CN110954132A - Method for carrying out navigation fault identification through GRNN (generalized regression neural network) assisted adaptive Kalman filtering - Google Patents

Method for carrying out navigation fault identification through GRNN (generalized regression neural network) assisted adaptive Kalman filtering Download PDF

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CN110954132A
CN110954132A CN201911055911.3A CN201911055911A CN110954132A CN 110954132 A CN110954132 A CN 110954132A CN 201911055911 A CN201911055911 A CN 201911055911A CN 110954132 A CN110954132 A CN 110954132A
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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 method for identifying navigation faults by GRNN auxiliary self-adaptive Kalman filtering, which comprises the following steps: firstly, establishing an error detection state equation based on the Mahalanobis distance; secondly, establishing a robust Kalman filtering equation and an adaptive Kalman filtering equation; thirdly, the generalized regression neural network algorithm assists robust adaptive Kalman filtering to identify faults of the navigation system, abnormal observation values of the GPS/BDS are eliminated, and optimal expansion factors of GRNN are adjusted on line in a dynamic initialization stage of the combined system; and performing GRNN network training by using the residual observed values and the optimal expansion factors and adopting a sliding window method, identifying the source of system faults by tracking a decision threshold, and automatically selecting robust or adaptive Kalman filtering for the integrated system. The method can improve the success rate of detecting, identifying and eliminating errors in the complex urban area, and can also improve the overall positioning precision of the GNSS signal during short-term interruption.

Description

Method for carrying out navigation fault identification through GRNN (generalized regression neural network) assisted adaptive Kalman filtering
Technical Field
The invention discloses a method for identifying navigation faults by GRNN (generalized regression neural network) assisted adaptive Kalman filtering, 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 land 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, which limits its reliability to satisfactory accuracy and position. Inertial Navigation Systems (INS) are capable of providing continuous position information and accurate attitude information in the event of GNSS signal failure. It is clear that a GNSS/INS combined navigation system may provide better performance than a standalone system. Kalman filtering has been applied 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 since observation and state residuals are simultaneously affected by the dynamic model errors and the observation errors, it is difficult to distinguish the dynamic model errors from the total observation errors by the observation and state residuals. While adaptive or robust kalman filtering can only effectively limit one.
Disclosure of Invention
The invention overcomes the defects of the prior art, and the technical problem to be solved is to provide the method for identifying the navigation fault by GRNN auxiliary self-adaptive Kalman filtering, 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 in short-term interruption.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
the method for identifying the navigation fault by GRNN auxiliary self-adaptive Kalman filtering comprises the following steps:
firstly, establishing an error detection state equation based on the Mahalanobis distance;
secondly, establishing a robust Kalman filtering equation and an adaptive Kalman filtering equation;
thirdly, the generalized regression neural network algorithm assists robust adaptive Kalman filtering to identify faults of the navigation system, and firstly, an abnormal observation value of the GPS/BDS is eliminated; then, in the dynamic initialization stage of the combined system, the optimal expansion factor of GRNN is adjusted on line; and finally, carrying out GRNN network training by using the residual observed values and the optimal expansion factors and adopting a sliding window method, identifying the source of system faults by tracking a decision threshold, and automatically selecting robust or adaptive Kalman filtering for the integrated system.
Preferably, in the first step, the method for establishing the mahalanobis distance-based error detection state equation 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, phik，k-1Being a state transition matrix, wk-1In order to be a vector of the process noise,
Figure BDA0002256548130000023
the covariance is predicted for the state of the k epoch,
Figure BDA0002256548130000024
predicting covariance, Q, for states of k-1 epochk-1Is wk-1T represents the transpose of the matrix;
the observation equation is: z is a radical ofk＝HkXk+vkIn the formula, zkRepresents the observed quantity, HkTo represent a relationship matrix, vkMeasuring a noise vector for the representation relationship matrix;
the measurement updating process comprises the following steps:
Figure BDA0002256548130000025
in the formula, KkAs Kalman gain, HkRepresenting a relationship matrix, RkTo observe the noise covariance, from the observed quantity ZkTo its mean value
Figure BDA0002256548130000026
Is considered to be the relevant test statistic ykExpressed as:
Figure BDA0002256548130000027
wherein M iskIs the Mahalanobis distance, zkThe amount of observation is represented by a graph,
Figure BDA0002256548130000028
is the observation of the prediction vector(s),
Figure BDA0002256548130000029
as covariance, the following is expressed:
Figure BDA00022565481300000210
Figure BDA00022565481300000211
when observation error and dynamic model noise wk-1Are all gaussian distributed, the test statistic gammakChi-square distribution with parameter m is satisfied:
Figure BDA0002256548130000031
where m is the degree of freedom, i.e., the dimension of the observed quantity,
Figure BDA0002256548130000032
is α threshold of significance level, when tested, statistic gammakMeasured value of
Figure BDA0002256548130000033
Greater than α indicates an observation error.
Preferably, in the second step, the robust kalman filter equation establishing method includes:
the observed noise covariance is as follows:
Figure BDA0002256548130000034
in the formula, λkIs a scale factor, and is a function of,
Figure BDA0002256548130000035
an updated observed noise covariance;
and further obtaining a new observation prediction vector:
Figure BDA0002256548130000036
in the formula (I), the compound is shown in the specification,
Figure BDA0002256548130000037
for new observation prediction vectors, n is the number of samples, nkFor the k-th sample, the number of samples,
Figure BDA0002256548130000038
is a covariance;
so the following equation is satisfied:
Figure BDA0002256548130000039
then, Newton iteration method is applied to solve the following steps:
Figure BDA00022565481300000310
Figure BDA00022565481300000311
wherein i is 0,1, 2;
the degree of freedom is predetermined to be 6, i.e., the significance level is 1%, so χα16.812;
introducing another scalar factor kkAnd adjusting the covariance of the observation prediction to ensure the robustness:
Figure BDA00022565481300000312
Figure BDA0002256548130000041
robust Kalman gain KkComprises the following steps:
Figure BDA0002256548130000042
through the steps, the proportion of observation quantity is small, the information weight of the dynamic model is large, and the influence of actual observation errors is effectively inhibited.
Preferably, in the second step, the adaptive kalman filter equation is established as follows:
the conventional adaptive kalman filter is as follows:
Figure BDA0002256548130000043
wherein, αkIs an adaptive factor;
Figure BDA0002256548130000044
tr is the trace of the matrix:
Figure BDA0002256548130000045
Figure BDA0002256548130000046
Figure BDA0002256548130000047
wherein, C0kIs the real covariance of the residual error,
Figure BDA0002256548130000048
is a sequence of the residual error that is,
Figure BDA0002256548130000049
by this method, the availability factor of the historical status 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 recurrent neural network algorithm in the third step structurally comprises four layers, namely an input layer, a mode layer, a summation layer and an output layer:
1) the number of neurons in the input layer is equal to the dimension t of an input vector in a learning sample, and an input variable is transmitted to the mode layer through the neurons in 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 learning samples, and the neuron transfer function of 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 for summation in the summation layer have two types, one is to sum the outputs of all the neurons in the mode layer arithmetically, the connection weight of the mode layer and each neuron is 1, and the transfer function SDComprises the following steps:
Figure BDA0002256548130000052
and another type of neuron carries out weighted summation on the neurons of all the mode layers, wherein the jth element in the input sample is the ith neuron in the mode layerTransfer function S through the connection weight of the j-th neuron in the element and summation layerzjComprises the following steps:
Figure BDA0002256548130000053
where j is the dimension of the output variable, yijIs the output state vector;
4) the output layer divides the two types of summation neurons transmitted by the summation layer, and the result is used as a predicted value:
Figure BDA0002256548130000054
the generalized regression neural network is a radial basis function network established on the basis of mathematical statistics, and the theoretical basis of the generalized regression neural network is nonlinear regression analysis. GRNN has strong nonlinear mapping capability and learning speed, has stronger advantages than RBF, and the network is finally converged in the optimized regression with more sample size aggregation, and has good prediction effect when the sample data is less and can also process unstable data. A generalized recurrent neural network can be built, in general, from radial basis neurons and linear neurons.
Preferably, the third step is specifically performed as follows:
taking the integral of the original acceleration and rotation speed as the training input of GRNN and as the sum of the angular and velocity increments; the GPS/BDS position difference is then used as a training output, which is a three-dimensional vector with north, east, and bottom positions as components. The expression is as follows:
Figure BDA0002256548130000061
wherein B is geodetic coordinates, str is a GRNN network structure,
Figure BDA0002256548130000062
is the original acceleration of the accelerometer and,
Figure BDA0002256548130000063
is the rate at which the spinning top is rotating,
Figure BDA0002256548130000064
is the position increment in the n coordinate system, Δ B, Δ L, Δ H are the difference of the geodetic coordinates, RmIs the meridian radius of curvature, RNIs the transverse radius of curvature;
on the premise that the differential navigation solution is reliable and the network learning is reasonable before k epoch, the network output can predict the optimal estimation of the state parameters of the dynamic model, so the reliable observation is the key premise for obtaining the optimal estimation. To this end, we propose the following strategy to improve the quality of the observed information.
Firstly, eliminating abnormal observation values of the GPS/BDS,
standard deviation of residual sequence
Figure 100002_1
Comprises the following steps:
Figure BDA0002256548130000066
Figure BDA0002256548130000067
is a residual sequence, if
Figure BDA0002256548130000068
GPS/BDS observation and corresponding residual sequence are removed, wherein c is a constant;
secondly, 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 predictions is expressed as:
Figure BDA0002256548130000069
wherein Z isGNSSFor observations of GNSS during training, ZpreIs the predicted value of the network, N is the epoch number, and then the network structure is trained by the following function:
Figure BDA00022565481300000610
wherein newgrnn represents the GRNN function; s is the propagation factor of the network;
after the network structure is determined, the GRNN output satisfies:
Figure BDA00022565481300000611
the optimal diffusion coefficient ensures to obtain the optimal output;
according to our experience, the initial value of the propagation factor s is 0.5 and the maximum value is 10, with the following criteria:
RMSpre＝min
thirdly, using the rest observed values and the optimal expansion factors to carry out GRNN network training by adopting a sliding window method,
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 position with the optimal GRNN can avoid the influence of fault or abnormal information which may occur in k epochs, and can be used for detecting and positioning current observation information. That is, the source of the system fault can be identified by tracking the decision threshold and automatically selecting robust or adaptive kalman filtering for the integrated system:
|Zpre-ZGNZZ|≥3RMSpre→robust Kalman filtering
|Zpre-ZGNZZ|＜3RMSpre→adaptive Kalman filtering。
compared with the prior art, the invention has the following beneficial effects:
by the method, the generalized regression neural network is utilized to assist the adaptive robust Kalman filtering, the system can realize fault detection in GNSS/INS integrated navigation, and the robust or adaptive Kalman filtering is selected automatically so as to adjust the influence of observation and dynamic models on navigation results.
Compared with a single system, the reliability of a GPS/BDS combined system is obviously improved, and the real-time positioning precision is also obviously improved.
(1) The generalized regression neural network GRNN is used in the method, the GRNN has strong nonlinear mapping capability and learning speed and has stronger advantages than RBF, the network is finally converged in the optimized regression with more sample size aggregation, the prediction effect is good when the sample data is less, and the network can also process unstable data.
(2) The method combines robust Kalman filtering and adaptive Kalman filtering.
(3) When the system fails, the output of the neural network is not directly used as an integral result, but the neural network is used for calculating a tracking decision threshold value to identify the source of the system failure, and the robust or the adaptive Kalman filtering is automatically selected for the integrated system.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention.
Fig. 2 is a structure of a conventional generalized recurrent neural network.
FIG. 3 is a graph of a comparison of longitude positioning errors between a vehicle navigation test performed by the method of the present invention and a classical Kalman filtering algorithm;
FIG. 4 is a comparison chart of latitude positioning errors of a vehicle navigation test and a classical Kalman filtering algorithm performed by the method of the invention.
Detailed Description
The invention will be further explained with reference to the drawings.
The method for identifying the navigation fault by GRNN auxiliary self-adaptive Kalman filtering comprises the following steps:
firstly, establishing an error detection state equation based on the 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, phik，k-1Being a state transition matrix, wk-1In order to be a vector of the process noise,
Figure BDA0002256548130000083
the covariance is predicted for the state of the k epoch,
Figure BDA0002256548130000084
predicting covariance, Q, for states of k-1 epochk-1Is wk-1T represents the transpose of the matrix;
the observation equation is: z is a radical ofk＝HkXk+vkIn the formula, zkRepresents the observed quantity, HkTo represent a relationship matrix, vkMeasuring a noise vector for the representation relationship matrix;
the measurement updating process comprises the following steps:
Figure BDA0002256548130000085
in the formula, KkAs Kalman gain, HkRepresenting a relationship matrix, RkTo observe the noise covariance, from the observed quantity ZkTo its mean value
Figure BDA0002256548130000086
Is considered to be the relevant test statistic ykExpressed as:
Figure BDA0002256548130000091
wherein M iskIs the Mahalanobis distance, zkThe amount of observation is represented by a graph,
Figure BDA0002256548130000092
is the observation of the prediction vector(s),
Figure BDA0002256548130000093
as covariance, the following is expressed:
Figure BDA0002256548130000094
Figure BDA0002256548130000095
when observation error and dynamic model noise wk-1Are all gaussian distributed, the test statistic gammakChi-square distribution with parameter m is satisfied:
Figure BDA0002256548130000096
Figure BDA0002256548130000097
where m is the degree of freedom, i.e., the dimension of the observed quantity,
Figure BDA0002256548130000098
is α threshold of significance level, when tested, statistic gammakMeasured value of
Figure BDA0002256548130000099
Greater than α indicates an observation error.
Secondly, establishing a robust Kalman filtering equation and an adaptive Kalman filtering equation;
the robust Kalman filtering equation establishment method comprises the following steps:
the observed noise covariance is as follows:
Figure BDA00022565481300000910
in the formula, λkIs a scale factor, and is a function of,
Figure BDA00022565481300000911
an updated observed noise covariance;
further obtaining:
Figure BDA00022565481300000912
in the formula (I), the compound is shown in the specification,
Figure BDA00022565481300000913
for new observation prediction vectors, n is the number of samples, nkFor the k-th sample, the number of samples,
Figure BDA00022565481300000914
is a covariance;
so the following equation is satisfied:
Figure BDA00022565481300000915
then, Newton iteration method is applied to solve the following steps:
Figure BDA0002256548130000101
Figure BDA0002256548130000102
wherein i is 0,1, 2;
the degree of freedom is predetermined to be 6, i.e., the significance level is 1%, so χα16.812;
another scalar factor is introduced to adjust the covariance of the observation prediction to ensure robustness:
Figure BDA0002256548130000103
Figure BDA0002256548130000104
the robust kalman gain is:
Figure BDA0002256548130000105
through the steps, the proportion of observation quantity is small, the information weight of the dynamic model is large, and the influence of actual observation errors is effectively inhibited.
The method for establishing the adaptive Kalman filtering equation comprises the following steps:
the conventional adaptive kalman filter is as follows:
Figure BDA0002256548130000106
wherein, αkIs an adaptive factor;
Figure BDA0002256548130000107
tr is the trace of the matrix:
Figure BDA0002256548130000108
Figure BDA0002256548130000109
Figure BDA0002256548130000111
wherein, C0kIn order to be the real covariance of the residual,
Figure BDA0002256548130000112
is a sequence of the residual error that is,
Figure BDA0002256548130000113
by this method, the availability factor of the historical status information is reduced, i.e. the current availability factor metric information is increased. Thereby effectively suppressing the influence of dynamic model errors.
Thirdly, the generalized regression neural network algorithm assists robust adaptive Kalman filtering to identify faults of the navigation system, and firstly, an abnormal observation value of the GPS/BDS is eliminated; then, in the dynamic initialization stage of the combined system, the optimal expansion factor of GRNN is adjusted on line; and finally, carrying out GRNN network training by using the residual observed values and the optimal expansion factors and adopting a sliding window method, identifying the source of system faults by tracking a decision threshold, and automatically selecting robust or adaptive Kalman filtering for the integrated system.
The generalized regression neural network is a radial basis function network established on the basis of mathematical statistics, and the theoretical basis of the generalized regression neural network is nonlinear regression analysis. GRNN has strong nonlinear mapping capability and learning speed, has stronger advantages than RBF, and the network is finally converged in the optimized regression with more sample size aggregation, and has good prediction effect when the sample data is less and can also process unstable data. A generalized recurrent neural network can be built, in general, from radial basis neurons and linear neurons. The generalized regression neural network algorithm structurally comprises four layers, namely an input layer, a mode layer, a summation layer and an output layer:
1) the number of neurons in the input layer is equal to the dimension t of an input vector in a learning sample, and an input variable is transmitted to the mode layer through the neurons in 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 learning samples, and the neuron transfer function of 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 for summation in the summation layer have two types, one is to sum the outputs of all the neurons in the mode layer arithmetically, the connection weight of the mode layer and each neuron is 1, and the transfer function SDComprises the following steps:
Figure BDA0002256548130000115
the other type of neuron carries out weighted summation on the neurons of all the mode layers, the jth element in the input sample is the connection weight value of the ith neuron in the mode layer and the jth neuron in the summation layer, and the transfer function SzjComprises the following steps:
Figure BDA0002256548130000121
where j is the dimension of the output variable, yijIs the output state vector;
4) the output layer divides the two types of summation neurons transmitted by the summation layer, and the result is used as a predicted value:
Figure BDA0002256548130000122
the generalized regression neural network is a radial basis function network established on the basis of mathematical statistics, and the theoretical basis of the generalized regression neural network is nonlinear regression analysis. GRNN has strong nonlinear mapping capability and learning speed, has stronger advantages than RBF, and the network is finally converged in the optimized regression with more sample size aggregation, and has good prediction effect when the sample data is less and can also process unstable data. A generalized recurrent neural network can be built, in general, from radial basis neurons and linear neurons.
The specific method for identifying the fault of the navigation system by using the generalized regression neural network algorithm to assist the robust adaptive Kalman filtering is as follows:
taking the integral of the original acceleration and rotation speed as the training input of GRNN and as the sum of the angular and velocity increments; the GPS/BDS position difference is then used as a training output, which is a three-dimensional vector with north, east, and bottom positions as components. The expression is as follows:
Figure BDA0002256548130000123
wherein B is geodetic coordinates, str is a GRNN network structure,
Figure BDA0002256548130000124
is the original acceleration of the accelerometer and,
Figure BDA0002256548130000125
is the rate at which the spinning top is rotating,
Figure BDA0002256548130000126
is the position increment in the n coordinate system, Δ B, Δ L, Δ H are the difference of the geodetic coordinates, RmIs the meridian radius of curvature, RNIs the transverse radius of curvature;
on the premise that the differential navigation solution is reliable and the network learning is reasonable before k epoch, the network output can predict the optimal estimation of the state parameters of the dynamic model, so the reliable observation is the key premise for obtaining the optimal estimation. To this end, we propose the following strategy to improve the quality of the observed information.
Firstly, eliminating abnormal observation values of the GPS/BDS,
standard deviation of residual sequence
Figure 100002_2
Comprises the following steps:
Figure BDA0002256548130000132
Figure BDA0002256548130000133
is a residual sequence, if
Figure BDA0002256548130000134
GPS/BDS observations and phasesRemoving all the corresponding residual sequences, wherein c is a constant;
secondly, 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 predictions is expressed as:
Figure BDA0002256548130000135
wherein Z isGNSSFor observations of GNSS during training, ZpreIs the predicted value of the network, N is the epoch number, and then the network structure is trained by the following function:
Figure BDA0002256548130000136
wherein newgrnn represents the GRNN function; s is the propagation factor of the network;
after the network structure is determined, the GRNN output satisfies:
Figure BDA0002256548130000137
the optimal diffusion coefficient ensures to obtain the optimal output;
according to our experience, the initial value of the propagation factor s is 0.5 and the maximum value is 10, with the following criteria:
RMSpre＝min
thirdly, using the rest observed values and the optimal expansion factors to carry out GRNN network training by adopting a sliding window method,
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 position with the optimal GRNN can avoid the influence of fault or abnormal information which may occur in k epochs, and can be used for detecting and positioning current observation information. That is, the source of the system fault can be identified by tracking the decision threshold and automatically selecting robust or adaptive kalman filtering for the integrated system:
|Zpre-ZGNZZ|≥3RMSpre→robust Kalman filtering
|Zpre-ZGNZZ|＜3RMSpre→adaptive Kalman filtering。
compared with a single system, the reliability of the GPS/BDS combined system is obviously improved, and the real-time positioning precision is also obviously improved.
And (3) vehicle navigation test:
the vehicle adopts an INS/GPS integrated navigation positioning system, the navigation system consists of a star-watching NVIMU300 inertial measurement unit and a JAVAD LexonGGD112T GPS receiver, and 1Hz C/A GPS data is output. In addition, another JAVAD Lexon-GGD112T GPS receiver placed at a local reference station provides 1Hz Differential GPS (DGPS) data along with a vehicle-mounted receiver. The maximum distance between the vehicle and the local reference station is less than 60km, and the DGPS positioning precision is less than 0.1m through post differential processing.
The vehicle navigation test was conducted in jin of shanxi province with a home position of 37 ° 44'44.4 "east longitude 112 ° 42' 07.3". The GPS receiver has a horizontal position error (RMS) of 5m, a height error (RMS) of 8m, and a velocity error (RMS) of 0.05 m/s. The initial speeds of east, north and day are 10m/s, 10m/s and 0m/s, respectively. The gyro constant drift was 0.1 °/h, and its white noise was 0.05 °/h. Accelerometer zero offset is 10-3g, white noise of 10-4g. The vehicle initial position error is (12m,12m,15m), the initial velocity error is (0.3m/s,0.3m/s,0.3 m/s), and the initial attitude error is (1.5 ', 1 ', 1 '). The test time is 1000s and the filter period is 1 s.
As shown in fig. 3 and 4, for the comparison between the current vehicle navigation test and the positioning error of the classical kalman filter algorithm, it can be seen from the figure that the error of the method is significantly smaller than that of the classical kalman filter algorithm. The method effectively and dynamically selects the ACKF and the RCKF, and simultaneously improves the overall positioning precision of the GNSS signal 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 gist of the present invention.

Claims (6)

  1. The method for carrying out navigation fault identification by GRNN auxiliary adaptive Kalman filtering is characterized by comprising the following steps:
    firstly, establishing an error detection state equation based on the Mahalanobis distance;
    secondly, establishing a robust Kalman filtering equation and an adaptive Kalman filtering equation;
    thirdly, the generalized regression neural network algorithm assists robust adaptive Kalman filtering to identify faults of the navigation system, and firstly, an abnormal observation value of the GPS/BDS is eliminated; then, in the dynamic initialization stage of the combined system, the optimal expansion factor of GRNN is adjusted on line; and finally, carrying out GRNN network training by using the residual observed values and the optimal expansion factors and adopting a sliding window method, identifying the source of system faults by tracking a decision threshold, and automatically selecting robust or adaptive Kalman filtering for the integrated system.
  2. 2. The method for identifying navigation faults through GRNN (generalized regression neural network) assisted adaptive Kalman filtering according to claim 1, wherein 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 FDA0002256548120000011
    where k is the epoch number, the superscript ^ represents the estimate of the variable,
    Figure FDA0002256548120000012
    a state vector representing the system is the systemEstimate of the state vector, Φk，k-1Being a state transition matrix, wk-1In order to be a vector of the process noise,
    Figure FDA0002256548120000013
    the covariance is predicted for the state of the k epoch,
    Figure FDA0002256548120000014
    predicting covariance, Q, for states of k-1 epochk-1Is wk-1T represents the transpose of the matrix;
    the observation equation is: z is a radical ofk＝HkXk+vkIn the formula, zkRepresents the observed quantity, HkTo represent a relationship matrix, vkMeasuring a noise vector for the representation relationship matrix;
    the measurement updating process comprises the following steps:
    Figure FDA0002256548120000021
    in the formula, KkAs Kalman gain, HkRepresenting a relationship matrix, RkTo observe the noise covariance, from the observed quantity ZkTo its mean value
    Figure FDA0002256548120000022
    Is considered to be the relevant test statistic ykExpressed as:
    Figure FDA0002256548120000023
    wherein M iskIs the Mahalanobis distance, zkThe amount of observation is represented by a graph,
    Figure FDA0002256548120000024
    is the observation of the prediction vector(s),
    Figure FDA0002256548120000025
    to assist inVariance, expressed as follows:
    Figure FDA0002256548120000026
    Figure FDA0002256548120000027
    when observation error and dynamic model noise wk-1Are all gaussian distributed, the test statistic gammakChi-square distribution with parameter m is satisfied:
    Figure FDA0002256548120000028
    where m is the degree of freedom, i.e., the dimension of the observed quantity,
    Figure FDA0002256548120000029
    is α threshold of significance level, when tested, statistic gammakMeasured value of
    Figure FDA00022565481200000210
    Greater than α indicates an observation error.
  3. 3. The method for identifying navigation faults through GRNN-assisted adaptive Kalman filtering according to claim 1, wherein in the second step, the robust Kalman filtering equation is established as follows:
    the observed noise covariance is as follows:
    Figure FDA00022565481200000211
    in the formula, λkIs a scale factor, and is a function of,
    Figure FDA00022565481200000212
    an updated observed noise covariance;
    further obtaining:
    Figure FDA00022565481200000213
    in the formula (I), the compound is shown in the specification,
    Figure FDA00022565481200000214
    for new observation prediction vectors, n is the number of samples, nkFor the k-th sample, the number of samples,
    Figure FDA00022565481200000215
    is a covariance;
    so the following equation is satisfied:
    Figure FDA0002256548120000031
    then, Newton iteration method is applied to solve the following steps:
    Figure FDA0002256548120000032
    Figure FDA0002256548120000033
    wherein i is 0,1, 2;
    the degree of freedom is predetermined to be 6, i.e., the significance level is 1%, so χα16.812;
    introducing another scalar factor kkAnd adjusting the covariance of the observation prediction to ensure the robustness:
    Figure FDA0002256548120000034
    Figure FDA0002256548120000035
    robust Kalman gain KkComprises the following steps:
    Figure FDA0002256548120000036
  4. 4. the GRNN-assisted adaptive kalman filter navigation fault identification method according to claim 1, wherein in the second step, the adaptive kalman filter equation establishment method is as follows:
    the conventional adaptive kalman filter is as follows:
    Figure FDA0002256548120000037
    wherein, αkIs an adaptive factor;
    Figure FDA0002256548120000038
    tr is the trace of the matrix:
    Figure FDA0002256548120000041
    Figure FDA0002256548120000042
    Figure FDA0002256548120000043
    wherein, C0kIs the real covariance of the residual error,
    Figure FDA0002256548120000044
    is a sequence of the residual error that is,
    Figure FDA0002256548120000045
  5. 5. the method of claim 1, wherein the generalized regression neural network algorithm in the third step structurally comprises four layers, namely an input layer, a mode layer, a summation layer and an output layer:
    1) the number of neurons in the input layer is equal to the dimension t of an input vector in a learning sample, and an input variable is transmitted to the mode layer through the neurons in 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 learning samples, and the neuron transfer function of the mode layer is as follows:
    Figure FDA0002256548120000046
    wherein n is the number of samples, sigma is a smoothing factor, and X is an input state vector;
    3) the neurons for summation in the summation layer have two types, one is to sum the outputs of all the neurons in the mode layer arithmetically, the connection weight of the mode layer and each neuron is 1, and the transfer function SDComprises the following steps:
    Figure FDA0002256548120000047
    the other type of neuron carries out weighted summation on the neurons of all the mode layers, the jth element in the input sample is the connection weight value of the ith neuron in the mode layer and the jth neuron in the summation layer, and the transfer function SzjComprises the following steps:
    Figure FDA0002256548120000048
    where j is the dimension of the output variable, yijIs the output state vector;
    4) the output layer divides the two types of summation neurons transmitted by the summation layer, and the result is used as a predicted value:
    Figure FDA0002256548120000051
  6. 6. the method for identifying navigation faults through GRNN-assisted adaptive Kalman filtering according to claim 1, wherein the third step is specifically as follows:
    taking the integral of the original acceleration and rotation speed as the training input of GRNN and as the sum of the angular and velocity increments; then, taking the GPS/BDS position difference as a training output, and the expression is as follows:
    Figure FDA0002256548120000052
    wherein B is geodetic coordinates, str is a GRNN network structure,
    Figure FDA0002256548120000053
    is the original acceleration of the accelerometer and,
    Figure FDA0002256548120000054
    is the rate at which the spinning top is rotating,
    Figure FDA0002256548120000055
    is the position increment in the n coordinate system, Δ B, Δ L, Δ H are the difference of the geodetic coordinates, RmIs the meridian radius of curvature, RNIs the transverse radius of curvature;
    firstly, eliminating abnormal observation values of the GPS/BDS,
    standard deviation of residual sequence
    Figure 2
    Comprises the following steps:
    Figure 1
    Figure FDA0002256548120000058
    is a residual sequence, if
    Figure FDA0002256548120000059
    GPS/BDS observation and corresponding residual sequence are removed, wherein c is a constant;
    secondly, in the dynamic initialization stage of the combined system, the optimal expansion factor of GRNN is adjusted on line, and the root mean square RMS of the GRNN prediction result is expressed as:
    Figure FDA00022565481200000510
    wherein Z isGNSSFor observations of GNSS during training, ZpreIs the predicted value of the network, N is the epoch number, and then the network structure is trained by the following function:
    Figure FDA00022565481200000511
    wherein newgrnn represents the GRNN function; s is the propagation factor of the network;
    after the network structure is determined, the GRNN output satisfies:
    Figure FDA0002256548120000061
    the optimal diffusion coefficient ensures to obtain the optimal output;
    thirdly, using the rest observed values and the optimal expansion factors to carry out GRNN network training by adopting a sliding window method,
    identifying the source of the system fault by tracking the decision threshold and automatically selecting robust or adaptive Kalman filtering for the integrated system:
    |Zpre-ZGNZZ|≥3RMSpre→robust Kalman filtering
    |Zpre-ZGNZZ|＜3RMSpre→adaptive Kalman filtering。
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