CN109000640B - Vehicle GNSS/INS integrated navigation method based on discrete grey neural network model - Google Patents

Abstract

The invention discloses a vehicle GNSS/INS integrated navigation method based on a discrete gray neural network model, comprising the following steps: S1: According to the angular increment and specific force output by a micro-inertial device, use an inertial navigation numerical update algorithm to solve the Attitude, speed and position; S2: Establish a discrete grayscale prediction model based on DGM(1,1); S3: Improve multi-layer neural network MLP; S4: Design a hybrid intelligent prediction algorithm DGM‑MLP based on discrete grayscale neural network; S5: The inertial navigation error equation is used as the state equation, the difference between the position calculated by the INS and the position of the GNSS is the observation value, or the difference between the position calculated by the INS and the pseudo GNSS position is the observation value, and the KF is used for the integrated navigation. The system performs state estimation; S6: The position, velocity and attitude errors obtained by the KF estimation of the Kalman filter are used for output correction of the inertial navigation solution results, and the gyro and table errors are used for feedback correction of the inertial navigation. The present invention can effectively solve the problem of reduced navigation accuracy when the GNSS signal fails.

Description

Vehicle GNSS/INS Integrated Navigation Method Based on Discrete Grey Neural Network Model

technical field

The invention relates to a vehicle integrated navigation technology, in particular to a vehicle GNSS/INS integrated navigation method based on a discrete gray neural network model.

Background technique

The integrated navigation system of MEMS-INS/GNSS has been more and more widely used due to its advantages of low cost and miniaturization, but the GNSS signal is easily blocked by tall buildings, bridges or tunnel lights and fails. When the GNSS signal fails, the integrated navigation system is in the state of pure inertial navigation. Due to the low accuracy of the MEMS-INS, the solution results will rapidly decrease or even diverge. In order to improve the navigation accuracy when the GNSS signal fails and ensure the reliability of the system, the main methods are as follows:

1. Adding additional sensors, such as machine vision and Doppler speedometer, this method can effectively improve the navigation accuracy, but it will lead to higher system cost and is not easy to integrate.

2. Add constraints, such as assuming that the vehicle lateral and sky velocities are zero to limit the rapid divergence of inertial navigation errors. This method is simple to implement, but has limited accuracy, and is only suitable for specific operating paths.

3. Improve the filtering algorithm. This method has a good effect in a short period of time when GNSS fails, but has limited effect when it is invalid for a long time.

4. Prediction through artificial intelligence algorithms, such as neural networks. This method requires more training samples, and the low-cost MEMS-based neural network model has low accuracy.

SUMMARY OF THE INVENTION

Purpose of the invention: The present invention proposes a vehicle GNSS/INS integrated navigation method based on a discrete gray neural network model, aiming at the problem of reduced navigation accuracy when the GNSS signal fails.

Technical scheme: in order to achieve this purpose, the present invention adopts the following technical scheme:

The vehicle GNSS/INS integrated navigation method based on the discrete grey neural network model according to the present invention comprises the following steps:

S1: According to the angular increment and specific force output by the micro-inertial device, use the inertial navigation numerical update algorithm to calculate the attitude, speed and position of the vehicle;

S2: Establish a discrete grayscale prediction model based on DGM(1,1);

S3: Improve multi-layer neural network MLP;

S4: Design a hybrid intelligent prediction algorithm DGM-MLP based on discrete grayscale neural network. When the GNSS signal is valid, use the DGM-MLP to train the GNSS position; when the GNSS signal is invalid, use the DGM-MLP to perform the GNSS position training. Predict, get pseudo GNSS position information;

S5: The inertial navigation error equation is used as the state equation, the difference between the position calculated by the INS and the position of the GNSS is the observation value, or the difference between the position calculated by the INS and the pseudo GNSS position is the observation value, and the KF is used for the integrated navigation. The system performs state estimation;

S6: The position, velocity and attitude errors estimated by the KF KF filter are used for output correction of the inertial navigation solution results, and the gyro and table errors are used for feedback correction of the inertial navigation.

Further, the step S1 specifically includes the following process: the INS uses a three-axis accelerometer and a three-axis gyroscope to measure the specific force and angular increment of the carrier, and calculates the navigation information of the carrier at the current moment according to the initial conditions; the navigation coordinate system n adopts The northeast sky geographic coordinate system, the carrier coordinate system b adopts the upper right coordinate system; the error differential equation of the INS includes the attitude error differential equation, the velocity error differential equation and the position error differential equation, as shown in equations (1)-(3) respectively. :

为 地球自转引起的旋转角速度，

为地球自转引起的旋转角速度的误差；

为载 体运动产生的位移角速度，

为载体运动产生的位移角速度的误差；εⁿ为陀螺漂 移在导航坐标系n系下的投影；Equation (1) is the attitude error differential equation, where ψ ⁿ =[ψ _E ψ _N ψ _U ] ^T is the attitude angle error in the navigation coordinate system n, ψ _E is the pitch angle error, and ψ _N is the roll angle error, ψ _U is the heading angle error,

is the angular velocity of rotation caused by the rotation of the earth,

is the error of the rotational angular velocity caused by the earth's rotation;

is the displacement angular velocity generated by the movement of the carrier,

is the error of the displacement angular velocity generated by the movement of the carrier; ε ⁿ is the projection of the gyro drift in the navigation coordinate system n;

Equation (2) is the velocity error differential equation, where V ⁿ =[V _E V _N V _U ] ^T is the velocity vector, V _E is the east velocity, V _N is the north velocity, V _U is the sky velocity, δV ⁿ is the velocity error; f ⁿ is the specific force vector; ▽ ⁿ is the projection of the accelerometer drift in the navigation coordinate system n;

Equation (3) is the position error differential equation, where L is the latitude, λ is the longitude, h is the height, δL is the latitude error, δλ is the longitude error, δh is the height error, R _E is the main radius of curvature of the unitary circle, R _N is the main curvature radius of the meridian circle, δV _N is the velocity error in the north direction, δV _E is the velocity error in the east direction, and δV _U is the velocity error in the sky direction.

Further, the step S2 specifically includes the following processes:

S2.1: Preprocessing raw data

Convert the original data into a non-negative sequence by formula (4);

X ⁽⁰⁾ = {x ⁽⁰⁾ (1),x ⁽⁰⁾ (2),…,x ⁽⁰⁾ (n)}(4)

In formula (4), X ^{(0) is} a non-negative number sequence, x ⁽⁰⁾ (k) is the kth number in X ⁽⁰⁾ , k=1,2,...,n, n is the original data length;

S2.2: Cumulative generation number

X ⁽¹⁾ is obtained by using an accumulation generation sequence, namely:

X ⁽¹⁾ = {x ⁽¹⁾ (1),x ⁽¹⁾ (2),…,x ⁽¹⁾ (n)}(5)

In formula (5),

S2.3: Establish a discrete grayscale prediction model based on DGM(1,1)

The discrete grayscale prediction model based on DGM(1,1) is established by formula (6):

为第l+1个数据的累加估计值，

为第l个数据的累 加估计值，U₁为一次项系数，U₂为常数偏值，l＝1,2,…,n,…,n+m-1，m为预测 数列长度，m≥1；In formula (6),

is the cumulative estimated value of the l+1th data,

is the accumulated estimated value of the lth data, U ₁ is the first-order coefficient, U ₂ is the constant bias value, l=1,2,…,n,…,n+m-1, m is the length of the predicted sequence, m≥ 1;

为参数列，且结合式(7)，则式(6)的最小二乘估计参数列满 足式(8)的条件；like

is a parameter sequence, and combined with formula (7), the least squares estimation parameter sequence of formula (6) satisfies the condition of formula (8);

S2.4: Inverse cumulative generation number

则还原值为：Pick

The restore value is:

为第l+1个数据的还原值；In formula (9),

is the restored value of the l+1th data;

The predicted value of the discrete grayscale prediction model can be obtained by subtracting the constant added from the original data from the restored value.

Further, the step S3 specifically includes the following processes:

S3.1: Introduce the momentum term, as shown in equations (10) and (11):

In formula (10), ω _{H, t+1} is the weight of the hidden layer at time t+1, ω _{H, t} is the weight of the hidden layer at time t, E _t is the error at time t, ω _{H, t-1} is the weight of the hidden layer at time t-1, η is the momentum factor, 0≤η≤1;

In formula (11), b _{H, t+1} is the bias value of the hidden layer at time t+1, b _{H, t} is the bias value of the hidden layer at time t, and b _{H, t-1} is the bias value of the hidden layer at time t-1. Bias value;

S3.2: Calculate according to formulas (12)-(13):

In formula (12), Δp _t is the adjustment amount of the weight or bias value at time t, p _t is the weight value or bias value at time t, p _t-1 is the weight value or bias value at time t-1, a> 0, b>0;

p _t ′=p _t +Δp _t (13)

In formula (13), p _t ' is the updated value of the weight or bias value at time t.

Further, the step S4 specifically includes the following processes:

则定义时刻T的残差为e⁽⁰⁾(T)，即

建立残差序列{e⁽⁰⁾(T)}的MLP网络模型，若S为预测阶 数，则MLP网络训练的输入样本为e⁽⁰⁾(k-1),e⁽⁰⁾(k-2),…,e⁽⁰⁾(k-S)，e⁽⁰⁾(k)为网 络的对应输出样本；When the GNSS signal is valid, the whole system is in the training mode; set the GNSS position information sequence to be {x ⁽⁰⁾ (k)}, k=1,2,...,n after preprocessing, use the DGM(1,1) model to it predicts

Then define the residual at time T as e ⁽⁰⁾ (T), that is,

Establish the MLP network model of the residual sequence {e ⁽⁰⁾ (T)}, if S is the prediction order, the input samples of the MLP network training are e ⁽⁰⁾ (k-1), e ⁽⁰⁾ (k- 2),...,e ⁽⁰⁾ (kS), e ⁽⁰⁾ (k) is the corresponding output sample of the network;

利用这一预测值构造所得预测值

将预测值

减去原始数据所加的常数就是离散灰 色神经网络模型的预测值。When the GNSS signal is invalid, the whole system is in prediction mode; the residual sequence predicted by the MLP network training model is

Use this predicted value to construct the resulting predicted value

the predicted value

The constant added by subtracting the original data is the predicted value of the discrete gray neural network model.

Further, the step S5 specifically includes the following processes:

S5.1: The discretized state equation is obtained by formula (14), and the discretized measurement equation is obtained by formula (15):

X _t =F _t,t-1 X _t-1 +G _t W _t (14)

In formula (14), X _t is the state value at time t, X _t-1 is the state value at time t-1, F _{t, t-1} is the system state transition matrix from time t-1 to time t; G _t is the noise allocation matrix at time t; W _t is the system noise at time t;

Z _t =H _t X _t +V _t (15)

In formula (15), Z _t is the observation quantity at time t, H _t is the observation matrix at time t, and V _t is the measurement noise at time t;

S5.2: Kalman filter includes time update and measurement update, as shown in equations (16)-(20):

为t-1时刻到t时刻状态量的更新值，

为t时刻的状态估计值，P_t,t-1为t-1时刻到t时刻协方差矩阵的更新值，P_t为t时刻的协方差矩阵，P_t-1为t-1时刻 的协方差矩阵，Q_t-1为t-1时刻的系统噪声矩阵，R_t为t时刻的量测噪声矩阵，K_t为t 时刻的增益矩阵。in,

is the update value of the state quantity from time t-1 to time t,

is the estimated state value at time t, P _t,t-1 is the updated value of the covariance matrix from time t-1 to time t, P _t is the covariance matrix at time t, and P _t-1 is the covariance matrix at time t-1 Variance matrix, Q _t-1 is the system noise matrix at time t-1, R _t is the measurement noise matrix at time t, and K _t is the gain matrix at time t.

Beneficial effects: The present invention discloses a vehicle GNSS/INS integrated navigation method based on a discrete gray neural network model, and compared with the prior art, the present invention has the following beneficial effects:

1) The present invention can effectively solve the problem of reduced navigation accuracy caused by tall buildings and tunnel lights blocking satellite signals;

2) The present invention does not need to introduce additional sensors, the calculation amount is small, the required training samples are few, and the implementation is simple.

Description of drawings

Fig. 1 is the training mode block diagram of the integrated navigation system when the GNSS signal is effective in the specific embodiment of the present invention;

Fig. 2 is a block diagram of the training mode of the integrated navigation system when the GNSS signal is invalid in the specific embodiment of the present invention.

Detailed ways

The technical solutions of the present invention will be further introduced below with reference to the specific embodiments and the accompanying drawings.

This specific embodiment discloses a vehicle GNSS/INS integrated navigation method based on a discrete gray neural network model, including the following steps:

S1: According to the angular increment and specific force output by the micro-inertial device, use the inertial navigation numerical update algorithm to calculate the attitude, speed and position of the vehicle;

S2: Establish a discrete grayscale prediction model based on DGM(1,1);

S3: Improve multi-layer neural network MLP;

S4: Design a hybrid intelligent prediction algorithm DGM-MLP based on discrete grayscale neural network. When the GNSS signal is valid, the DGM-MLP is used to train the GNSS position; when the GNSS signal is invalid, the DGM-MLP is used to train the GNSS position. Predict, get pseudo GNSS position information;

S5: The inertial navigation error equation is used as the state equation, the difference between the position calculated by the INS and the position of the GNSS is the observation value, or the difference between the position calculated by the INS and the pseudo GNSS position is the observation value, and the KF is used for the integrated navigation. The system performs state estimation;

S6: The position, velocity and attitude errors estimated by the KF KF filter are used for output correction of the inertial navigation solution results, and the gyro and table errors are used for feedback correction of the inertial navigation.

Step S1 specifically includes the following process: the INS uses a three-axis accelerometer and a three-axis gyroscope to measure the specific force and angular increment of the carrier, and calculates the navigation information of the carrier at the current moment according to the initial conditions; the navigation coordinate system n adopts the geographic coordinates of the northeast sky. The carrier coordinate system b adopts the upper right coordinate system; the error differential equation of the INS includes the attitude error differential equation, the velocity error differential equation and the position error differential equation, as shown in equations (1)-(3) respectively:

为 地球自转引起的旋转角速度，

为地球自转引起的旋转角速度的误差；

为载 体运动产生的位移角速度，

为载体运动产生的位移角速度的误差；εⁿ为陀螺漂 移在导航坐标系n系下的投影；Equation (1) is the attitude error differential equation, where ψ ⁿ =[ψ _E ψ _N ψ _U ] ^T is the attitude angle error in the navigation coordinate system n, ψ _E is the pitch angle error, and ψ _N is the roll angle error, ψ _U is the heading angle error,

is the angular velocity of rotation caused by the rotation of the earth,

is the error of the rotational angular velocity caused by the earth's rotation;

is the displacement angular velocity generated by the movement of the carrier,

is the error of the displacement angular velocity generated by the movement of the carrier; ε ⁿ is the projection of the gyro drift in the navigation coordinate system n;

Equation (2) is the velocity error differential equation, where V ⁿ =[V _E V _N V _U ] ^T is the velocity vector, V _E is the east velocity, V _N is the north velocity, V _U is the sky velocity, δV ⁿ is the velocity error; f ⁿ is the specific force vector; ▽ ⁿ is the projection of the accelerometer drift in the navigation coordinate system n;

Equation (3) is the position error differential equation, where L is the latitude, λ is the longitude, h is the height, δL is the latitude error, δλ is the longitude error, δh is the height error, R _E is the main radius of curvature of the unitary circle, R _N is the main curvature radius of the meridian circle, δV _N is the velocity error in the north direction, δV _E is the velocity error in the east direction, and δV _U is the velocity error in the sky direction.

Step S2 specifically includes the following processes:

S2.1: Preprocessing raw data

Convert the original data into a non-negative sequence by formula (4);

X ⁽⁰⁾ = {x ⁽⁰⁾ (1),x ⁽⁰⁾ (2),…,x ⁽⁰⁾ (n)}(4)

In formula (4), X ^{(0) is} a non-negative number sequence, x ⁽⁰⁾ (k) is the kth number in X ⁽⁰⁾ , k=1,2,...,n, n is the original data length;

S2.2: Cumulative generation number

X ⁽¹⁾ is obtained by using an accumulation generation sequence, namely:

X ⁽¹⁾ = {x ⁽¹⁾ (1),x ⁽¹⁾ (2),…,x ⁽¹⁾ (n)}(5)

In formula (5),

S2.3: Establish a discrete grayscale prediction model based on DGM(1,1)

The discrete grayscale prediction model based on DGM(1,1) is established by formula (6):

为第l+1个数据的累加估计值，

为第l个数据的累 加估计值，U₁为一次项系数，U₂为常数偏值，l＝1,2,…,n,…,n+m-1，m为预测 数列长度，m≥1；In formula (6),

is the cumulative estimated value of the l+1th data,

is the accumulated estimated value of the lth data, U ₁ is the first-order coefficient, U ₂ is the constant bias value, l=1,2,…,n,…,n+m-1, m is the length of the predicted sequence, m≥ 1;

为参数列，且结合式(7)，则式(6)的最小二乘估计参数列满 足式(8)的条件；like

is a parameter sequence, and combined with formula (7), the least squares estimation parameter sequence of formula (6) satisfies the condition of formula (8);

S2.4: Inverse cumulative generation number

则还原值为：Pick

The restore value is:

为第l+1个数据的还原值；In formula (9),

is the restored value of the l+1th data;

The predicted value of the discrete grayscale prediction model can be obtained by subtracting the constant added from the original data from the restored value.

Step S3 specifically includes the following processes:

S3.1: Introduce the momentum term, as shown in equations (10) and (11):

In formula (10), ω _{H, t+1} is the weight of the hidden layer at time t+1, ω _{H, t} is the weight of the hidden layer at time t, E _t is the error at time t, ω _{H, t-1} is the weight of the hidden layer at time t-1, η is the momentum factor, 0≤η≤1;

In formula (11), b _{H, t+1} is the bias value of the hidden layer at time t+1, b _{H, t} is the bias value of the hidden layer at time t, and b _{H, t-1} is the bias value of the hidden layer at time t-1. Bias value;

S3.2: Calculate according to formulas (12)-(13):

In formula (12), Δp _t is the adjustment amount of the weight or bias value at time t, p _t is the weight value or bias value at time t, p _t-1 is the weight value or bias value at time t-1, a> 0, b>0;

p _t ′=p _t +Δp _t (13)

In formula (13), p _t ' is the updated value of the weight or bias value at time t.

Step S4 specifically includes the following processes:

则定义时刻T的残差为e⁽⁰⁾(T)，即

建立残差序列{e⁽⁰⁾(T)}的MLP网络模型，若S为预测阶 数，则MLP网络训练的输入样本为e⁽⁰⁾(k-1),e⁽⁰⁾(k-2),…,e⁽⁰⁾(k-S)，e⁽⁰⁾(k)为网 络的对应输出样本；When the GNSS signal is valid, the whole system is in the training mode, as shown in Figure 1; the GNSS position information sequence is preprocessed as {x ⁽⁰⁾ (k)}, k=1,2,...,n, using DGM ( 1,1) The model predicts it

Then define the residual at time T as e ⁽⁰⁾ (T), that is,

Establish the MLP network model of the residual sequence {e ⁽⁰⁾ (T)}, if S is the prediction order, the input samples of the MLP network training are e ⁽⁰⁾ (k-1), e ⁽⁰⁾ (k- 2),...,e ⁽⁰⁾ (kS), e ⁽⁰⁾ (k) is the corresponding output sample of the network;

利用这一预测值构造所得预测值

将预测值

减去原始数据所加的常数就是离散灰 色神经网络模型的预测值。When the GNSS signal is invalid, the whole system is in prediction mode, as shown in Figure 2; the residual sequence predicted by the MLP network training model is

Use this predicted value to construct the resulting predicted value

the predicted value

The constant added by subtracting the original data is the predicted value of the discrete gray neural network model.

Step S5 specifically includes the following processes:

S5.1: The discretized state equation is obtained by formula (14), and the discretized measurement equation is obtained by formula (15):

X _t =F _t,t-1 X _t-1 +G _t W _t (14)

In formula (14), X _t is the state value at time t, X _t-1 is the state value at time t-1, F _{t, t-1} is the system state transition matrix from time t-1 to time t; G _t is the noise allocation matrix at time t; W _t is the system noise at time t;

Z _t =H _t X _t +V _t (15)

In formula (15), Z _t is the observation quantity at time t, H _t is the observation matrix at time t, and V _t is the measurement noise at time t;

S5.2: Kalman filter includes time update and measurement update, as shown in equations (16)-(20):

为t-1时刻到t时刻状态量的更新值，

为t时刻的状态估计值，P_t,t-1为t-1时刻到t时刻协方差矩阵的更新值，P_t为t时刻的协方差矩阵，P_t-1为t-1时刻 的协方差矩阵，Q_t-1为t-1时刻的系统噪声矩阵，R_t为t时刻的量测噪声矩阵，K_t为t 时刻的增益矩阵。in,

is the update value of the state quantity from time t-1 to time t,

is the estimated state value at time t, P _t,t-1 is the updated value of the covariance matrix from time t-1 to time t, P _t is the covariance matrix at time t, and P _t-1 is the covariance matrix at time t-1 Variance matrix, Q _t-1 is the system noise matrix at time t-1, R _t is the measurement noise matrix at time t, and K _t is the gain matrix at time t.

Claims (4)

1. The vehicle GNSS/INS combined navigation method based on the discrete grey neural network model is characterized in that: the method comprises the following steps:

s1: calculating the attitude, the speed and the position of the vehicle by using an inertial navigation numerical value updating algorithm according to the angular increment and the specific force output by the micro inertial device;

s2: establishing a discrete gray prediction model based on DGM (1, 1);

s3: improving a multilayer neural network (MLP);

s4: designing a DGM-MLP (hybrid intelligent prediction algorithm) based on a discrete gray neural network, and training the position of the GNSS by using the DGM-MLP when the GNSS signal is effective; when the GNSS signal is invalid, predicting the position of the GNSS by utilizing the DGM-MLP to obtain pseudo GNSS position information;

s5: taking an inertial navigation error equation as a state equation, taking the difference between the position solved by the INS and the position of the GNSS as an observed quantity or taking the difference between the position solved by the INS and the position of the pseudo GNSS as an observed quantity, and carrying out state estimation on the combined navigation system by utilizing a Kalman filter KF;

s6: the position, speed and attitude errors obtained by Kalman filter KF estimation carry out output correction on the inertial navigation resolving result, and the gyroscope and adding table errors carry out feedback correction on the inertial navigation;

wherein, the step S3 specifically includes the following processes:

s3.1: momentum terms are introduced, and are shown in a formula (10) and a formula (11):

in the formula (10), ω_H,t+1Is the weight of the hidden layer at the time of t +1, omega_H,tIs the weight of the hidden layer at time t, E_tIs time tError of (a), ω_H,t-1Is the weight of the hidden layer at the time t-1, eta is a momentum factor, and eta is more than or equal to 0 and less than or equal to 1;

in the formula (11), b_H,t+1Is the bias of the hidden layer at time t +1, b_H,tIs the bias of the hidden layer at time t, b_H,t-1Is the bias value of the hidden layer at the time of t-1;

s3.2: the calculation is performed according to equations (12) to (13):

in formula (12), Δ p_tIs the adjustment of the weight or bias at time t, p_tIs the weight or bias value at time t, p_t-1The weight value or the bias value at the moment t-1 is that a is more than 0 and b is more than 0;

p_t′＝p_t+Δp_t (13)

in the formula (13), p_t' is an updated value of the weight or the bias value at the time t;

wherein, the step S4 specifically includes the following processes:

when the GNSS signal is effective, the whole system is in a training mode; setting the GNSS position information sequence as { x after preprocessing⁽⁰⁾(k) 1,2, …, n, predicted by DGM (1,1) model

Then the residual error at time T is defined as e⁽⁰) (T) that is

Building a residual sequence e⁽⁰⁾(T) in the MLP network model, if S is the prediction order, the input sample of the MLP network training is e⁽⁰⁾(k-1),e⁽⁰⁾(k-2),…,e⁽⁰⁾(k-S)，e⁽⁰⁾(k) Corresponding output samples for the network;

when the GNSS signal is invalid, the whole system is in a prediction mode; the residual sequence predicted by the MLP network training model is

Constructing a resulting prediction value using this prediction value

Will predict the value

The constant added by subtracting the original data is the predicted value of the discrete grey neural network model.

2. The integrated GNSS/INS navigation method of a vehicle based on discrete gray neural network model as claimed in claim 1, wherein: the step S1 specifically includes the following steps: the INS measures the specific force and the angular increment of the carrier by using a triaxial accelerometer and a triaxial gyroscope, and calculates the navigation information of the carrier at the current moment according to the initial condition; the navigation coordinate system n adopts a northeast geographic coordinate system, and the carrier coordinate system b adopts a right-front upper coordinate system; the error differential equations of the INS include an attitude error differential equation, a velocity error differential equation, and a position error differential equation, which are respectively expressed by equations (1) to (3):

equation (1) is an attitude error differential equation, whereⁿ＝[ψ_E ψ_N ψ_U]^TFor attitude angle error in the navigation coordinate system n, psi_EFor pitch angle error, psi_NFor roll angle error, psi_UIn order to be the error of the course angle,

is the angular velocity of rotation caused by the rotation of the earth,

an error of a rotational angular velocity caused by rotation of the earth;

for the angular velocity of the displacement caused by the motion of the carrier,

error in displacement angular velocity for carrier motion; epsilonⁿThe projection of the gyro drift under a navigation coordinate system n system;

equation (2) is a velocity error differential equation, where Vⁿ＝[V_E V_N V_U]^TIs a velocity vector, V_EEast speed, V_NIs the north velocity, V_UIs the speed in the direction of the sky, delta VⁿIs the speed error; f. ofⁿIs a specific force vector;

projecting the accelerometer drift under a navigation coordinate system n;

equation (3) is a position error differential equation, where L is latitude, λ is longitude, h is altitude, δ L is latitude error, δ λ is longitude error, δ h is altitude error, R_EIs a major curvature radius of the fourth prime circle, R_NIs the radius of the meridian principal curvature, δ V_NFor north velocity error, δ V_EFor east velocity error, δ V_UIs the error in the speed in the direction of the day.

3. The integrated GNSS/INS navigation method of a vehicle based on discrete gray neural network model as claimed in claim 1, wherein: the step S2 specifically includes the following steps:

s2.1: preprocessing raw data

Converting original data into a non-negative sequence through an equation (4);

X⁽⁰⁾＝{x⁽⁰⁾(1),x⁽⁰⁾(2),…,x⁽⁰⁾(n)} (4)

in the formula (4), X⁽⁰⁾Is a non-negative sequence, x⁽⁰⁾(k) Is X⁽⁰⁾The number k in (1), 2, …, n, n is the original data length;

s2.2: accumulated to generate number

Generating a sequence using a one-time accumulation to obtain X⁽¹⁾Namely:

X⁽¹⁾＝{x⁽¹⁾(1),x⁽¹⁾(2),…,x⁽¹⁾(n)} (5)

in the formula (5), the reaction mixture is,

s2.3: building discrete gray prediction model based on DGM (1,1)

A discrete gray prediction model based on DGM (1,1) is established by the following formula (6):

in the formula (6), the reaction mixture is,

is the accumulated estimate of the (l + 1) th data,

for cumulative estimates of the I-th data, U₁Is a coefficient of a first order term, U₂Is constant bias value, l is 1,2, …, n, …, n + m-1, m is the length of the prediction sequence, m is more than or equal to 1;

if it is

Is the parameter sequence, and combines with equation (7), the least square estimation parameter sequence of equation (6) satisfies the condition of equation (8);

s2.4: inverse accumulation of the generated number

Get

The reduction value is then:

in the formula (9), the reaction mixture is,

is the reduction value of the l +1 th data;

and subtracting the constant added by the original data from the reduction value to obtain the prediction value of the discrete gray prediction model.

4. The integrated GNSS/INS navigation method of a vehicle based on discrete gray neural network model as claimed in claim 1, wherein: the step S5 specifically includes the following steps:

s5.1: the discretized state equation is obtained by equation (14), and the discretized measurement equation is obtained by equation (15):

X_t＝F_t,t-1X_t-1+G_tW_t (14)

in formula (14), X_tIs the value of the state at the time t,X_t-1is the state value at time t-1, F_t,t-1A system state transition matrix from the t-1 moment to the t moment; g_tDistributing a matrix for the noise at the time t; w_tSystem noise at time t;

Z_t＝H_tX_t+V_t (15)

in the formula (15), Z_tIs an observed quantity at time t, H_tIs an observation matrix at time t, V_tThe measurement noise at time t;

s5.2: the kalman filter includes time updates and measurement updates, as shown in equations (16) - (20):

wherein,

for the updated value of the state quantity from time t-1 to time t,

is a state estimate at time t, P_t,t-1Is t-1 orUpdate value of covariance matrix at moment t, P_tIs a covariance matrix at time t, P_t-1Is a covariance matrix, Q, at time t-1_t-1Is the system noise matrix at time t-1, R_tIs the measured noise matrix at time t, K_tIs the gain matrix at time t.

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