CN110954132B - GRNN-assisted self-adaptive Kalman filtering navigation fault identification method - Google Patents

GRNN-assisted self-adaptive Kalman filtering navigation fault identification method Download PDF

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CN110954132B
CN110954132B CN201911055911.3A CN201911055911A CN110954132B CN 110954132 B CN110954132 B CN 110954132B CN 201911055911 A CN201911055911 A CN 201911055911A CN 110954132 B CN110954132 B CN 110954132B
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李灯熬
赵菊敏
毋羽琦
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Taiyuan University of Technology
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Abstract

The invention discloses a GRNN-assisted self-adaptive Kalman filtering navigation fault identification method, which comprises the following steps: firstly, establishing an error detection state equation based on a mahalanobis distance; secondly, establishing a robust Kalman filtering equation and an adaptive Kalman filtering equation; thirdly, a generalized regression neural network algorithm assists a robust self-adaptive Kalman filter to identify faults of a navigation system, eliminates abnormal observation values of GPS/BDS, and adjusts optimal expansion factors of GRNN on line in a dynamic initialization stage of a combined system; and (3) utilizing the residual observed value and the optimal expansion factor, adopting a sliding window method to carry out GRNN network training, identifying the source of the system fault by tracking the decision threshold, and automatically selecting robust or self-adaptive Kalman filtering for the integrated system. The method can improve the success rate of detecting, identifying and eliminating errors in complex urban areas, and can also improve the overall positioning accuracy of GNSS signals during short-term interruption.

Description

GRNN-assisted self-adaptive Kalman filtering navigation fault identification method
Technical Field
The invention discloses a GRNN-assisted self-adaptive Kalman filtering navigation fault identification method, and belongs to the technical field of navigation fault detection.
Background
GNSS is a technology commonly used in Location Based Services (LBS). A typical GNSS-based terrestrial vehicle navigation system must operate in dense urban areas where GNSS signals are either blocked or severely degraded due to cycle slip or multipath effects, etc., which limits its reliability to satisfactory accuracy and positioning. An Inertial Navigation System (INS) is capable of providing continuous position information and accurate attitude information in the event of a GNSS signal failure. It is apparent that the GNSS/INS integrated navigation system may provide better performance than the separate system. Kalman filtering has been used for many years, and an optimal data fusion method is provided for a GPS/INS integrated module. However, the GNSS/INS integrated system has not only dynamic model errors but also observation errors, and it is difficult to distinguish between dynamic model errors and total observation errors by using the observation and state residuals because the observation and state residuals are affected by both dynamic model errors and observation errors. Whereas adaptive or robust kalman filtering can only effectively limit one of them.
Disclosure of Invention
The invention overcomes the defects existing in the prior art, and aims to provide a GRNN-assisted self-adaptive Kalman filtering navigation fault identification method which can improve the success rate of detecting, identifying and eliminating errors in a complex urban area and can also improve the overall positioning precision of GNSS signals during short-term interruption.
In order to solve the technical problems, the invention adopts the following technical scheme:
the GRNN assisted self-adaptive Kalman filtering navigation fault identification method comprises the following steps:
firstly, establishing an error detection state equation based on a mahalanobis distance;
secondly, establishing a robust Kalman filtering equation and an adaptive Kalman filtering equation;
thirdly, a generalized regression neural network algorithm assists a robust self-adaptive Kalman filter to identify faults of a navigation system, and firstly, abnormal observation values of GPS/BDS are eliminated; then, in the dynamic initialization stage of the combined system, the optimal expansion factor of the GRNN is adjusted on line; and finally, utilizing the residual observation value and the optimal expansion factor, adopting a sliding window method to carry out GRNN network training, identifying the source of the system fault by tracking the decision threshold value, and automatically selecting robust or self-adaptive Kalman filtering for the integrated system.
Preferably, in the first step, the method for establishing the error detection state equation based on the mahalanobis distance is as follows:
the basic equation for Kalman filtering is as follows:
the state prediction and state prediction covariance equations are:
Figure BDA0002256548130000021
where k is the epoch number, the superscript "<" > represents the estimated value of the variable,
Figure BDA0002256548130000022
the state vector representing the system is an estimate of the state vector of the system, Φ k，k-1 Is a state transition matrix, w k-1 For process noise vector, ++>
Figure BDA0002256548130000023
Predicting covariance for state of k epoch, +.>
Figure BDA0002256548130000024
Predicting covariance for state of k-1 epoch, Q k-1 Is w k-1 T represents the transpose of the matrix;
the observation equation is: z k ＝H k X k +v k Wherein z is k Indicating observed quantity, H k To represent the relationship matrix, v k Measuring noise vectors for the representation relation matrix;
the measurement updating process comprises the following steps:
Figure BDA0002256548130000025
wherein K is k For Kalman gain, H k Representing a relationship matrix, R k To observe the noise covariance, from the observed quantity Z k To its mean value
Figure BDA0002256548130000026
The square of the mahalanobis distance is considered to be the relevant test statistic gamma k Expressed as:
Figure BDA0002256548130000027
wherein M is k Is the mahalanobis distance, z k The observed quantity is represented by a value representing the observed quantity,
Figure BDA0002256548130000028
is the observation prediction vector, +.>
Figure BDA0002256548130000029
As covariance, expressed as follows:
Figure BDA00022565481300000210
Figure BDA00022565481300000211
when observing errors and dynamic model noise w k-1 Are all gaussian distributions, then the test statistic gamma k Chi-square distribution satisfying parameter m:
Figure BDA0002256548130000031
where m is the degree of freedom, i.e. the dimension of the observed quantity,
Figure BDA0002256548130000032
is a significant level of alpha threshold; when testing statistics gamma k Is>
Figure BDA0002256548130000033
If the value is larger than alpha, the existence of an observation error is indicated.
Preferably, in the second step, the method for establishing the robust kalman filter equation is as follows:
the observed noise covariance is as follows:
Figure BDA0002256548130000034
wherein lambda is k As a scale factor of the dimensions of the device,
Figure BDA0002256548130000035
is an updated observed noise covariance;
and then a new observation prediction vector is obtained:
Figure BDA0002256548130000036
in the method, in the process of the invention,
Figure BDA0002256548130000037
for a new observation prediction vector, n is the number of samples, n k For the kth sample, +.>
Figure BDA0002256548130000038
Is covariance;
the following formula is satisfied:
Figure BDA0002256548130000039
and solving by applying Newton iteration method to obtain:
Figure BDA00022565481300000310
Figure BDA00022565481300000311
wherein i=0, 1, 2;
the degree of freedom is predetermined to be 6, i.e. the significant level is 1%, so χ α 16.812;
introducing another scalar factor kappa k The covariance of the observed predictions is adjusted to ensure robustness:
Figure BDA00022565481300000312
Figure BDA0002256548130000041
robust Kalman gain K k The method comprises the following steps:
Figure BDA0002256548130000042
through the steps, the occupied proportion of the observed quantity is smaller, the information weight of the dynamic model is large, and the influence of the actual observation error is effectively restrained.
Preferably, in the second step, the method for establishing the adaptive kalman filter equation is as follows:
the conventional adaptive kalman filtering is as follows:
Figure BDA0002256548130000043
wherein alpha is k Is an adaptive factor;
Figure BDA0002256548130000044
tr is the trace of the matrix:
Figure BDA0002256548130000045
Figure BDA0002256548130000046
Figure BDA0002256548130000047
wherein C is 0k As the real covariance of the residual error,
Figure BDA0002256548130000048
is a residual sequence,/->
Figure BDA0002256548130000049
In this way, the availability factor of the historical state information is reduced, i.e., the current availability factor metric information is increased. Thereby effectively suppressing the influence of dynamic model errors. />
Preferably, the generalized regression neural network algorithm in the third step is structurally composed of four layers, namely an input layer, a mode layer, a summation layer and an output layer:
1) The number of the neurons of the input layer is equal to the dimension t of the input vector in the learning sample, and the input variable is transmitted to the mode layer through the neurons of the input layer;
2) Each neuron in the mode layer corresponds to different samples respectively, the number of the neurons is equal to the number n of the learning samples, and the transfer function of the neurons in the mode layer is as follows:
Figure BDA0002256548130000051
wherein n is the number of samples, sigma is a smoothing factor, and X is an input state vector;
3) The neurons used for summation in the summation layer are two types, one is to arithmetically sum the outputs of all the neurons in the mode layer, the connection weight of the mode layer and each neuron is 1, and the transfer function S D The method comprises the following steps:
Figure BDA0002256548130000052
the other neuron performs weighted summation on the neurons of all the mode layers, and the jth element in the input sample is the connection weight of the ith neuron in the mode layer and the jth neuron in the summation layer, and the transfer function S zj The method comprises the following steps:
Figure BDA0002256548130000053
where j is the dimension of the output variable, y ij Is the output state vector;
4) The output layer divides the two types of summation neurons transmitted by the summation layer, and the result is taken as a predicted value:
Figure BDA0002256548130000054
the generalized regression neural network is a radial basis function network based on mathematical statistics, and the theoretical basis is nonlinear regression analysis. The GRNN has strong nonlinear mapping capability and learning speed, has stronger advantages than RBF, and finally the network is converged to the optimal regression with more sample size aggregation, the prediction effect is good when the sample data is small, and the network can also process unstable data. Generalized recurrent neural networks can be established generally by radial basis neurons and linear neurons.
Preferably, the specific method of the third step is as follows:
taking the integral of the original acceleration and the rotation speed as the training input of the GRNN and as the sum of the angular and speed increment; the GPS/BDS position difference is then taken as a training output, which is a three-dimensional vector with north, east, and bottom positions as components. The expression is:
Figure BDA0002256548130000061
wherein B is the geodetic coordinates, str is the GRNN network structure,
Figure BDA0002256548130000062
for the original acceleration of the accelerometer, +.>
Figure BDA0002256548130000063
Is the rate of rotation gyro>
Figure BDA0002256548130000064
Is the position increment in an n coordinate system, and delta B, delta L and delta H are respectively the geodetic coordinatesR is the difference of R m Is the radius of curvature of meridian, R N Is the transverse radius of curvature;
under the precondition that the differential navigation solution is reliable and the network learning is reasonable before the k epoch, the network output can predict the optimal estimation of the state parameters of the dynamic model, so that the reliable observation is a key precondition for obtaining the optimal estimation. For this purpose, we propose the following strategy to improve the quality of the observed information.
In the first step, the abnormal observations of the GPS/BDS are eliminated,
standard deviation of residual sequence
Figure BDA0002256548130000065
The method comprises the following steps:
Figure BDA0002256548130000066
Figure BDA0002256548130000067
for residual sequences, if->
Figure BDA0002256548130000068
Removing the GPS/BDS observation and the corresponding residual sequences, wherein c is a constant;
second, in the dynamic initialization stage of the combined system, the optimal expansion factor of GRNN is adjusted on line,
the root mean square RMS of the GRNN prediction is expressed as:
Figure BDA0002256548130000069
wherein Z is GNSS For observations of GNSS during training, Z pre Is a predicted value for the network, N is the epoch number, and then the network structure is trained by the following functions:
Figure BDA00022565481300000610
wherein newgrnn represents a GRNN function; s is the propagation factor of the network;
after the network structure is determined, the GRNN output meets the following conditions:
Figure BDA00022565481300000611
the optimal diffusion coefficient ensures that the optimal output is obtained;
according to our experience, the initial value of the propagation factor s is 0.5, the maximum value is 10, and the criteria are as follows:
RMS pre ＝min
thirdly, utilizing the residual observation value and the optimal expansion factor, adopting a sliding window method to carry out GRNN network training,
the method sets the sliding window width to 50. By preprocessing the network input, the GRNN neural network is more efficient, reliable and stable. The predicted location with the optimal GRNN can avoid the influence of possible faults or abnormal information of the k epoch, and can be used for detecting and positioning the current observation information. That is, the source of the system failure can be identified by tracking decision thresholds and automatically selecting a robust or adaptive kalman filter for the integrated system:
|Z pre -Z GNZZ |≥3RMS pre →robust Kalman filtering
|Z pre -Z GNZZ |＜3RMS pre →adaptive Kalman filtering。
compared with the prior art, the invention has the following beneficial effects:
according to the method, the generalized regression neural network is utilized to assist the self-adaptive robust Kalman filtering, the system can realize fault detection in GNSS/INS combined navigation, and the robust or self-adaptive Kalman filtering is selected automatically so as to adjust the influence of the observation and dynamic model on the navigation result.
Compared with a single system, the generalized regression neural network algorithm assists a robust self-adaptive Kalman filtering to perform a fault recognition algorithm of a navigation system, the reliability of a GPS/BDS combined system is obviously improved, and the real-time positioning accuracy is also obviously improved.
(1) The method uses a generalized regression neural network GRNN, the GRNN has strong nonlinear mapping capability and learning speed, has stronger advantages than RBF, the network finally converges to optimal regression with more sample size aggregation, the prediction effect is good when the sample data is small, and the network can also process unstable data.
(2) The method combines a robust Kalman filter with an adaptive Kalman filter.
(3) The invention does not directly use the output of the neural network as an overall result when the system fails, but calculates a tracking decision threshold by using the neural network to identify the source of the system failure, and automatically selects robust or self-adaptive Kalman filtering for the integrated system.
Drawings
FIG. 1 is a schematic flow chart of the method of the invention.
Fig. 2 is a structure of a conventional generalized recurrent neural network.
FIG. 3 is a graph comparing the longitude positioning errors of a vehicle navigation test and a classical Kalman filtering algorithm performed by the method of the present invention;
FIG. 4 is a graph showing the comparison of the latitude positioning errors of the method of the present invention for a vehicle navigation test and a classical Kalman filtering algorithm.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The GRNN assisted self-adaptive Kalman filtering navigation fault identification method comprises the following steps:
firstly, establishing an error detection state equation based on a mahalanobis distance, wherein the method comprises the following steps:
the basic equation for Kalman filtering is as follows:
the state prediction and state prediction covariance equations are:
Figure BDA0002256548130000081
where k is the epoch number, the superscript "<" > represents the estimated value of the variable,
Figure BDA0002256548130000082
the state vector representing the system is an estimate of the state vector of the system, Φ k，k-1 Is a state transition matrix, w k-1 For process noise vector, ++>
Figure BDA0002256548130000083
Predicting covariance for state of k epoch, +.>
Figure BDA0002256548130000084
Predicting covariance for state of k-1 epoch, Q k-1 Is w k-1 T represents the transpose of the matrix;
the observation equation is: z k ＝H k X k +v k Wherein z is k Indicating observed quantity, H k To represent the relationship matrix, v k Measuring noise vectors for the representation relation matrix;
the measurement updating process comprises the following steps:
Figure BDA0002256548130000085
wherein K is k For Kalman gain, H k Representing a relationship matrix, R k To observe the noise covariance, from the observed quantity Z k To its mean value
Figure BDA0002256548130000086
The square of the mahalanobis distance is considered to be the relevant test statistic gamma k Expressed as: />
Figure BDA0002256548130000091
Wherein M is k Is the mahalanobis distance, z k The observed quantity is represented by a value representing the observed quantity,
Figure BDA0002256548130000092
is the observation prediction vector, +.>
Figure BDA0002256548130000093
As covariance, expressed as follows:
Figure BDA0002256548130000094
Figure BDA0002256548130000095
when observing errors and dynamic model noise w k-1 Are all gaussian distributions, then the test statistic gamma k Chi-square distribution satisfying parameter m:
Figure BDA0002256548130000096
Figure BDA0002256548130000097
where m is the degree of freedom, i.e. the dimension of the observed quantity,
Figure BDA0002256548130000098
is a significant level of alpha threshold; when testing statistics gamma k Is>
Figure BDA0002256548130000099
If the value is larger than alpha, the existence of an observation error is indicated.
Secondly, establishing a robust Kalman filtering equation and an adaptive Kalman filtering equation;
the robust Kalman filter equation establishment method is as follows:
the observed noise covariance is as follows:
Figure BDA00022565481300000910
wherein lambda is k As a scale factor of the dimensions of the device,
Figure BDA00022565481300000911
is an updated observed noise covariance;
and then obtain:
Figure BDA00022565481300000912
in the method, in the process of the invention,
Figure BDA00022565481300000913
for a new observation prediction vector, n is the number of samples, n k For the kth sample, +.>
Figure BDA00022565481300000914
Is covariance;
the following formula is satisfied:
Figure BDA00022565481300000915
and solving by applying Newton iteration method to obtain:
Figure BDA0002256548130000101
Figure BDA0002256548130000102
wherein i=0, 1, 2;
the degree of freedom is predetermined to be 6, i.e. the significant level is 1%, so χ α Is 16.812；
Another scalar factor is introduced to adjust the covariance of the observed predictions to ensure robustness:
Figure BDA0002256548130000103
Figure BDA0002256548130000104
the robust kalman gain is:
Figure BDA0002256548130000105
through the steps, the occupied proportion of the observed quantity is smaller, the information weight of the dynamic model is large, and the influence of the actual observation error is effectively restrained.
The method for establishing the adaptive Kalman filter equation comprises the following steps:
the conventional adaptive kalman filtering is as follows:
Figure BDA0002256548130000106
wherein alpha is k Is an adaptive factor;
Figure BDA0002256548130000107
tr is the trace of the matrix:
Figure BDA0002256548130000108
Figure BDA0002256548130000109
Figure BDA0002256548130000111
wherein C is 0k As the real covariance of the residual is obtained,
Figure BDA0002256548130000112
is a residual sequence,/->
Figure BDA0002256548130000113
In this way, the availability factor of the historical state information is reduced, i.e., the current availability factor metric information is increased. Thereby effectively suppressing the influence of dynamic model errors.
Thirdly, a generalized regression neural network algorithm assists a robust self-adaptive Kalman filter to identify faults of a navigation system, and firstly, abnormal observation values of GPS/BDS are eliminated; then, in the dynamic initialization stage of the combined system, the optimal expansion factor of the GRNN is adjusted on line; and finally, utilizing the residual observation value and the optimal expansion factor, adopting a sliding window method to carry out GRNN network training, identifying the source of the system fault by tracking the decision threshold value, and automatically selecting robust or self-adaptive Kalman filtering for the integrated system.
The generalized regression neural network is a radial basis function network based on mathematical statistics, and the theoretical basis is nonlinear regression analysis. The GRNN has strong nonlinear mapping capability and learning speed, has stronger advantages than RBF, and finally the network is converged to the optimal regression with more sample size aggregation, the prediction effect is good when the sample data is small, and the network can also process unstable data. Generalized recurrent neural networks can be established generally by radial basis neurons and linear neurons. The generalized regression neural network algorithm structurally consists of four layers, namely an input layer, a mode layer, a summation layer and an output layer:
1) The number of the neurons of the input layer is equal to the dimension t of the input vector in the learning sample, and the input variable is transmitted to the mode layer through the neurons of the input layer;
2) Each neuron in the mode layer corresponds to different samples respectively, the number of the neurons is equal to the number n of the learning samples, and the transfer function of the neurons in the mode layer is as follows:
Figure BDA0002256548130000114
wherein n is the number of samples, sigma is a smoothing factor, and X is an input state vector;
3) The neurons used for summation in the summation layer are two types, one is to arithmetically sum the outputs of all the neurons in the mode layer, the connection weight of the mode layer and each neuron is 1, and the transfer function S D The method comprises the following steps:
Figure BDA0002256548130000115
the other neuron performs weighted summation on the neurons of all the mode layers, and the jth element in the input sample is the connection weight of the ith neuron in the mode layer and the jth neuron in the summation layer, and the transfer function S zj The method comprises the following steps:
Figure BDA0002256548130000121
where j is the dimension of the output variable, y ij Is the output state vector;
4) The output layer divides the two types of summation neurons transmitted by the summation layer, and the result is taken as a predicted value:
Figure BDA0002256548130000122
the generalized regression neural network is a radial basis function network based on mathematical statistics, and the theoretical basis is nonlinear regression analysis. The GRNN has strong nonlinear mapping capability and learning speed, has stronger advantages than RBF, and finally the network is converged to the optimal regression with more sample size aggregation, the prediction effect is good when the sample data is small, and the network can also process unstable data. Generalized recurrent neural networks can be established generally by radial basis neurons and linear neurons.
The specific method for fault identification of the navigation system by the generalized regression neural network algorithm assisted robust self-adaptive Kalman filtering is as follows:
taking the integral of the original acceleration and the rotation speed as the training input of the GRNN and as the sum of the angular and speed increment; the GPS/BDS position difference is then taken as a training output, which is a three-dimensional vector with north, east, and bottom positions as components. The expression is:
Figure BDA0002256548130000123
wherein B is the geodetic coordinates, str is the GRNN network structure,
Figure BDA0002256548130000124
for the original acceleration of the accelerometer, +.>
Figure BDA0002256548130000125
Is the rate of rotation gyro>
Figure BDA0002256548130000126
Is the position increment in an n coordinate system, delta B, delta L and delta H are the difference value of the geodetic coordinates respectively, R m Is the radius of curvature of meridian, R N Is the transverse radius of curvature;
under the precondition that the differential navigation solution is reliable and the network learning is reasonable before the k epoch, the network output can predict the optimal estimation of the state parameters of the dynamic model, so that the reliable observation is a key precondition for obtaining the optimal estimation. For this purpose, we propose the following strategy to improve the quality of the observed information.
In the first step, the abnormal observations of the GPS/BDS are eliminated,
standard deviation of residual sequence
Figure BDA0002256548130000131
The method comprises the following steps:
Figure BDA0002256548130000132
Figure BDA0002256548130000133
for residual sequences, if->
Figure BDA0002256548130000134
Removing the GPS/BDS observation and the corresponding residual sequences, wherein c is a constant;
second, in the dynamic initialization stage of the combined system, the optimal expansion factor of GRNN is adjusted on line,
the root mean square RMS of the GRNN prediction is expressed as:
Figure BDA0002256548130000135
wherein Z is GNSS For observations of GNSS during training, Z pre Is a predicted value for the network, N is the epoch number, and then the network structure is trained by the following functions:
Figure BDA0002256548130000136
wherein newgrnn represents a GRNN function; s is the propagation factor of the network;
after the network structure is determined, the GRNN output meets the following conditions:
Figure BDA0002256548130000137
the optimal diffusion coefficient ensures that the optimal output is obtained;
according to our experience, the initial value of the propagation factor s is 0.5, the maximum value is 10, and the criteria are as follows:
RMS pre ＝min
thirdly, utilizing the residual observation value and the optimal expansion factor, adopting a sliding window method to carry out GRNN network training,
the method sets the sliding window width to 50. By preprocessing the network input, the GRNN neural network is more efficient, reliable and stable. The predicted location with the optimal GRNN can avoid the influence of possible faults or abnormal information of the k epoch, and can be used for detecting and positioning the current observation information. That is, the source of the system failure can be identified by tracking decision thresholds and automatically selecting a robust or adaptive kalman filter for the integrated system:
|Z pre -Z GNZZ |≥3RMS pre →robust Kalman filtering
|Z pre -Z GNZZ |＜3RMS pre →adaptive Kalman filtering。
compared with a single system, the reliability of the GPS/BDS combined system is obviously improved, and the real-time positioning accuracy is also obviously improved.
Vehicle navigation test:
the vehicle adopts an INS/GPS combined navigation positioning system, and the navigation system consists of a satellite-viewing NVIMU300 inertia measurement unit and a JAVA D LexonGGD112T GPS receiver, and outputs 1Hz C/A GPS data. In addition, another JAVA D Lexon-GGD112T GPS receiver placed at the local reference station provides 1Hz Differential GPS (DGPS) data with the receiver mounted on the vehicle. The maximum distance between the vehicle and the local reference station is smaller than 60km, and the DGPS positioning accuracy is smaller than 0.1m through post-differential processing.
The vehicle navigation test was performed in Jinzhong, shanxi province, with a starting position of 37 ° 44'44.4 "east longitude 112 ° 42'07.3" north latitude. The GPS receiver has a horizontal position error (RMS) of 5m, a height error (RMS) of 8m, and a velocity error (RMS) of 0.05m/s. The initial speeds of the east, north and the day are respectively 10m/s, 10m/s and 0m/s. The gyro constant drift is 0.1 DEG/h, and the white noise is 0.05 DEG/h. Zero offset of accelerometer 10 -3 g, white noise of 10 -4 g. The error of the initial position of the vehicle is (12 m,12m15 m), the initial velocity error is (0.3 m/s,0.3m/s,0.3 m/s), and the initial attitude error is (1.5 ',1',1 '). The test time was 1000s and the filter period was 1s.
As shown in fig. 3 and 4, in order to compare the positioning error of the present vehicle navigation test with that of the classical kalman filter algorithm, it can be seen from the figure that the error of the present method is significantly smaller than that of the classical kalman filter algorithm. Because the method effectively and dynamically selects the ACKF and the RCKF, and simultaneously improves the overall positioning accuracy of the GNSS signals in short-term interruption. Therefore, the method has stronger adaptability and robustness and higher navigation precision.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present invention.

Claims (4)

  1. The method for identifying navigation faults by GRNN assisted self-adaptive Kalman filtering is characterized by comprising the following steps of:
    firstly, establishing an error detection state equation based on a mahalanobis distance;
    secondly, establishing a robust Kalman filtering equation and an adaptive Kalman filtering equation;
    thirdly, a generalized regression neural network algorithm assists a robust self-adaptive Kalman filter to identify faults of a navigation system, and firstly, abnormal observation values of GPS/BDS are eliminated; then, in the dynamic initialization stage of the combined system, the optimal expansion factor of the GRNN is adjusted on line; finally, utilizing the residual observation value and the optimal expansion factor, adopting a sliding window method to carry out GRNN network training, identifying the source of the system fault through tracking the decision threshold value, and automatically selecting robust or self-adaptive Kalman filtering for the integrated system;
    in the second step, the method for establishing the robust Kalman filter equation is as follows:
    the observed noise covariance is as follows:
    Figure FDA0004167310170000011
    wherein lambda is k As a scale factor of the dimensions of the device,
    Figure FDA0004167310170000012
    is an updated observed noise covariance;
    and then obtain:
    Figure FDA0004167310170000013
    in the method, in the process of the invention,
    Figure FDA0004167310170000014
    for a new observation prediction vector, n is the number of samples, n k For the kth sample, +.>
    Figure FDA0004167310170000015
    Is covariance;
    the following formula is satisfied:
    Figure FDA0004167310170000016
    and solving by applying Newton iteration method to obtain:
    Figure FDA0004167310170000017
    Figure FDA0004167310170000018
    wherein i=0, 1, 2;
    the degree of freedom is predetermined to be 6, i.e. the significant level is 1%, so χ α 16.812;
    introducing another scalar factor kappa k Regulating observed prediction assistant recipePoor to ensure robustness:
    Figure FDA0004167310170000021
    Figure FDA0004167310170000022
    robust Kalman gain K k The method comprises the following steps:
    Figure FDA0004167310170000023
    in the second step, the method for establishing the adaptive Kalman filtering equation is as follows:
    the conventional adaptive kalman filtering is as follows:
    Figure FDA0004167310170000024
    wherein alpha is k Is an adaptive factor;
    Figure FDA0004167310170000025
    tr is the trace of the matrix:
    Figure FDA0004167310170000026
    Figure FDA00041673101700000210
    Figure FDA0004167310170000027
    wherein C is 0k As the real covariance of the residual error,
    Figure FDA0004167310170000028
    is a residual sequence,/->
    Figure FDA0004167310170000029
  2. 2. The method for performing navigation fault identification by GRNN-assisted adaptive kalman filtering according to claim 1, wherein in the first step, the error detection state equation establishment method based on the mahalanobis distance is as follows:
    the basic equation for Kalman filtering is as follows:
    the state prediction and state prediction covariance equations are:
    Figure FDA0004167310170000031
    where k is the epoch number, the superscript "<" > represents the estimated value of the variable,
    Figure FDA00041673101700000312
    the state vector representing the system is an estimate of the state vector of the system, Φ k，k-1 Is a state transition matrix, w k-1 For process noise vector, ++>
    Figure FDA00041673101700000313
    Covariance is predicted for the state of the k epoch,
    Figure FDA00041673101700000314
    predicting covariance for state of k-1 epoch, Q k-1 Is w k-1 T represents the transpose of the matrix;
    the observation equation is: z k ＝H k X k +v k Wherein z is k Indicating observed quantity, H k To represent the relationship matrix, v k Measuring noise vectors for the representation relation matrix;
    the measurement updating process comprises the following steps:
    Figure FDA0004167310170000032
    wherein K is k For Kalman gain, H k Representing a relationship matrix, R k To observe the noise covariance, from the observed quantity Z k To its mean value
    Figure FDA0004167310170000033
    The square of the mahalanobis distance is considered to be the relevant test statistic gamma k Expressed as: />
    Figure FDA0004167310170000034
    Wherein M is k Is the mahalanobis distance, z k The observed quantity is represented by a value representing the observed quantity,
    Figure FDA0004167310170000035
    is the observation prediction vector, +.>
    Figure FDA0004167310170000036
    As covariance, expressed as follows:
    Figure FDA0004167310170000037
    Figure FDA0004167310170000038
    when observing errors and dynamic model noise w k-1 Are all gaussian distributions, then the test statistic gamma k Chi-square distribution satisfying parameter m:
    Figure FDA0004167310170000039
    where m is the degree of freedom, i.e. the dimension of the observed quantity,
    Figure FDA00041673101700000310
    is a significant level of alpha threshold; when testing statistics gamma k Is>
    Figure FDA00041673101700000311
    If the value is larger than alpha, the existence of an observation error is indicated.
  3. 3. The method for navigation fault identification by GRNN-assisted adaptive kalman filtering according to claim 1, wherein the generalized regression neural network algorithm in the third step is structurally composed of four layers, namely an input layer, a mode layer, a summation layer and an output layer:
    1) The number of the neurons of the input layer is equal to the dimension t of the input vector in the learning sample, and the input variable is transmitted to the mode layer through the neurons of the input layer;
    2) Each neuron in the mode layer corresponds to different samples respectively, the number of the neurons is equal to the number n of the learning samples, and the transfer function of the neurons in the mode layer is as follows:
    Figure FDA0004167310170000041
    wherein n is the number of samples, sigma is a smoothing factor, and X is an input state vector;
    3) The neurons used for summation in the summation layer are two types, one is to arithmetically sum the outputs of all the neurons in the mode layer, the connection weight of the mode layer and each neuron is 1, and the transfer function S D The method comprises the following steps:
    Figure FDA0004167310170000042
    the other neuron performs weighted summation on the neurons of all the mode layers, and the jth element in the input sample is the connection weight of the ith neuron in the mode layer and the jth neuron in the summation layer, and the transfer function S zj The method comprises the following steps:
    Figure FDA0004167310170000043
    where j is the dimension of the output variable, y ij Is the output state vector;
    4) The output layer divides the two types of summation neurons transmitted by the summation layer, and the result is taken as a predicted value:
    Figure FDA0004167310170000044
  4. 4. the method for navigation fault identification by GRNN-assisted adaptive kalman filtering according to claim 1, wherein the specific method of the third step is as follows:
    taking the integral of the original acceleration and the rotation speed as the training input of the GRNN and as the sum of the angular and speed increment; then, the GPS/BDS position difference is taken as training output, and the expression is:
    Figure FDA0004167310170000051
    wherein B is the geodetic coordinates, str is the GRNN network structure,
    Figure FDA0004167310170000052
    for the original acceleration of the accelerometer, +.>
    Figure FDA0004167310170000053
    Is the rate of rotation gyro>
    Figure FDA0004167310170000054
    Is the position increment in an n coordinate system, delta B, delta L and delta H are the difference value of the geodetic coordinates respectively, R m Is the radius of curvature of meridian, R N Is the transverse radius of curvature;
    in the first step, the abnormal observations of the GPS/BDS are eliminated,
    standard deviation of residual sequence
    Figure FDA0004167310170000055
    The method comprises the following steps:
    Figure FDA0004167310170000056
    Figure FDA00041673101700000511
    for residual sequences, if->
    Figure FDA0004167310170000057
    Removing the GPS/BDS observation and the corresponding residual sequences, wherein c is a constant;
    secondly, in the dynamic initialization stage of the combined system, the optimal expansion factor of the GRNN is adjusted on line, and the root mean square RMS of the GRNN prediction result is expressed as:
    Figure FDA0004167310170000058
    wherein Z is GNSS For observations of GNSS during training, Z pre Is a predicted value for the network, N is the epoch number, and then the network structure is trained by the following functions:
    Figure FDA0004167310170000059
    wherein newgrnn represents a GRNN function; s is the propagation factor of the network;
    after the network structure is determined, the GRNN output meets the following conditions:
    Figure FDA00041673101700000510
    the optimal diffusion coefficient ensures that the optimal output is obtained;
    thirdly, utilizing the residual observation value and the optimal expansion factor, adopting a sliding window method to carry out GRNN network training,
    identifying the source of the system failure by tracking decision thresholds and automatically selecting a robust or adaptive kalman filter for the integrated system:
    |Z pre -Z GNZZ |≥3RMS pre →robust Kalman filtering
    |Z pre -Z GNZZ |＜3RMS pre →adaptive Kalman filtering。
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