A Federated EKF Filtering Method Based on Graph Theory Analysis and Its Application

Abstract

The present invention discloses a federated EKF filtering method based on graph theory analysis and its application, which relates to the technical field of filtering methods. The method includes introducing graph theory analysis into a federated filtering model to construct a centerless iterative data fusion model, wherein each positioning subsystem of the federated filter is used as a node of a graph in the graph theory analysis, and the correlation between each node is used as an edge to obtain the centerless iterative data fusion model. The present invention optimizes the traditional "local-center" mode into a centerless iterative data fusion mode by establishing a decentralized federated EKF iterative data fusion model, which can still provide a more accurate estimation result when a node fails or has a large amount of measurement noise, thereby improving the robustness of the entire data fusion system and ensuring the long-term reliability of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of filtering methods, and in particular to a federal EKF filtering method based on graph theory analysis and an application thereof. Background Art

[0002] Compared with traditional train positioning methods, the multi-sensor combined train positioning system can make better optimal estimates of the train's position and speed. It is an effective means to improve train operation efficiency and reduce trackside equipment. The coordinated optimization and comprehensive processing of multi-source information is an effective way to improve the accuracy of sensor solutions.

[0003] In the process of multi-sensor information fusion, designing a high-performance information fusion filter is the technical core of the integrated navigation system. Among them, the federated filter based on the information allocation principle can effectively improve the system fault tolerance and estimation accuracy. Some people use adaptive filter factors to construct the information allocation factor in the federated filter, propose an adaptive federated filtering algorithm, and use the inertial navigation system to provide a higher initial value accuracy for PPP; others use the adaptive information sharing factor federated filter (AISFF) to fuse data and adaptively adjust the information sharing factor of the federated filter to keep the INS / CNS / DVL combined system available as a backup solution and improve the reliability of the entire system. However, the adaptive weighting factor is sensitive to system noise. When a subsystem fails, it cannot be isolated systematically, which will interfere with the final fusion result of the system. In addition, due to the continuous accumulation of positioning errors of the inertial navigation system over time, the GNSS positioning system is susceptible to interference from multipath and receiver errors. Moreover, due to the large span and long time of the train operation range and the complex and changeable positioning environment, the solution accuracy of each sensor in the combined system is different at different times. If the traditional federal filter model is used, the large error in a local node will directly affect the optimal estimation result of the global filtering. In the actual combined navigation system, each sensor will fail or be affected by the complex environment, and its output result will contain unpredictable noise, such as large position output error when the satellite signal is blocked. At this time, if the local measurement information participates in the global optimal estimation again, the estimation result will show a large error offset, and the failure of the traditional federal filter fusion center will directly lead to a large error in the fusion result.

[0004] In addition, since the information transmission between nodes depends on the correlation of their measurement data, the accuracy of the positioning system gradually increases with the increase in the number of fused nodes, and the estimation result of each node is closely related to its parent node. If the parent node data fails, it will directly affect the estimation accuracy of the child node. The traditional federated filtering method does not consider the optimization problem of the initial node; there is also the problem that the traditional centroid algorithm cannot identify its noise, and the obtained centroid position point contains a lot of system noise, resulting in large errors. Summary of the invention

[0005] In order to solve the above problems, the present invention provides an EKF filtering method based on graph theory analysis and its application. By optimizing the traditional "local-central" mode into a centerless iterative data fusion model, it can still provide more accurate estimation results when a node fails or there is a large amount of measurement noise, thereby improving the robustness of the entire data fusion system, ensuring the long-term reliability of the system, and ensuring the reliability of the initial node through a weighted centroid algorithm.

[0006] In order to achieve the above object, one of the technical solutions adopted by the present invention is: a federated EKF filtering method based on graph theory analysis, the method comprising:

[0007] The graph theory analysis method is introduced into the federated filtering model to construct a centerless iterative data fusion model. In the centerless iterative data fusion model, each positioning subsystem of the federated filter is used as a node of a graph in the graph theory analysis, and the correlation between the nodes is used as an edge to obtain the centerless iterative data fusion model.

[0008] Furthermore, the decentralized iterative data fusion model is specifically:

[0009] Each subsystem processes its own position estimate, and the first subsystem selects the optimal transmission unit based on the processing results of each system

[0010] The second subsystem fuses its own position estimate with the output of the first subsystem and passes the optimal fused estimate to the next subsystem. After multiple iterations, the last subsystem obtains the global optimal fused estimate result.

[0011] Furthermore, the specific process of calculating the optimal fusion estimation of each subsystem through the centerless iterative data fusion model is as follows:

[0012] Assume that Moment The subsystem receives The optimal fusion estimate of the subsystem, then its observation equation can be divided into its own observation and mutual observation Two parts, namely:

[0013] (1)

[0014] in, Indicates Autocorrelation measurement of each subsystem, Indicates subsystem and Cross-correlation measurement of subsystems, Indicates The noise of each subsystem, Indicates subsystem and The cross-correlated noise of the subsystems, Representation Subsystem exist The state value at the moment, then its linearization model is:

[0015] (2)

[0016] in, , ; Representation Subsystem exist The state estimate at time Representation System The observation noise is Indicates system The measurement noise, Representation System and The cross-correlated noise.

[0017] If it is assumed that the system motion noise and observation noise both obey Gaussian distribution, then the conditional probability is expressed as:

[0018] (3)

[0019] Representation Subsystem The observation noise distribution is Representation Subsystem The measurement noise distribution is represents the observation-based sensor-dependent objective function, describing the cross-correlation between sensors;

[0020] Assumption System Sensors form a collection , in Sensor pairs not fused The subsystems perform conditional probability calculations and select the one with the greatest correlation for data fusion;

[0021] Jordi The time-varying discrete linear random system of sensors can be expressed as:

[0022] (4)

[0023] represents the system state transfer matrix, represents the system state error transfer matrix, represents the system measurement transfer matrix.

[0024] Then the error cross-covariance matrix is:

[0025] (5)

[0026] Then its weighting coefficient is:

[0027] (6)

[0028] Denotes the error cross-covariance matrix Trace of.

[0029] In the The optimal fusion estimate and error covariance matrix of the subsystem is:

[0030] (7)

[0031] (8).

[0032] Furthermore, the method also includes selecting an initial optimal node, and the initial optimal node selects the node with the smallest distance to the centroid among all nodes as the initial optimal node through a weighted centroid algorithm.

[0033] Furthermore, the specific process of selecting the point with the smallest distance from the centroid as the initial optimal node by the weighted centroid algorithm is as follows:

[0034] Assume that There is always The sensors involved in positioning constitute a set , No. The position measurement result of each sensor is , assuming that a virtual node is the optimal measurement position of the sensor system, that is, the centroid ;

[0035] Hypothesis set The weight coefficients of each node are , then the measured value and weighting coefficient of the system satisfy equations (9) and (10):

[0036] (9)

[0037] (10)

[0038] The total mean square error of the system is See formula (11):

[0039] (11)

[0040] If the sensor measurements are independent of each other, then , formula (11) can be expressed as:

[0041] (12)

[0042] in, Indicates sensor To ensure Minimum, then you need to ensure Minimum, for formula (12) By finding the partial derivative, we can infer that the weight of each node is:

[0043] (13)

[0044] Therefore, get the centroid of the initial node:

[0045] (14)

[0046] Then the Euclidean distance from the node to the centroid can be expressed as:

[0047] (15)

[0048] Traverse all nodes and select the point with the smallest distance as the initial optimal node.

[0049] The second technical solution adopted by the present invention is: an application of the federal EKF filtering method based on graph theory analysis described in any of the above technical solutions in train combination positioning.

[0050] Furthermore, the train combined positioning is a train combined positioning based on GNSS / SINS / ODO.

[0051] Beneficial effects of the present invention:

[0052] The present invention introduces graph theory analysis on the basis of traditional federated EKF, improves the traditional hierarchical data fusion structure of the federated filter, establishes a decentralized federated EKF iterative data fusion model, and optimizes the traditional "local-central" mode to a centerless iterative data fusion mode. When a node fails or has large measurement noise, it can still provide more accurate estimation results, thereby improving the robustness of the entire data fusion system and ensuring the long-term reliability of the system.

[0053] In addition, in order to ensure the accuracy of the initial node selection, the present invention adopts a weighted centroid algorithm to obtain the weight of each node under the criterion of minimizing the total mean square error of the system, thereby solving the problem that the traditional centroid algorithm cannot identify its noise, and the obtained centroid position point contains a large amount of system noise and has a large error.

[0054] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0056] Figure 1 is a conventional federated EKF structure diagram of an embodiment of the present invention;

[0057] Figure 2 A structural diagram of a centerless iterative data fusion model according to an embodiment of the present invention;

[0058] Figure 3 GNSS / SINS / ODO simulation trajectory of the simulation experiment of the embodiment of the present invention;

[0059] Figure 4 is the east position error of the simulation experiment of the embodiment of the present invention;

[0060] Figure 5 is the north position error of the simulation experiment of the embodiment of the present invention;

[0061] Figure 6 A test route map for an on-vehicle experiment of an embodiment of the present invention;

[0062] Figure 7 A test platform for the vehicle-mounted experiment of the embodiment of the present invention;

[0063] Figure 8 It is the vehicle-mounted experiment trajectory processing of an embodiment of the present invention;

[0064] Fig. 9 is an eastward speed error diagram of a vehicle-mounted experiment according to an embodiment of the present invention;

[0065] Fig.10 A northbound velocity error diagram of a vehicle-mounted experiment according to an embodiment of the present invention;

[0066] Fig.11 is a longitude error diagram of a vehicle-mounted experiment according to an embodiment of the present invention;

[0067] Fig.12 FIG. 4 is a latitude error diagram of a vehicle-mounted experiment according to an embodiment of the present invention. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0069] A federated EKF filtering method based on graph theory analysis, the method comprising:

[0070] The graph theory analysis method is introduced into the federated filtering model to construct a centerless iterative data fusion model. In the centerless iterative data fusion model, each positioning subsystem of the federated filter is used as a node of the graph in the graph theory analysis, and the correlation between the nodes is used as an edge to obtain the centerless iterative data fusion model.

[0071] Based on the traditional federated EKF, graph theory analysis method is introduced to improve the traditional federated filter hierarchical data fusion structure, and a decentralized federated EKF iterative data fusion model is established. The traditional "local-central" mode is corrected to a centerless iterative data fusion mode. When a node fails or there is a large amount of measurement noise, it can still provide more accurate estimation results, thereby improving the robustness of the entire data fusion system and ensuring the long-term reliability of the system.

[0072] Among them, the structure of the traditional federated extended Kalman filter (EKF) is as follows Figure 1 As shown, the structure of the centerless iterative data fusion model of the present invention is as follows Figure 2 shown.

[0073] The centerless iterative data fusion model is specifically:

[0074] Each subsystem processes its own position estimate, and the first subsystem selects the optimal transmission unit based on the processing results of each system

[0075] The second subsystem fuses its own position estimate with the output of the first subsystem and passes the optimal fused estimate to the next subsystem. After multiple iterations, the last subsystem obtains the global optimal fused estimate result.

[0076] The specific process of calculating the optimal fusion estimation of each subsystem through the centerless iterative data fusion model is as follows:

[0077] Assume that Moment The subsystem receives The optimal fusion estimate of the subsystem, then its observation equation can be divided into its own observation and mutual observation Two parts, namely:

[0078] (1)

[0079] in, Indicates Autocorrelation measurement of each subsystem, Indicates subsystem and Cross-correlation measurement of subsystems, Indicates The noise of each subsystem, Indicates subsystem and The cross-correlated noise of the subsystems, Representation Subsystem exist The state value at the moment, then its linearization model is:

[0080] (2)

[0081] in, , ,; Representation Subsystem exist The state estimate at time Representation System The observation noise is Indicates system The measurement noise, Representation System and The cross-correlated noise.

[0082] If it is assumed that the system motion noise and observation noise both obey Gaussian distribution, then the conditional probability is expressed as:

[0083] (3)

[0084] Representation Subsystem The observation noise distribution is Representation Subsystem The measurement noise distribution is represents the observation-based sensor-dependent objective function, describing the cross-correlation between sensors;

[0085] Assumption System Sensors form a collection , in Sensor pairs not fused The subsystems perform conditional probability calculations and select the one with the greatest correlation for data fusion;

[0086] Jordi The time-varying discrete linear random system of sensors can be expressed as:

[0087] (4)

[0088] represents the system state transfer matrix, represents the system state error transfer matrix, represents the system measurement transfer matrix.

[0089] Then the error cross-covariance matrix is:

[0090] (5)

[0091] Then its weighting coefficient is:

[0092] (6)

[0093] Denotes the error cross-covariance matrix Trace of.

[0094] In the The optimal fusion estimate and error covariance matrix of the subsystem is:

[0095] (7)

[0096] (8).

[0097] The advantage of this model is that when a node fails or the measurement value is abnormal, the correlation with the parent node is low, the weighting coefficient is small, and the impact on the final fusion result is reduced.

[0098] In addition to constructing the above-mentioned centerless iterative data fusion model, the present invention also uses a weighted centroid algorithm to select the initial optimal node:

[0099] The method further includes selecting an initial optimal node, wherein the initial optimal node selects a node with the smallest distance from the centroid among all nodes as the initial optimal node through a weighted centroid algorithm.

[0100] The specific process of selecting the point with the smallest distance from the centroid as the initial optimal node by the weighted centroid algorithm is as follows:

[0101] Assume that There is always The sensors involved in positioning constitute a set , No. The position measurement result of each sensor is , assuming that a virtual node is the optimal measurement position of the sensor system, that is, the centroid ;

[0102] Hypothesis set The weight coefficients of each node are , then the measured value and weighting coefficient of the system satisfy equations (9) and (10):

[0103] (9)

[0104] (10)

[0105] The total mean square error of the system is See formula (11):

[0106] (11)

[0107] If the sensor measurements are independent of each other, then , formula (11) can be expressed as:

[0108] (12)

[0109] in, Indicates sensor To ensure Minimum, then you need to ensure Minimum, for formula (12) By finding the partial derivative, we can infer that the weight of each node is:

[0110] (13)

[0111] Therefore, get the centroid of the initial node:

[0112] (14)

[0113] Then the Euclidean distance from the node to the centroid can be expressed as:

[0114] (15)

[0115] Traverse all nodes and select the point with the smallest distance as the initial optimal node.

[0116] The information transmission between nodes depends on the correlation of their measurement data. The accuracy of the positioning system gradually increases with the increase of the number of fused nodes, and the estimation result of each node is closely related to its parent node. If the parent node data fails, it will directly affect the estimation accuracy of the child node. Therefore, the selection of the initial node has a greater impact on the estimation result. To this end, the present invention adopts a weighted centroid algorithm to obtain the weight of each node under the criterion of minimum total mean square error of the system, which solves the problem that the traditional centroid algorithm cannot identify its noise, and the obtained centroid position point contains a large amount of system noise and has a large error.

[0117] In one of the embodiments, the graph-theoretic analysis-based federated EKF filtering method of the present invention is applied to train combination positioning.

[0118] A simulation experiment was also conducted on the combined positioning of trains based on GNSS / SINS / ODO, where GNSS stands for Global Navigation Satellite System, SINS stands for Strapdown Inertial Navigation System, and ODO stands for Odometer Method. The detailed experimental process and results are as follows:

[0119] The simulation parameters are shown in Table 1.

[0120] Table 1 Simulation parameters

[0121]

[0122] Figure 3 It represents the GNSS / SINS / ODO combined positioning simulation trajectory. Figure 4 , 5 They represent the east and north position errors of the system under simulation. It can be seen from the simulation results that in the absence of GNSS, a system that relies solely on the combination of SINS / ODO will have a large cumulative error. In the case of good GNSS signals, the iterative fusion algorithm of the present invention has higher position solution accuracy than the traditional federated algorithm.

[0123] In order to verify the robustness of the graph-theoretic analysis-based federated KEF algorithm of the present invention in improving multi-sensor data fusion, a field test was carried out through a vehicle-mounted experiment. Figure 6 , 7 They are the campus test route and the vehicle-mounted platform respectively. There are obstructions such as trees and buildings around the test route, and the satellite signal will be lost for a short time, which meets the test requirements.

[0124] Since the experiment lacks absolute reference data, the processing results are compared with the speed and position output by GNSS.

[0125] Figure 8 For the test track processing of this experiment, Figure 9-12 are the experimental speed and position errors respectively.

[0126] To further illustrate the scientific nature of the data, the root mean square error (RMSE) is introduced to further process the data. The root mean square error is the square root of the ratio of the square of the deviation between the observed value and the true value and the number of observations. It can well measure the deviation of the observed value. Its formula is as follows (16):

[0127] (16)

[0128] Table 2-3 is a comparison table of speed and position errors in this test:

[0129] Table 2 Speed ​​error

[0130]

[0131] Table 3 Position error

[0132]

[0133] Through error comparison, it can be seen that compared with the traditional federal filtering method, the method of this application improves the calculation accuracy of eastward speed, northward speed, longitude and latitude by 57.2%, 1.2%, 50.4% and 50% respectively.

[0134] Through error comparison, it can be seen that compared with the traditional federal filtering method, the method of the present application has improved the calculation accuracy of the eastward speed, northward speed, longitude and latitude.

[0135] 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 principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A federated EKF filtering method based on graph theory analysis, characterized in that: The method comprises: A graph theory analysis method is introduced into the federated filtering model to construct a centerless iterative data fusion model, in which each positioning subsystem of the federated filter is used as a node of a graph in the graph theory analysis, and the correlation between each node is used as an edge to obtain a centerless iterative data fusion model; The centerless iterative data fusion model is specifically: Each subsystem processes its own position estimate, and the first subsystem selects the optimal transmission unit based on the processing results of each system; The second subsystem fuses its own position estimate with the output of the first subsystem and transmits the optimal fused estimate to the next subsystem. After multiple iterations, the last subsystem obtains the global optimal fused estimate result. The specific process of calculating the optimal fusion estimation of each subsystem through the centerless iterative data fusion model is as follows: Assuming that at time k+1, the ith subsystem receives the optimal fusion estimate of the jth subsystem, its observation equation can be divided into its own observation and mutual observation Two parts, namely: in, represents the autocorrelation measure of the ith subsystem, represents the cross-correlation measurement between the ith subsystem and the jth subsystem, V i (k) represents the noise of the ith subsystem, V ij (k) represents the cross-correlation noise between the ith subsystem and the jth subsystem, x i (k) represents the state value of subsystem i at time k, and its linearized model is: in, represents the state estimate of subsystem i at time k, represents the observation noise of system i, represents the measurement noise of the system, represents the cross-correlation noise of systems i and j; If it is assumed that the system motion noise and observation noise both obey Gaussian distribution, then the conditional probability is expressed as: represents the observation noise distribution of subsystem i, represents the measurement noise distribution of subsystem i, then represents the observation-based sensor-dependent objective function, describing the cross-correlation between sensors; Assume that the system has m sensors forming a set (1,2,3,...,m)∈Θ, and perform conditional probability calculation on the n subsystems that have not been fused at the jth sensor, and select the one with the greatest correlation for data fusion; If the time-varying discrete linear random system of the i-th sensor is expressed as: φ i (k) represents the system state transfer matrix, Γ i (k) represents the system state error transfer matrix, H i (k) represents the system measurement transfer matrix; Then the error cross-covariance matrix is: Then its weighting coefficient is: tP i Denotes the error cross-covariance matrix P i traces; Then the optimal fusion estimate and error covariance matrix of the i-th subsystem is: The method further includes selecting an initial optimal node, wherein the initial optimal node selects a node with the smallest distance from the centroid among all nodes as the initial optimal node through a weighted centroid algorithm; The specific process of selecting the point with the smallest distance from the centroid as the initial optimal node by the weighted centroid algorithm is as follows: Assume that at time k there are m sensors participating in positioning, forming a set (1, 2, 3, ..., m) ∈ Θ, and the position measurement result of the i-th sensor is X i =[x i y i z i ], assuming that a virtual node is the optimal measurement position of the sensor system, that is, the centroid X = [xyz]; Assume that the weight coefficients of each node in the set Θ are η1, η2, ..., η m , then the measured value and weighting coefficient of the system satisfy equations (9) and (10): Then the total mean square error σ of the system is 2 See formula (11): If the measurements of each sensor are independent of each other, then E[(XX i )(XX j )]=0, formula (11) can be expressed as: Among them, η i represents the weight of sensor i; to ensure σ 2 Minimum, then you need to ensure Minimum, for formula (12) By finding the partial derivative, we can infer that the weight of each node is: Therefore, get the centroid of the initial node: Then the Euclidean distance from the node to the centroid can be expressed as: Traverse all nodes and select the point with the smallest distance as the initial optimal node.

2. An application of the graph-theoretic analysis-based federated EKF filtering method as claimed in claim 1 in train combination positioning.

3. The use according to claim 2, characterized in that: The train combined positioning is a train combined positioning based on GNSS / SINS / ODO.

Images