WO2021063136A1

WO2021063136A1 - Data-driven high-precision integrated navigation data fusion method

Info

Publication number: WO2021063136A1
Application number: PCT/CN2020/111697
Authority: WO
Inventors: 崔冰波; 龚辰; 魏新华; 卢泽民; 李晋阳
Original assignee: 江苏大学
Priority date: 2019-09-30
Filing date: 2020-08-27
Publication date: 2021-04-08
Also published as: GB2591954A; GB2591954B; GB202105557D0; CN110702095B; CN110702095A

Abstract

A data-driven high-precision integrated navigation data fusion method. The Gaussian process is used to achieve a precise estimation of posterior distribution of the navigation parameters of an integrated navigation system and the data-driven transformation of an error matrix of sampling points. Specifically, after the integrated navigation system is powered on, fitting of an error propagation model of the sampling points is performed when time t _k<t _n; and when time t _k>t _n, approximation of an model error is performed on the basis of IMU original data and prediction of the error matrix of the sampling points is performed. On the basis of the predicted error matrix of the sampling points, the output angle increment of an upward gyroscope and the specific force of a carrier in the traveling direction in the integrated navigation system are used as input variables of the error propagation model of the sampling points to achieve updating of the sampling points, and the approximation of a matrix matching error of the system model is directly performed on the basis of sensor data. Therefore, the precise estimation of the navigation parameters of the integrated system is realized, and the robustness of a parameterized model of the integrated navigation system is improved.

Description

A data-driven high-precision integrated navigation data fusion method

Technical field

The invention belongs to the field of integrated navigation and multi-source data fusion, and specifically relates to a data-driven high-precision integrated navigation data method.

Background technique

Navigation and positioning are widely used in the fields of national defense, industry and agriculture, such as satellite navigation, inertial navigation, visual navigation and LiDAR. Since a single navigation system is often unable to handle navigation problems in complex environments, the application needs to be based on multiple sources. Integrated navigation system with sensors. In particular, new navigation and positioning applications represented by unmanned driving have extremely demanding requirements on the robustness and intelligence of the navigation system, and multi-source integrated navigation has become the preferred solution. The nonlinear filtering technology represented by extended Kalman filter (EKF) is widely used in the field of integrated navigation, and the combined filtering of the nonlinear filtering model can be satisfied by linearizing the model function at the model prediction point. However, affected by the uncertainty of the system and measurement, EKF cannot meet the requirements of the actual integrated navigation system in terms of the accuracy of moment matching, the efficiency of measurement update, and the robustness. The deterministic sampling point approximation strategy represented by Unscented Kalman Filter (UKF) can obtain better moment matching accuracy and convergence speed than EKF. For the problem of integrated navigation filtering with higher state dimension, volumetric Kalman filter (CKF) has better stability than UKF.

Due to the use of limited deterministic sampling points, which cannot match the overall probability distribution function of the state model, the estimation of CKF is often too optimistic, that is, its variance value is too small. The prior art does not consider the influence of the nonlinearity of the measurement model on the filter update, and assumes that the second moment of the random variable in the Gaussian approximation process can be accurately matched, ignoring the influence of the system uncertainty on the state estimation model.

Summary of the invention

In order to overcome the shortcomings of the prior art, the present invention proposes a data-driven high-precision integrated navigation data fusion method, which approximates model errors based on IMU (Inertial Measurement Unit) raw data, realizes accurate estimation of integrated system navigation parameters, and improves The robustness of the CKF combined filtering algorithm is improved.

In order to achieve the above-mentioned objective, the technical solution adopted by the present invention is as follows:

A data-driven high-precision integrated navigation data fusion method. When the integrated navigation system is working normally, the navigation parameters and sampling points are recursively updated based on the data of multi-source heterogeneous sensors; when the integrated navigation system is interfered, the sampling point error propagation model The integrated navigation system is provided with continuous auxiliary measurement updates, and the sampling point error propagation model uses an extreme learning machine combined with the original data of the inertial measurement unit to update the sampling points.

Further, the input of the extreme learning machine is the priori prediction distribution information of the state model, the output angle increment of the sky gyro and the travel direction ratio, and the output is the posterior sampling point error matrix.

Furthermore, the prior prediction distribution information includes a sampling point prediction error matrix

with

Furthermore, the

among them

Is the sampling point prediction matrix of the system function,

Is the mean value of the state prior distribution.

Furthermore, the

among them

Is the sampling point prediction matrix of the measurement function,

Is the mean value of the likelihood function.

Furthermore, the state prior distribution and likelihood function are calculated by using Gaussian process integral moment matching GPQMT.

Further, the input parameter frequency of the extreme learning machine is asynchronous data, and the output parameter frequency can be selected as any one of the input parameter frequencies.

Further, the training process of the sampling point error propagation model is as follows:

Is the input variable, γ=1,...,2n,

Is the output variable; where

Is the output angle increment of the sky gyro at time k,

Is the specific output of the direction of travel of the carrier at time k,

All are the sampling point prediction error matrix, n is the state dimension of the integrated navigation system;

The sampling point error propagation model takes the following form:

1≤j≤N, where ρ _i is the network output weight, N=2n is the number of CKF sampling points, φ _i is the input weight connecting the input variable and the hidden layer node, b _i is the bias, and M is the hidden layer The number of nodes; the above formula is written as a matrix with Hρ = Π, where ρ = (ρ ₁ ,...,ρ _M ) is the weight connecting the hidden layer nodes with the network output, and Π = (Π ₁ … Π _N ) is the sample Output variables:

The training process of the extreme learning machine keeps the randomly generated initial input weights and biases unchanged. The unknown network output weight ρ is obtained by solving the solution ρ = H ⁺ Π under the minimum mean square error, where H ⁺ is the generalized matrix H inverse.

The present invention provides a data-driven high-precision integrated navigation data fusion method, which has the following beneficial effects compared with the prior art:

(1) In order to overcome the defect of low variance estimation accuracy of Gaussian filtering model, the present invention proposes a sampling point prediction error generation method based on Gaussian process integral moment matching (GPQMT), which improves the sampling point generation during the training process of the sampling point error propagation model The quality of the state prior distribution and the variance estimation accuracy of the likelihood function are further improved.

(2) In order to improve the filter output continuity and stability of the integrated navigation system, the present invention proposes a data-driven transformation of the sampling point error matrix to update the sampling points, which improves the efficiency of non-linear measurement updates and improves the state posterior distribution Update frequency.

(3) The present invention obtains the sampling point prediction error matrix

with

The output angle increment of the sky gyro in the integrated navigation system and the specific force of the carrier travel direction are used as the input variables of the sampling point error propagation model, which realizes the direct coupling of the sampling point update and the unobservable state quantity, and the system model moment is directly based on the sensor data The approximation of the matching error improves the robustness of the parameterized model of the integrated navigation system.

Description of the drawings

Figure 1 is a flow chart of data-driven sampling point update of the present invention;

Fig. 2 is a flowchart of sampling point error conversion based on ELM of the present invention.

Detailed ways

The present invention will be further explained below in conjunction with the accompanying drawings.

A data-driven high-precision integrated navigation data fusion method. When the integrated navigation system is working normally, the navigation parameters and sampling points are recursively updated based on the data of multi-source heterogeneous sensors; when the integrated navigation system is interfered, the Gaussian process is used to achieve the combination The accurate estimation of the posterior distribution of navigation parameters of the navigation system and the realization of the data-driven transformation of the sampling point error matrix. The process of the data-driven transformation of the sampling point error matrix includes: After the integrated navigation system is powered on, it is performed at time t _k <t _n Fitting of the sampling point error propagation model; when t _k > t _n , the model error is approximated based on the original IMU data, and the sampling point error matrix is predicted.

The specific process is as follows:

Step (1), sampling point prediction error matrix calculation

As shown in Figure 1, when t _k <t _n , firstly, the volume point vector Θ _{k is} initialized by the CKF sampling point generation method, and the integrated navigation system function f(x _k-1 ) and the measurement function h(x _k ) Is calculated to obtain the sampling point prediction matrix

with

Then, get the state prior distribution based on GPQMT

And likelihood function

P _k|k-1 represents the mean and variance of the state prior distribution,

Represents the mean and variance of the likelihood function, where Z _k-1 = z _{1: k-1} is the measurement sequence of the combined system up to time k-1; finally, the sampling point prediction error matrix is calculated

with

The implementation process of the GPQMT is as follows: suppose that the system model of the integrated navigation system includes a system function x _k =f(x _k-1 )+w _k and a measurement function z _k =h(x _k )+v _k , w _k , v _k is the system noise and the measurement noise respectively. The above equation is defined as a unified form y _i =g(x _i )+ε _i , GPQMT is based on the known data set D = {X:=[x ₁ ,...,x _N ] ^T ,Y:=[y ₁ ,…,y _N ]} infer the posterior distribution of the function g, where

Represents the mapping from n-dimensional real number space to 1-dimensional real number space, and

σ _ε is the standard deviation of the model noise; set

It is a Gaussian random variable with known statistical properties, and then based on the posterior distribution of the function g to _{predict the value of the g(x *} ) function; X:=[x ₁ ,...,x _N ] ^T is the set of sampling points, y:= [y ₁ ,...,y _N ] is the set of instantiated values of the corresponding function g, and N=2n is the number of CKF sampling points. The following takes the approximation of the system function f(x _k-1 ) as an example to describe the estimation process of the posterior distribution of the function. Set the training dimension index as a, a=1,...,N, then there is a mean value for the a-th dimension variable :

among them

i and j represent the point index of the training data set of the integrated navigation system, i≠j, i,j=1,...,N, I is the n-dimensional unit matrix, and y _a is the expected target of the a-th dimension variable for Gaussian process training,

Is the noise variance generated by fitting the system equation,

The kernel function of the a-th dimension state variable propagated through f(x _{k-1 );}

Is the hyperparameter of the kernel function, which represents the signal variance of the a-th dimension state variable,

Where l _f,i are the length scaling factors, i=1,...,N. Choose the same kernel function parameters for different state dimensions of f(x _{k-1 ), namely}

Similarly, the variance of the a-th dimension state variable has:

among them

When calculating the variance between the a-th dimension state variable and the b-th dimension state variable, the off-diagonal element of the posterior variance is calculated;

Suppose the variance of the system noise w _k _{is Q k} , then

That is, the diagonal elements of the posterior variance are generated, and the posterior variance generated based on GPQMT can be obtained by comprehensive formula (5).

Similarly, construct the kernel function of the a-th dimension state variable of _{h(x k)}

Is the hyperparameter of the kernel function, which represents the signal variance of the a-th dimension state variable. Based on equations (1), (3) and (5), the estimated value of the posterior moment predicted _{by h(x k) can be obtained, and then the measurement} The variance of noise R _k can be obtained

Choose the same kernel function parameters for different state dimensions of h(x _{k ), namely}

When predicting the _{posterior distribution of f(x k-1} ) and h(x _k ), choose different hyperparameter sets θ _f :={k _f ,α _f ,l _f,i }, θ _h :={k _h ,α _h ,l _h,i }.

Step (2), training and prediction of sampling point error propagation model

First, based on the CKF filtering framework and the volume point vector Θ _k , the predicted covariance matrix of the joint probability distribution of navigation parameters

The mean and variance of the state posterior distribution are

P _k|k , and calculate the posterior sampling point error matrix

as follows:

Inertial measurement unit (IMU) sky gyro output angle increment

Specific force output in the direction of carrier travel

Is the input variable, with

The sampling point error matrix transfer function Τ(Ξ) is fitted for the expected output, where the subscript s1 indicates that the current error matrix is the posterior information of the training phase. Secondly, when t _k > t _N , the sampling point error matrix is predicted, and the steps are shown by the dotted line in Figure 2: 1)

As the input variable of the prediction model, the posterior propagation error matrix of the sampling point at time _{t k is predicted}

The subscript s2 indicates that the current error matrix is the posterior information of the prediction phase; 2) The mean and variance of the posterior distribution of the state variable calculated by CKF are

P _k|k , a posterior sampling point error matrix with IMU output frequency 200Hz

Prediction and the posterior distribution of 5Hz output

Make corrections; 3) change

versus

Add up to get the sampling point at _{t k+1}

Then complete the initialization of the sampling points of the next filtering period and the calculation of the error matrix of the predicted sampling points.

The training and prediction process of the sampling point error propagation model (that is, the transfer function Τ(Ξ)) is implemented by an extreme learning machine (ELM), and its content is:

Is the input variable, γ=1,...,2n,

The output variable is the posterior sampling point error matrix. Assuming that the number of learning samples is N=2n, that is, the number of CKF sampling points, a single hidden layer feedforward neural network (extreme learning machine) with M hidden layer nodes can be expressed as:

Where ρ _i is the network output weight, φ _i is the input weight connecting the input variable and the hidden layer node, and b _i is the bias; the above formula is written as a compact matrix with Hρ=Π, where ρ=(ρ ₁ ,... ,ρ _M ) is the weight connecting the hidden layer node and the network output, Π = (Π ₁ ,...,Π _N ) is the sample output variable:

The ELM training process keeps the randomly generated initial input weights and biases unchanged. The unknown network output weights ρ can be obtained by solving the solution ρ = H ⁺ Π under the minimum mean square error, where H ⁺ is the generalized inverse of matrix H . After the training process completes the calculation of the network output weights, when the model is working in the prediction mode, the input variable Ξ can get the predicted sampling point error matrix output

γ=1,...,2n.

based on

with

The output angle increment of the sky gyro in the integrated navigation system and the specific force of the carrier travel direction are used as the input variables of the sampling point error propagation model, which realizes the direct coupling between the sampling point update and the unobservable state quantity, and the system model is directly based on the sensor data (System function f(x _k-1 ) and measurement function h(x _k )) The approximation of the moment matching error improves the robustness of the parameterized model of the integrated navigation system.

The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications are also It should be regarded as the protection scope of the present invention.

Claims

A data-driven high-precision integrated navigation data fusion method, characterized in that: when the integrated navigation system is working normally, navigation parameters and sampling points are recursively updated based on the data of multi-source heterogeneous sensors; when the integrated navigation system is disturbed, sampling The point error propagation model provides continuous auxiliary measurement updates to the integrated navigation system, and the sampling point error propagation model uses an extreme learning machine combined with the original data of the inertial measurement unit to update the sampling points.
The data-driven high-precision integrated navigation data fusion method according to claim 1, characterized in that: the input of the extreme learning machine is a priori prediction distribution information of the state model, the gyro output angle increment and the travel direction ratio The output is the posterior sampling point error matrix.
The data-driven high-precision integrated navigation data fusion method according to claim 2, wherein the a priori prediction distribution information includes a sampling point prediction error matrix
with
The data-driven high-precision integrated navigation data fusion method according to claim 3, characterized in that:
among them
Is the sampling point prediction matrix of the system function,
Is the mean value of the state prior distribution.
The data-driven high-precision integrated navigation data fusion method according to claim 3, characterized in that:
among them
Is the sampling point prediction matrix of the measurement function,
Is the mean value of the likelihood function.
The data-driven high-precision integrated navigation data fusion method according to claim 4 or 5, wherein the state prior distribution and the likelihood function are calculated by using Gaussian process integral moment matching GPQMT.
The data-driven high-precision integrated navigation data fusion method according to claim 2, wherein the input parameter frequency of the extreme learning machine is asynchronous data, and the output parameter frequency can be selected as any one of the input parameter frequencies.
The data-driven high-precision integrated navigation data fusion method according to claim 1, wherein the training process of the sampling point error propagation model is:
Is the input variable, γ=1,...,2n,
Is the output variable; where
Is the output angle increment of the sky gyro at time k,
Is the specific output of the direction of travel of the carrier at time k,
All are the sampling point prediction error matrix, n is the state dimension of the integrated navigation system;

The sampling point error propagation model takes the following form:
Where ρ i is the network output weight, N=2n is the number of CKF sampling points, φ i is the input weight connecting the input variable and the hidden layer node, b i is the bias, and M is the number of hidden layer nodes; The formula is written as a matrix with Hρ=Π, where ρ=(ρ 1 ,...,ρ M ) is the weight connecting the hidden layer node and the network output, and Π = (Π 1 … Π N ) is the sample output variable:

The training process of the extreme learning machine keeps the randomly generated initial input weights and biases unchanged. The unknown network output weight ρ is obtained by solving the solution ρ = H + Π under the minimum mean square error, where H + is the generalized matrix H inverse.