem into a non-convex optimization problem, set the hyperparameter items, and use the non-convex optimization algorithm to solve the optimal solution of the hyperparameters;

[0010] Step 4: Pass the optimal solution of the hyperparameters to the real-time Kalman filter as the parameter input value of the current epoch in the filter model.

[0011] Preferably, in step 2, the original coordinates obtained by GNSS positioning are as follows:

[0012] [..., x I-n , ..., x I-1 , x I ]

[0013] Where I is the epoch, n is the size of the sliding window, x I is the original GNSS positioning result of the current epoch. The positioning results of n epochs before the current epoch are used as the observation values ​​of the self-tuning Kalman smoothing, and are divided into a training set S and a validation set T.

[0014] Preferably, in step 3, in order to achieve automatic adjustment and optimization of the Kalman smoothing parameters, the Kalman smoothing problem is constructed as the following constrained least squares problem:

[0015]

[0016] Where k is the epoch, is the state estimation vector, F(k) is the state transfer matrix, and W is the process noise variance matrix; z(i) is the estimated value and observed value, H(k) is the design matrix, V is the observation noise variance matrix, and κ is the effective observation value. In order to solve the multi-objective Kalman smoothing problem, the problem is superimposed as a single-objective problem.

[0017]

[0018] in According to the estimated parameter q and the existing observation data, B and c can be reconstructed. The process noise variance matrix W and the observation noise variance matrix V are automatically adjusted and optimized as hyperparameters θ

[0019] θ=(W -1 / 2 , V -1 / 2 )

[0020] Preferably, in step 3, the observed data is divided into a training set S and a test set T to automatically optimize the parameter θ, and the observed data in the training set S is used to solve the following formula:

[0021]

[0022] Then we get the smoothed value of the data corresponding to the epoch in the test set T, and use the following objective function to evaluate

[0023] min F(θ)=L(θ)+r(θ)

[0024] Among them, F(θ) is the objective function, is the prediction error, r(θ) is the regularization term; the self-tuning Kalman smoothing problem is transformed into a non-convex optimization problem, and the proximal gradient descent method is used to iteratively solve the hyperparameter θ to minimize the objective function

[0025]

[0026] Where k is the number of iterations, t k is the step length, prox is the proximal operator, is the derivative of the prediction error L(θ) with respect to the hyperparameter θ.

[0027] Preferably, in step 4, the proximal gradient descent method iteratively solves the optimal solution of the hyperparameter θ as the parameter of the real-time Kalman filter, passes the optimal solution of the process noise variance to the prediction part of the filtering model, and passes the optimal solution of the observation noise variance to the update part of the filtering model to solve the optimal positioning result estimate.

[0028] In the invention, the coordinates of the GNSS positioning result are first obtained to obtain the observation value that meets the filter model as the input source of the real-time Kalman filter; then, a sliding window of a certain size is set before the current epoch, and the GNSS positioning result in the window is used as the observation value of the self-tuning Kalman smoothing model; then, the self-tuning Kalman smoothing is used to convert the problem into a non-convex optimization problem, and the proximal gradient descent method is used to iteratively solve the local optimal solution of the hyperparameter; finally, the optimal solution of the hyperparameter is passed to the real-time Kalman filter to obtain the optimal state estimation. The present invention can effectively estimate the adaptive positioning result and can effectively improve the positioning accuracy of GNSS. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A schematic diagram of a flow chart of a GNSS adaptive positioning method based on sliding window self-tuning provided by an embodiment of the present invention;

[0030] Figure 2 A schematic diagram of simulation data of linear motion positioning results of a GNSS adaptive positioning method based on sliding window self-tuning provided in an embodiment of the present invention;

[0031] Figure 3 A schematic diagram of simulation data of nonlinear motion positioning results of a GNSS adaptive positioning method based on sliding window self-tuning provided in an embodiment of the present invention;

[0032] Figure 4 A schematic diagram of the time-coordinate component and time-error of the simulated linear motion positioning of the GNSS adaptive positioning method based on sliding window self-tuning provided by an embodiment of the present invention;

[0033] Figure 5 A schematic diagram of the time-coordinate component and time-error of the simulated nonlinear motion positioning of the GNSS adaptive positioning method based on sliding window self-tuning provided by an embodiment of the present invention;

[0034] Figure 6 A schematic diagram of positioning data in a field experiment of a GNSS adaptive positioning method based on sliding window self-tuning provided in an embodiment of the present invention.

[0035] Figure 7 A comparison diagram of the time-coordinate component and the time-positioning result estimation error in a field experiment of the GNSS adaptive positioning method based on sliding window self-tuning provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention aims to explore a GNSS adaptive positioning method based on sliding window self-tuning, divides the observation data set in the sliding window into a training set and a validation set, automatically adjusts and optimizes the hyperparameters of Kalman smoothing by the proximal gradient descent method, and then uses the tuned hyperparameters as the parameter input values ​​of the real-time Kalman filter to estimate the positioning result.

[0037] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0038] This embodiment provides a GNSS adaptive positioning method based on sliding window self-tuning, which mainly includes the following steps:

[0039] Step 1: Obtain the coordinates of the GNSS positioning results and obtain the observation values ​​that meet the filter model as the data input source for the real-time Kalman filter.

[0040] Step 2: Set a fixed-size sliding window before the current epoch of the Kalman filter, and divide the GNSS positioning results in the window into a test set and a validation set as observations for self-tuning Kalman smoothing. Specifically, the sliding window method is used to construct Kalman smoothing observations. The component time of the coordinates obtained by GNSS positioning is as follows

[0041] [..., x I-n , ..., x I-1 , x I ]

[0042] Where I is the epoch, n is the size of the sliding window, x I is the original GNSS positioning result of the current epoch. The positioning results of n epochs before the current epoch are used as the observation values ​​of the self-tuning Kalman smoothing, and are divided into a training set S and a validation set T.

[0043] Step 3: Use self-tuning Kalman smoothing to convert the problem into a non-convex optimization problem, and use the proximal gradient descent method to iteratively solve the optimal solution for the hyperparameters. Specifically, in order to achieve automatic tuning of the Kalman smoothing hyperparameters, the Kalman smoothing problem is constructed as the following constrained least squares problem.

[0044]

[0045] Where k is the epoch, is the state estimation vector, F(k) is the state transfer matrix, and W is the process noise variance matrix; z(i) are the estimated value and observed value respectively, H(k) is the design matrix, V is the observation noise variance matrix, and κ is the effective observation value; in order to solve the multi-objective Kalman smoothing problem, the problem is superimposed as a single-objective problem.

[0046]

[0047] in According to the estimated parameter q and the existing observation data, B and c can be reconstructed. The process noise variance matrix W and the observation noise variance matrix V are automatically adjusted and optimized as hyperparameters θ

[0048] θ=(W -1 / 2 , V -1 / 2 )

[0049] The present invention is further described below.

[0050] See also Figure 1 , a GNSS adaptive positioning method based on sliding window self-tuning provided in this embodiment mainly includes the following steps: obtaining GNSS positioning results, dividing the positioning results into a training set and a validation set, using non-convex optimization to obtain the optimal solution of Kalman smoothing hyperparameters, and using the optimized hyperparameters as the initial value of the real-time Kalman filter to obtain the optimal positioning estimate.

[0051] Several main parts of this embodiment are explained below.

[0052] 1.1 Sliding Window Settings

[0053] Acquire the coordinates of the GNSS positioning results and obtain observations that conform to the filtering model as the data input source for GNSS adaptive positioning based on sliding window self-tuning; then, set a sliding window of fixed size before the current epoch of the real-time Kalman filter, and divide the GNSS positioning results in the window into a test set and a verification set as observations for self-tuning Kalman smoothing. The observations may include non-model errors, such as multipath, atmospheric delay residuals, or positioning offsets caused by external factors such as atmospheric refraction and tree shade. In order to reduce the impact of the information of the previous epoch in the filtering model on the process noise variance matrix and the observation noise variance matrix of the current epoch, the present invention uses a sliding window to determine the two noise matrices. The original coordinates obtained by the above GNSS positioning are as follows:

[0054] [..., x I-n , ..., x I-1 , x I ]

[0055] Where I is the epoch, n is the size of the sliding window, x I is the original GNSS positioning result of the current epoch. The positioning results of n epochs before the current epoch are used as the observation values ​​of the self-tuning Kalman smoothing, and are divided into a training set S and a validation set T.

[0056] 1.2 Self-tuning Kalman smoothing

[0057] Compared with the traditional Kalman filter, the Kalman smoothing model can estimate the state more accurately. However, it is still necessary to manually adjust the hyperparameters in the smoothing model. In order to achieve self-tuning of Kalman smoothing parameters, the Kalman smoothing problem is reconstructed as the following constrained least squares problem.

[0058]

[0059] Where k is the epoch, is the state estimation vector, F(k) is the state transfer matrix, and W is the process noise variance matrix; z(i) are the estimated value and observed value respectively, H(k) is the design matrix, V is the observation noise variance matrix, and κ is the effective observation value; in order to solve the multi-objective Kalman smoothing problem, the problem is superimposed as a single-objective problem.

[0060]

[0061] in Based on the estimated parameter q and the existing observation data, B and c can be reconstructed; and

[0062]

[0063] in, so The optimization condition is

[0064]

[0065] Where η is the dual variable of the equality constraint. On the above training set S and test set T, the process noise variance matrix W and the observation noise variance matrix V in the least squares problem with constraints are used as hyperparameters θ, and a non-convex optimization algorithm is used to iteratively solve and automatically adjust the optimization.

[0066] θ=(W -1 / 2 , V -1 / 2 )

[0067] In Kalman smoothing, the hyperparameter θ is the key. The observed data is divided into a training set S and a test set T to automatically optimize the parameter θ. Using the training data set S, by solving Get the observed smoothed value corresponding to each epoch in the test set T. Then use the test set T to evaluate the quality of the smoothing model using the following objective function.

[0068] min F(θ)=L(θ)+r(θ)

[0069] Among them, F(θ) is the objective function, is the prediction error, r(θ) is the regularization term; the self-tuning Kalman smoothing problem is transformed into a non-convex optimization problem, and the proximal gradient descent method is used to iteratively solve the hyperparameter θ to minimize the objective function

[0070]

[0071] Where k is the number of iterations, t k is the step length, prox is the proximal operator, is the derivative of the prediction error L(θ) with respect to the hyperparameter θ.

[0072] The proximal gradient descent method iteratively solves the optimal solution of the hyperparameter θ as the parameter of the real-time Kalman filter, passes the optimal solution of the process noise variance to the prediction part of the filter model, and passes the optimal solution of the observation noise variance to the update part of the filter model to solve the optimal positioning result estimation.

[0073] In order to verify the effect of the present invention, the following is a description in conjunction with experimental results.

[0074] According to the requirements, the present invention designs simulation experiments and field experiments. The results of both simulation experiments and field experiments show that the adaptive positioning effect of self-tuning Kalman smoothing is better than other methods. The simulation experiment results are as follows Figure 4 and Figure 5As shown, the positioning result estimated by the method adopted by the present invention is closer to the reference positioning result, and the positioning error is minimal. After statistical comparison, in terms of mean square error (RMS), the Kalman filter in the linear motion simulation experiment improved by 58.96% compared with the original observation, and the sliding window self-tuning Kalman filter improved by 49.68% compared with the Kalman filter; in the nonlinear motion simulation experiment, the Kalman filter improved by 41.48% compared with the original observation, and the sliding window self-tuning Kalman filter improved by 18.69% compared with the Kalman filter. In addition, the field experiment results are as follows Figure 6 As shown in the figure, the adaptive positioning estimation result of the sliding window self-tuning Kalman smoothing has the best fitting effect with the reference positioning result. After statistical comparison, in terms of mean square error (RMS), the Kalman filter in the field experiment improved by 11.57% compared with the original observation, and the sliding window self-tuning Kalman filter improved by 4.00% compared with the Kalman filter.

[0075] Finally, it should be noted that the above specific implementation methods are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to examples, a person of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the present invention, which should be covered by the scope of the patent claims of the present invention.

Claims

1. A global navigation satellite system (GNSS) adaptive positioning method based on sliding window self-tuning, characterized in that: The following steps are included Step 1: Obtain the coordinates of the GNSS positioning results and obtain the observation values ​​that meet the filter model as the data input source of the real-time Kalman filter; Step 2: Set a sliding window of fixed size before the current epoch of the Kalman filter, and divide the GNSS positioning results in the window into a test set and a validation set as observation values ​​for the self-tuning Kalman smoothing; Step 3: Use self-tuning Kalman smoothing to convert the self-tuning problem into a non-convex optimization problem, set the hyperparameter items, and use the non-convex optimization algorithm to solve the optimal solution of the hyperparameters; Step 4: Pass the optimal solution of the hyperparameters to the real-time Kalman filter as the parameter input value of the current epoch in the filter model.

2. The GNSS adaptive positioning method based on sliding window self-tuning according to claim 1, characterized in that: In step 2, the original coordinates obtained by GNSS positioning are as follows [...,x I-n ,...,x I-1 ,x I ] Where I is the epoch, n is the size of the sliding window, x I is the original GNSS positioning result of the current epoch. The positioning results of n epochs before the current epoch are used as the observation values ​​of the self-tuning Kalman smoothing, and are divided into a training set S and a validation set T.

3. The GNSS adaptive positioning method based on sliding window self-tuning according to claim 1, characterized in that: In step 3, in order to achieve automatic adjustment and optimization of the Kalman smoothing parameters, the Kalman smoothing problem is constructed as the following least squares problem with constraints: Where k is the epoch, is the state estimation vector, F(k) is the state transfer matrix, and W is the process noise variance matrix; z(i) is the estimated value and observed value, H(k) is the design matrix, V is the observed noise variance matrix, and κ is the effective observed value. On the above training set S and test set T, the process noise variance matrix W and the observed noise variance matrix V in the constrained least squares problem are used as hyperparameters θ, and a non-convex optimization algorithm is used to iteratively solve and automatically adjust the optimization. θ=(W -1 / 2 ,V -1 / 2 ) 4. The GNSS adaptive positioning method based on sliding window self-tuning according to claim 1, characterized in that: In step 4, the non-convex optimization algorithm iteratively solves the optimal solution of the hyperparameter θ as the parameter of the real-time Kalman filter, passes the optimal solution of the process noise variance to the prediction part of the filter model, and passes the optimal solution of the observation noise variance to the update part of the filter model to solve the optimal positioning result estimate.

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