CN117516524A - GPS/INS Kalman filtering positioning method based on CNN-GRU prediction - Google Patents

Abstract

The invention relates to a GPS/INS Kalman filtering positioning method based on CNN-GRU prediction, and belongs to the technical field of positioning and navigation. The technical scheme is as follows: establishing an INS inertial navigation mechanized model; establishing a CNN-GRU neural network prediction model; establishing an integrated navigation extended Kalman filtering model, and carrying out data fusion on GNSS positioning information and INS positioning information to obtain a compensation value of the INS inertial navigation positioning information, thereby obtaining accurate positioning information; the GPS/INS Kalman filtering positioning model based on CNN-GRU prediction can improve the positioning precision to a greater extent when the GPS signal is interrupted. The invention combines the advantages that the CNN neural network can effectively automatically extract and learn the characteristics from the multidimensional sequence data and the problem that the GRU can use the historical data, has simple structure and few parameters, can effectively predict GNSS pseudo signals when the GNSS is interrupted, and further improves the navigation positioning accuracy.

Description

GPS/INS Kalman filtering positioning method based on CNN-GRU prediction

Technical Field

The invention relates to a GPS/INS Kalman filtering positioning method based on CNN-GRU prediction, in particular to algorithm optimization for predicting INS-GPS integrated navigation under the condition of poor GPS signal condition by using a neural network, and belongs to the technical field of positioning and navigation.

Background

With the rapid development of navigation technology, the requirements of various fields on navigation precision are higher and higher. Among them, inertial Navigation Systems (INS) based on microelectromechanical systems (MEMS) devices are widely used in the military field, and GNSS is widely used by people with its advantages of long-term high precision and low cost. In addition, the INS and the GNSS have good complementary characteristics, and on one hand, the high-precision measurement of the INS autonomous navigation system in a short period is realized; on the other hand, GNSS can keep good precision for a long time, and the combination of the GNSS and the GNSS can obtain a navigation scheme which is more stable and higher in precision than that of a single navigation system.

However, in integrated navigation systems, the level of MEMS devices and the quality of GPS satellite signals play a decisive role. Satellite signals are easily interfered in complex environments of high-rise buildings, trees and tunnels, at the moment, the GPS is interrupted, and the system enters a pure inertial navigation mode, so that the Kalman filter cannot accurately fuse multi-sensor information. In this case, a linear decrease in navigation ability results. In order to improve navigation accuracy, prediction during GPS outage has become a research hotspot.

Disclosure of Invention

The invention aims to provide a GPS/INS Kalman filtering positioning method based on CNN-GRU prediction, which utilizes a neural network method to generate pseudo GNSS signals when the problem of navigation accuracy reduction caused by GNSS lock loss possibly occurs under complex conditions, temporarily replaces original GNSS signals to ensure the navigation accuracy in the lock loss state, and solves the problems in the background technology.

The technical scheme of the invention is as follows:

a GPS/INS Kalman filtering positioning method based on CNN-GRU prediction comprises the following steps:

1) Establishing an INS inertial navigation mechanized model to obtain the position information of the INS at each moment;

2) Establishing a CNN-GRU neural network prediction model, rapidly extracting input characteristics by using CNN, and outputting a pseudo GPS signal by using a GRU network as a compensation object;

3) Establishing an integrated navigation extended Kalman filtering model, and obtaining a compensation value of INS inertial navigation positioning information by carrying out data fusion on GNSS positioning information and INS positioning information so as to obtain accurate positioning information;

4) The GPS/INS Kalman filtering positioning model based on CNN-GRU prediction can improve the positioning precision to a greater extent when the GPS signal is interrupted.

In the step 1), an INS mechanized module in the INS inertial navigation mechanized model calculates the attitude, the speed and the position of the aircraft or the vehicle by adopting a kinetic equation of inertial mechanization, wherein the three main parts comprise a common coordinate system, coordinate system conversion and an inertial navigation system updating algorithm, and the three main parts are as follows:

(1) common coordinate system

Common coordinate systems include an inertial coordinate system, a geocentric fixed coordinate system, a navigation coordinate system and a carrier coordinate system; the method comprises the following steps:

(1) Inertial coordinate system (i system)

The origin of the inertial coordinate system is the earth centroid, the x-axis corresponds to the spring branching line pointing to the earth, the z-axis points to the north pole, the y-axis is perpendicular to the xoz plane and meets the right-hand rule, the inertial coordinate system is static relative to the star, and the observed quantity measured by the inertial measurement device is relative to the inertial coordinate system;

(2) Geocentric earth fixed coordinate system (e system)

The origin of the geocentric earth fixed coordinate system is the earth centroid, the x-axis points to the zero meridian, the z-axis coincides with the earth rotation axis, the y-axis points to the east 90-degree meridian, and the xoy plane coincides with the earth equatorial plane;

(3) Navigation coordinate system (n system)

The navigation coordinate system is a geographic coordinate system, and typical geographic coordinate systems are an northeast (ENU) coordinate system and a Northeast (NED) coordinate system; the northeast-north-day coordinate system takes the mass center of the carrier as a coordinate origin, takes the local direction of the positive east as an x axis, the direction of the positive north as a y axis and the direction of the zenith as a z axis;

(4) Carrier coordinate system (b system)

The carrier coordinate system takes the center of mass of the carrier as an origin, the y axis points forward along the longitudinal axis of the carrier, the x axis points rightward along the transverse direction of the carrier, the z axis points above the carrier, and the three axes together form a right-hand rule;

(2) coordinate system conversion

(1) Conversion of inertial coordinate system to geocentric geodetic coordinate system

The rotation matrix of the inertial frame to the geocentric, fixed frame can be expressed as:

wherein t is time, ω _ie Is the earth rotation speed;

(2) Conversion of geocentric geodetic coordinate system to navigation coordinate system

The rotation matrix of the geocentric fixed coordinate system to the navigation coordinate system can be expressed as:

wherein λ represents the latitude of the origin of the carrier, and L represents the longitude of the origin of the carrier;

(3) Conversion of a carrier coordinate system into a navigation coordinate system

The relative relation between a carrier coordinate system b system and a navigation coordinate system n system is the posture of the carrier, gamma, theta and psi are defined as the roll angle, the pitch angle and the yaw angle of the carrier respectively, the navigation coordinate system rotates around the z axis by a y angle, then rotates around the x axis by a theta angle, and finally rotates around the y axis by a gamma angle to convert the body coordinate system; the rotation matrix of both can be expressed as:

(3) inertial navigation system update algorithm

The signal output by the IMU sensor is calculated through an INS mechanized algorithm: the specific settlement method comprises the following steps of:

(1) Settlement of attitude information

By adopting the quaternion method, quaternion is defined as:

Q＝q ₀ +q ₁ i+q ₂ j+q ₃ k (4)

quaternion describing the pose of a carrier isThe differential equation is expressed as follows:

wherein the method comprises the steps of For the projection of the carrier at the angular velocity of b-series to n-series, the expression is:

in the method, in the process of the invention,for the angular velocity of the carrier,/>For the gesture matrix +.>For the projection of the rotational angular velocity of the earth in the navigation coordinate system,/->For the rotation angular velocity of the navigation coordinate system relative to the geocentric fixed coordinate system, the following formula is satisfied:

wherein v is _n ,v _e Respectively represent the north speed and the east speed of the carrier, R _m Represents the radius of curvature of the meridian, h represents the elevation, R _n Representing the radius of curvature of the circle of mortise;

solving the differential equation (6) and updatingObtaining an implementation rotation matrix of the carrier:

(2) Settlement of speed information

Let the velocity of carrier solution under navigation coordinate system be v ⁿ The derivative of speed with respect to time in the navigation coordinate system and the derivative with respect to time in the inertial coordinate system have the following relationship:

the local gravity vector can be expressed as:from the earth gravitational acceleration g and centripetal acceleration +.>The composition is as follows:

wherein f ^b Is the specific force information output by the accelerometer; from equations (10) and (11), a differential equation for the velocity update can be obtained:

wherein f ⁿ For specific force acceleration in the navigational coordinate system,is a brother correction term;

discretizing equation (13) yields a velocity update equation:

(3) Settlement of location information

In the navigation coordinate system, the update equation of the position can be obtained by the speed integral:

wherein,respectively represent the east direction speed, the north direction speed and the sky direction speed under the navigation coordinate system.

In the step 2), the main principle of the CNN-GRU neural network prediction model is as follows:

in the neural network prediction algorithm, the GRU network solves the problem that the traditional neural network cannot use historical data, however, the input of the model involves the coupling of a plurality of sensors and a plurality of latitudes; thus, the input features are often difficult to find, affecting the time and accuracy of the training; the CNN can effectively automatically extract and learn the features from the sequence data, so that the feature extraction speed can be increased, and the performance of the GRU network can be improved; therefore, the CNN is combined with the GRU network to compensate the navigation system;

the convolution kernel of the CNN is adjusted to be one-dimensional, and the convolution kernel can be regarded as a window sliding on a number axis by taking time as an axis; the size of the convolution kernel is 20 multiplied by 1, and the step length is 8 multiplied by 1; conv2 has a convolution kernel size of 5×1 and a step size of 2×1; the area size of Pooling1 is 4×1, and the area size of Pooling2 is 2×1; setting a Pooling mode as Max-Pooling by adopting a ReLU function as an activation function of CNN; in order to reduce the occurrence of the over-fitting phenomenon, a Dropout layer is added, and the forgetting rate is set to be 0.01; the flat layer is used to change the multi-dimensional input into one dimension without affecting the batch size; the LSTM model calls 100 neurons for calculation; finally, selecting an Adam algorithm to optimize the model, and selecting a Mean Square Error (MSE) as a loss function;

CNN, a deep neural network, generally comprises two parts, a filtering layer and a classification layer; the filtering part comprises a convolution layer and a pooling layer, and has the main functions of filtering input data, reducing noise and dimension and obtaining required characteristics; classification grades play an important role in classification and are typically composed of several fully connected layers; a gated loop unit (GRU) is a variant of a Recurrent Neural Network (RNN) for processing sequence data; the GRU can better treat the long-term dependency and gradient disappearance problems by introducing a gating mechanism; the GRU has an update gate and a reset gate, which control the flow and retention of information in the loop layer;

given the current time X _t Implicit coding h of the input data of (a) and immediately preceding _t-1 The GRU uses the update gate and the reset gate to output the implicit code of the current moment, and transmits information backwards through the implicit code; the information update equation is as follows:

updating gate information output:

z _t ＝sigmoid(W _z x _t +U _z h _t-1 +b _z ) (26)

and (3) outputting reset gate information:

r _t ＝sigmoid(W _r x _t +U _r h _t-1 +b _r ) (27)

implicit coded output:

in the three formulas, W, U is a weight matrix among different structures; subscripts r, z, h respectively represent reset gate, update gate and hidden state; b _z ,b _r ,b _h Respectively representing offset vectors of the corresponding structures, wherein the parameters need to be optimized through training; the update gate decides which information is forgotten and which new information needs to be added and is used for controlling the degree of keeping the state of the previous moment to the current state;

the CNN-GRU combines the advantages of CNN and GRU, and is suitable for processing sequence data and image data; in this architecture, CNN is used to extract spatial features and local structures in sensor input data, the extracted features are passed to the GRU layer, the GRU further processes the features and learns timing dependencies in the data; the structure enables the CNN-GRU to capture the space and time sequence information of the data at the same time, so that complex input data can be better understood and processed, and the overall high navigation precision is improved.

In the step 3), the principle of the integrated navigation extended kalman filter model is as follows:

the extended Kalman Filter is an extension to the classical Kalman Filter (KF) for state estimation and filtering in a nonlinear system, and the algorithm is as follows:

the state equation and the observation equation of the mathematical model of the linear discrete system are as follows

Wherein X is _K A state vector representing the system; selected system state vectorδP and δV represent the three-dimensional position and velocity error vector of inertial system, respectively, +.>Representing the attitude angle error vector, Z _K Representing the observation vector of the system, Z in this model _K Representing GPS and INS position and velocityA difference between; phi _k/k-1 Representing a one-step state transition matrix of the system; Γ -shaped structure _k/k-1 Representing a system allocation noise matrix; h _k Representing an observation matrix; w (W) _k-1 Represents process noise, satisfying the formula [ W _k W _j ^T ]＝Q _k δ _kj ；V _k Satisfy equation [ V _k V _j ^T ]＝R _k δ _kj The method comprises the steps of carrying out a first treatment on the surface of the In these two equations, Q _k And R is _k Represents W _k-1 And V _k Is a concomitant covariance of (1); w (W) _k-1 And V _k Are gaussian white noise subject to normal distribution; />And epsilon represents inertial system accelerometer bias and gyro drift;

prediction stage:

updating:

kalman filter gain K:

the corresponding state quantity updating section:

X _k ＝X _k/k-1 +K _k V _k (23)

a corresponding state covariance update section:

P _k ＝[I-K _k H _k ]P _k/k-1 (24)

from the above equation, the actual filtering results from some components of the system state estimate X in equation (24), where the Kalman filter gain K is a compromise between the state prediction value and the observed error value; if K is small, such as equal to 0, the filtering result is more similar to the recursive result given by the system state estimate; if K is large, for example, equal to 1, the filtering result is more approximate to the state variable calculated by the back calculation of the observed value; the value of K is calculated by equation (23), where the value of P is calculated by equations (20) (25), reflecting the magnitude of Q, so the magnitude of the value of K can be illustrated by the following:

thus, the K value is related to the ratio of Q to R, and is not related to the absolute value of Q to R; therefore, in different algorithms, the values of Q and R can be greatly changed according to different dimensions of the reaction, but the ratio of the values determines whether the filtering value is more from information of the evolution of the system model or from information of the observation signal;

the above is the understanding of K and the value problem of Q and R, namely, from the whole integrated navigation, the optimal estimated solution Z of the current K moment is obtained through EKF _k/k As error compensation of INS output value, more accurate positioning information (position speed and attitude) is obtained.

In the step 4), the GPS/INS Kalman filtering positioning model predicted by the CNN-GRU is divided into two cases of uninterrupted GPS and uninterrupted GPS, and the specific steps are as follows:

when a GPS signal is available, the system works in a training stage, the angular speed and the specific force provided by the IMU are respectively input into KF by making differences between the position and the speed obtained by mechanization and the position and the speed obtained by the GPS, and then position errors and speed errors are obtained; correcting the resolving result of the strapdown inertial navigation by utilizing the errors to obtain an output value of the integrated navigation system; meanwhile, training a CNN-LSTM model, and finding out the relation between the angular speed and the specific force provided by the IMU and the position error and the speed error output by the Kalman filtering;

when the GPS signal is interrupted and the GNSS is out of lock, the neural network stops training, and a trained CNN-GRU neural network fitting model is utilized to predict a pseudo signal of a position information difference value between the GNSS and the INS according to the instantaneous calculated forward speed of the inertial navigation system INS and the angular speed and specific force obtained by the measurement of the IMU; the false signal value is input into the EKF to be used as an observation value, so that an error value output by the EKF can be obtained; and finally correcting the strapdown inertial navigation by utilizing the error to obtain the output of the integrated navigation.

The beneficial effects of the invention are as follows: the method combines the advantages that the CNN neural network can effectively extract and learn features from the multidimensional sequence data automatically and the problem that the GRU can effectively use historical data, has the advantages of simple structure, few parameters and the like, can effectively predict GNSS pseudo signals when the GNSS is interrupted, and further improves navigation positioning accuracy.

Drawings

FIG. 1 is an overall block diagram of the present invention;

FIG. 2 is a block diagram of the INS mechanization algorithm of the present invention;

FIG. 3 is a diagram of the CNN-GRU structure of the invention;

FIG. 4 is a diagram showing a GPS interrupt structure of a GPS/INS Kalman filtering positioning model according to the present invention;

FIG. 5 is a diagram showing the GPS uninterrupted structure of the GPS/INS Kalman filtering positioning model of the invention.

Detailed Description

The invention will be further illustrated by way of example with reference to the accompanying drawings.

As shown in FIG. 1, the GPS/INS Kalman filtering positioning method based on CNN-GRU prediction comprises the following steps:

1) An INS mechanized model is built, and position information of each moment of the INS is obtained;

2) In order to improve the performance of the traditional GRU network when processing the strongly coupled navigation data, a convolutional gating cyclic unit neural network (CNN-GRU) model is established, the CNN is utilized to rapidly extract the input characteristics, and the GRU network is utilized to output pseudo GPS signals as compensation objects;

3) Establishing an integrated navigation extended Kalman filtering model, and obtaining a compensation value of INS inertial navigation positioning information by carrying out data fusion on GNSS positioning information and INS positioning information so as to obtain accurate positioning information;

4) The GPS/INS navigation compensation positioning model based on CNN-GRU prediction can improve positioning accuracy to a greater extent when GPS signals are interrupted.

The specific implementation process is as follows:

in the step 1), the INS mechanization module calculates the attitude, speed and position of the aircraft or vehicle by adopting a kinetic equation of inertial mechanization, including three major parts of a common coordinate system, coordinate transformation and inertial navigation updating algorithm, and the specific description is as follows:

common coordinate system

The problem of posture involved in the INS mechanization process is essentially the problem of transformation of different coordinate systems, wherein common coordinate systems are an inertial coordinate system, a geodetic coordinate system, a navigation coordinate system and a carrier coordinate system. As will be described in detail below.

(1) Inertial coordinate system (i system)

The origin of the inertial coordinate system is the earth centroid, the x-axis corresponds to the spring branching line pointing to the earth, the z-axis points to the north pole, the y-axis is perpendicular to the xoz plane and meets the right-hand rule, the inertial coordinate system is static relative to the star, and the observed quantity measured by the inertial measurement device is relative to the inertial coordinate system.

(2) Geocentric earth fixed coordinate system (e system)

The origin of the earth-centered earth-fixed coordinate system is the earth centroid, the x-axis points to the zero meridian, the z-axis coincides with the earth rotation axis, the y-axis points to the east-longitude 90-degree meridian, and the xoy plane coincides with the earth equatorial plane.

(3) Navigation coordinate system (n system)

The navigation coordinate system is a geographical coordinate system, typically the northeast (ENU) coordinate system and the Northeast (NED) coordinate system. The northeast coordinate system takes the mass center of the carrier as the origin of coordinates, the local direction of the northeast direction as the x axis, the direction of the northeast direction as the y axis and the zenith direction as the z axis.

(4) Carrier coordinate system (b system)

The carrier coordinate system takes the center of mass of the carrier as an origin, the y axis points forward along the longitudinal axis of the carrier, the x axis points rightward along the transverse direction of the carrier, the z axis points above the carrier, and the three axes together form a right-hand rule.

(two) coordinate System conversion

(1) Conversion of inertial coordinate system to geocentric geodetic coordinate system

The rotation matrix of the inertial frame to the geocentric, fixed frame can be expressed as:

wherein t is time, ω _ie Is the earth rotation speed.

(2) Conversion of geocentric geodetic coordinate system to navigation coordinate system

The rotation matrix of the geocentric fixed coordinate system to the navigation coordinate system can be expressed as:

where λ represents the latitude where the origin of the carrier is located, and L represents the longitude where the origin of the carrier is located.

(3) Conversion of carrier coordinates to a navigation coordinate system

The conversion between the carrier coordinate system b system and the navigation coordinate system n system is an important content in inertial navigation, and the relative relationship between the two is the posture of the carrier. And defining gamma, theta and psi as roll angle, pitch angle and yaw angle of the carrier respectively, rotating the navigation coordinate system by y angle around the z axis, rotating by theta angle around the x axis and finally rotating by gamma angle around the y axis to convert the body coordinate system. The rotation matrix of both can be expressed as:

(III) inertial navigation system updating algorithm

INS mechanization as shown in fig. 2, the signal output by the IMU sensor is calculated by an INS mechanization algorithm: attitude information, velocity information, and position information. The settlement method of the above three information will be described in detail.

(1) Settlement of attitude information

The attitude updating algorithm mainly comprises an Euler angle method, a direction cosine method and a quaternion method. The quaternion method only needs to calculate one matrix differential equation, so that the calculated amount is small, and the singular value problem of the Euler angle can be avoided, so that the quaternion method is the most common attitude matrix updating algorithm. The quaternion is defined as:

Q＝q ₀ +q ₁ i+q ₂ j+q ₃ k (4)

quaternion describing the pose of a carrier isIts differential equation is expressed as follows:

wherein the method comprises the steps of For the projection of the carrier at the angular velocity of b-series to n-series, the expression is:

in the method, in the process of the invention,for the angular velocity of the carrier,/>For the gesture matrix +.>For the projection of the rotational angular velocity of the earth in the navigation coordinate system,/->The rotation angular velocity of the navigation coordinate system relative to the geocentric fixed coordinate system is as follows:

wherein v is _n ,v _e Respectively represent the north speed and the east speed of the carrier, R _m Represents the radius of curvature of the meridian, h represents the elevation, R _n And represents the radius of curvature of the circle of mortise and tenon.

Solving the differential equation (6) and updatingObtaining an implementation rotation matrix of the carrier:

(2) Settlement of speed information

Let the velocity of carrier solution under navigation coordinate system be v ⁿ The derivative of speed with respect to time in the navigation coordinate system and the derivative with respect to time in the inertial coordinate system have the following relationship:

the local gravity vector can be expressed as:from the earth gravitational acceleration g and centripetal acceleration +.>The composition is as follows:

wherein f ^b Is the specific force information output by the accelerometer. From equations (10) and (11), a differential equation for the velocity update can be obtained:

wherein f ⁿ For specific force acceleration in the navigational coordinate system,is a brother correction term.

Discretizing equation (13) yields a velocity update equation:

(3) Settlement of location information

In the navigation coordinate system, the update equation of the position can be obtained by the speed integral:

wherein,respectively represent the east direction speed, the north direction speed and the sky direction speed under the navigation coordinate system.

In the step 2), the main principle and analysis of the CNN-GRU prediction model are as follows:

in the neural network prediction algorithm, the GRU network solves the problem that the traditional neural network cannot use historical data, and has the advantages of simple structure and few parameters. Satisfactory results are achieved in integrated navigation system compensation. However, the input of the model involves the coupling of multiple sensors and multiple latitudes. Thus, the input features are often difficult to find, affecting the time and accuracy of the training. CNNs can effectively automatically extract and learn features from sequence data. The method can accelerate the feature extraction speed and improve the performance of the GRU network. Therefore, we combine CNN with GRU network to compensate the navigation system. The proposed model is shown in fig. 3.

The input data of CNN is mostly two-dimensional, but since the input data of the present invention is one-dimensional time series, the convolution kernel of CNN is adjusted to be one-dimensional. The convolution kernel can be seen as a window that slides on the number axis with time as the axis. The size of the convolution kernel is 20×1, and the step size is 8×1.Conv2 has a convolution kernel size of 5×1 and a step size of 2×1. The area size of Pooling1 is 4×1, and the area size of Pooling2 is 2×1. And setting the Pooling mode as Max-Pooling by adopting the ReLU function as an activation function of the CNN. In order to reduce the occurrence of the overfitting phenomenon, a Dropout layer was added, and the forgetting rate was set to 0.01. The flat layer is used to change the multi-dimensional input to one-dimensional without affecting the batch size. The LSTM model calls 100 neurons for computation. Finally, adam's algorithm is chosen to optimize the model, and the Mean Square Error (MSE) is chosen as the loss function.

CNNs, as a kind of deep neural network, generally include two parts, a filtering layer and a classification layer. The filtering section includes a convolution layer and a pooling layer. The main function of the method is to filter input data, reduce noise and dimension, and obtain required characteristics. Classification grades play an important role in classification and are typically composed of several fully connected layers. A gated loop unit (GRU) is a variant of a Recurrent Neural Network (RNN) for processing sequence data. Compared with the traditional RNN, the GRU can better treat the long-term dependency and gradient disappearance problems by introducing a gating mechanism. The GRU has update and reset gates that control the flow and retention of information in the loop layer. This makes the GRU excellent in tasks such as sequence modeling and timing prediction.

Given the current time X _t Implicit coding h of the input data of (a) and immediately preceding _t-1 The GRU outputs an implicit code of the current time using the update gate and the reset gate, and transmits information backward through the implicit code. The information update equation is as follows:

updating gate information output:

z _t ＝sigmoid(W _z x _t +U _z h _t-1 +b _z ) (26)

and (3) outputting reset gate information:

r _t ＝sigmoid(W _r x _t +U _r h _t-1 +b _r ) (27)

implicit coded output:

in the three formulas, W, U is a weight matrix among different structures; subscripts r, z, h respectively represent reset gate, update gate and hidden state; b _z ,b _r ,b _h Representing the offset vectors of the corresponding structures, respectively, these parameters need to be optimized by training. The update gate decides which information is forgotten, which new information needs to be added,and is used to control the extent to which the state immediately before is retained to the current state.

The CNN-GRU combines the advantages of CNN and GRU, and is suitable for processing sequence data and image data. In this architecture, CNNs are used to extract spatial features and local structures in sensor input data, the extracted features are passed to the GRU layer, which further processes the features and learns timing dependencies in the data. The structure enables the CNN-GRU to capture the space and time sequence information of the data at the same time, so that complex input data can be better understood and processed, and the overall high navigation precision is improved.

In the step 3), the principle of the integrated navigation Kalman filtering model is as follows:

the Kalman filtering algorithm has strong filtering capability and is widely applied to the positioning and sensor data fusion of the integrated navigation system. The classical Kalman filtering algorithm is suitable for linear random systems, and the dynamic model and the observation model of the system are both linear. However, inertial navigation systems are mostly nonlinear, which results in classical kalman filtering not being directly applicable. To address the state estimation and filtering issues of nonlinear systems, extended kalman filtering (Extended Kalman Filter, EKF) was introduced. Extended Kalman filtering is an extension to classical Kalman Filters (KF) for state estimation and filtering in nonlinear systems. The algorithm is described below.

The state equation and the observation equation of the mathematical model of the linear discrete system are as follows

Wherein X is _K Representing a state vector of the system. The system state vector selected by the inventionδP and δV represent the three-dimensional position and velocity error vector of inertial system, respectively, +.>Representing the attitude angle error vector, Z _K Representing the observation vector of the system, Z in this model _K Representing the difference between GPS and INS position and velocity; phi _k/k-1 Representing a one-step state transition matrix of the system; Γ -shaped structure _k/k-1 Representing a system allocation noise matrix; h _k Representing an observation matrix; w (W) _k-1 Represents process noise, satisfying the formula [ W _k W _j ^T ]＝Q _k δ _kj ；V _k Satisfy equation [ V _k V _j ^T ]＝R _k δ _kj The method comprises the steps of carrying out a first treatment on the surface of the In these two equations, Q _k And R is _k Represents W _k-1 And V _k Is a co-variance. W (W) _k-1 And V _k Are gaussian white noise that obey normal distribution. />And ε represents inertial system accelerometer bias and gyro drift.

Prediction stage:

/>

updating:

kalman filter gain K:

the corresponding state quantity updating section:

X _k ＝X _k/k-1 +K _k V _k (23)

a corresponding state covariance update section:

P _k ＝[I-K _k H _k ]P _k/k-1 (24)

from the above formulas, the results of the actual filtering result from some components of the system state estimate X in formula (24), and the results of formula (14) are calculated from the state prediction value obtained by formula (19) and from the observed quantity Z. Wherein the kalman filter gain K is a compromise between the state prediction value and the observed error value. If K is small, such as equal to 0, the filtering result is more similar to the recursive result given by the system state estimate; if K is large, for example equal to 1, the filtering result is much closer to the state variable that the observed value is back calculated. The value of K is calculated by equation (23), where the value of P is calculated by equations (20) (25), reflecting the magnitude of Q, so the magnitude of the value of K can be illustrated by the following:

thus, the K value is related to the ratio of Q and R, and is not related to the absolute value of Q and R. Therefore, in different algorithms, the values of Q and R may vary greatly according to different dimensions of the reaction, but their ratio determines whether the filtered values should come from more information of the evolution of the system model or from the observed signal information.

The above is the understanding of K and the value problem of Q and R, from the whole integrated navigation, the best estimated solution Z at the current K moment is simply obtained through EKF _k/k As error compensation of INS output value, accurate positioning information (position speed and attitude) is obtained.

In the step 4), the GPS/INS Kalman filtering positioning model predicted by the CNN-GRU is divided into two cases of uninterrupted GPS and uninterrupted GPS, as shown in fig. 4 and 5, the specific flow is as follows:

when (one) GPS signal is available

The system works in a training stage, the angular speed and the specific force provided by the IMU are input into the KF through the difference between the position and the speed obtained by mechanization and the position and the speed obtained by the GPS respectively, and then the position error and the speed error are obtained. And correcting the resolving result of the strapdown inertial navigation by utilizing the errors to obtain the output value of the integrated navigation system. Meanwhile, training a CNN-LSTM model to find out the relation between the angular speed and the specific force provided by the IMU and the position error and the speed error output by the Kalman filtering.

(II) when GPS signal is interrupted

And stopping training by the neural network, and predicting a false signal of the position information difference between the GNSS and the INS by using a trained CNN-GRU neural network fitting model according to the forward speed calculated by the inertial navigation system INS instantaneously and the angular speed and specific force obtained by measuring the IMU. The error value output by the EKF can be obtained by inputting the artifact value into the EKF as an observed value. And finally correcting the strapdown inertial navigation by utilizing the error to obtain the output of the integrated navigation.

According to the invention, through the multidimensional property of the data, the CNN-GRU composite neural network is adopted for prediction, and the CNN neural network can effectively and automatically extract and learn the characteristics from the multidimensional sequence data. The method improves the performance of the GRU network by extracting features among multidimensional data. And the GRU neural network solves the problem that the traditional neural network cannot use historical data, and has the advantages of simple structure and few parameters. The CNN-GRU prediction model combines the advantages of the two neural networks, and the positioning accuracy and reliability of the GNSS and INS integrated navigation system after GNSS lock loss are improved to a greater extent.

The foregoing description is, of course, merely illustrative of preferred embodiments of the present invention, and it should be understood that the present invention is not limited to the above-described embodiments, but is intended to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

Claims (4)

1. A GPS/INS Kalman filtering positioning method based on CNN-GRU prediction is characterized in that: comprises the following steps:

1) Establishing an INS inertial navigation mechanized model to obtain the position information of the INS at each moment;

2) Establishing a CNN-GRU neural network prediction model, rapidly extracting input characteristics by using CNN, and outputting a pseudo GPS signal by using a GRU network as a compensation object;

3) Establishing an integrated navigation extended Kalman filtering model, and obtaining a compensation value of INS inertial navigation positioning information by carrying out data fusion on GNSS positioning information and INS positioning information so as to obtain accurate positioning information;

4) The GPS/INS Kalman filtering positioning model based on CNN-GRU prediction can improve the positioning precision to a greater extent when the GPS signal is interrupted.

2. The CNN-GRU prediction-based GPS/INS kalman filter positioning method according to claim 1, wherein the method is characterized by: in the step 1), an INS mechanized module in the INS inertial navigation mechanized model calculates the attitude, the speed and the position of the aircraft or the vehicle by adopting a kinetic equation of inertial mechanization, wherein the three main parts comprise a common coordinate system, coordinate system conversion and an inertial navigation system updating algorithm, and the three main parts are as follows:

(1) common coordinate system

Common coordinate systems include an inertial coordinate system, a geocentric fixed coordinate system, a navigation coordinate system and a carrier coordinate system; the method comprises the following steps:

(1) Inertial coordinate system i system

The origin of the inertial coordinate system is the earth centroid, the x-axis corresponds to the spring branching line pointing to the earth, the z-axis points to the north pole, the y-axis is perpendicular to the xoz plane and meets the right-hand rule, and the inertial coordinate system is static relative to the star;

(2) Geocentric geodetic coordinate system e

The origin of the geocentric earth fixed coordinate system is the earth centroid, the x-axis points to the zero meridian, the z-axis coincides with the earth rotation axis, the y-axis points to the east 90-degree meridian, and the xoy plane coincides with the earth equatorial plane;

(3) Navigation coordinate system n system

The navigation coordinate system is a geographic coordinate system, wherein the northeast coordinate system takes the mass center of the carrier as the origin of coordinates, the local direction of the northwest direction as the x axis, the direction of the northwest direction as the y axis and the zenith direction as the z axis;

(4) Carrier coordinate system b

The carrier coordinate system takes the center of mass of the carrier as an origin, the y axis points forward along the longitudinal axis of the carrier, the x axis points rightward along the transverse direction of the carrier, the z axis points above the carrier, and the three axes together form a right-hand rule;

(2) coordinate system conversion

(1) Conversion of inertial coordinate system to geocentric geodetic coordinate system

The rotation matrix of the inertial frame to the geocentric, fixed frame can be expressed as:

wherein t is time, ω _ie Is the earth rotation speed;

(2) Conversion of geocentric geodetic coordinate system to navigation coordinate system

The rotation matrix of the geocentric fixed coordinate system to the navigation coordinate system can be expressed as:

wherein λ represents the latitude of the origin of the carrier, and L represents the longitude of the origin of the carrier;

(3) Conversion of a carrier coordinate system into a navigation coordinate system

The relative relation between a carrier coordinate system b system and a navigation coordinate system n system is the posture of the carrier, gamma, theta and psi are defined as the roll angle, the pitch angle and the yaw angle of the carrier respectively, the navigation coordinate system rotates around the z axis by a y angle, then rotates around the x axis by a theta angle, and finally rotates around the y axis by a gamma angle to convert the body coordinate system; the rotation matrix of both can be expressed as:

(3) inertial navigation system update algorithm

The signal output by the IMU sensor is calculated through an INS mechanized algorithm: the specific settlement method comprises the following steps of:

(1) Settlement of attitude information

By adopting the quaternion method, quaternion is defined as:

Q＝q ₀ +q ₁ i+q ₂ j+q ₃ k (4)

quaternion describing the pose of a carrier isThe differential equation is expressed as follows:

wherein the method comprises the steps of For the projection of the carrier at the angular velocity of b-series to n-series, the expression is:

in the method, in the process of the invention,for the angular velocity of the carrier,/>For the gesture matrix +.>For the projection of the rotational angular velocity of the earth in the navigation coordinate system,/->For the rotation angular velocity of the navigation coordinate system relative to the geocentric fixed coordinate system, the following formula is satisfied:

wherein v is _n ,v _e Respectively represent the north speed and the east speed of the carrier, R _m Represents the radius of curvature of the meridian, h represents the elevation, R _n Representing the radius of curvature of the circle of mortise;

solving the differential equation (6) and updatingObtaining an implementation rotation matrix of the carrier:

(2) Settlement of speed information

Let the velocity of carrier solution under navigation coordinate system be v ⁿ The derivative of speed with respect to time in the navigation coordinate system and the derivative with respect to time in the inertial coordinate system have the following relationship:

the local gravity vector can be expressed as:from the earth gravitational acceleration g and centripetal accelerationThe composition is as follows:

wherein f ^b Is the specific force information output by the accelerometer; from equations (10) and (11), a differential equation for the velocity update can be obtained:

wherein f ⁿ For specific force acceleration in the navigational coordinate system,is a brother correction term;

discretizing equation (13) yields a velocity update equation:

(3) Settlement of location information

In the navigation coordinate system, the update equation of the position can be obtained by the speed integral:

wherein,respectively represent the east direction speed, the north direction speed and the sky direction speed under the navigation coordinate system.

3. The CNN-GRU prediction-based GPS/INS kalman filter positioning method according to claim 1, wherein the method is characterized by: in the step 3), the principle of the integrated navigation extended kalman filter model is as follows:

the extended Kalman filtering is an extension of classical Kalman filtering and is used for state estimation and filtering in a nonlinear system, and the algorithm is as follows:

the state equation and the observation equation of the mathematical model of the linear discrete system are as follows

Wherein X is _K A state vector representing the system; selected system state vectorδP and δV represent the three-dimensional position and velocity error vector of inertial system, respectively, +.>Representing the attitude angle error vector, Z _K Representing the observation vector of the system, Z in this model _K Representing the difference between GPS and INS position and velocity; phi _k/k-1 Representing a one-step state transition matrix of the system; Γ -shaped structure _k/k-1 Representing system allocation noiseAn array; h _k Representing an observation matrix; w (W) _k-1 Represents process noise, satisfying the formula [ W _k W _j ^T ]＝Q _k δ _kj ；V _k Satisfy equation [ V _k V _j ^T ]＝R _k δ _kj The method comprises the steps of carrying out a first treatment on the surface of the In these two equations, Q _k And R is _k Represents W _k-1 And V _k Is a concomitant covariance of (1); w (W) _k-1 And V _k Are gaussian white noise subject to normal distribution; and epsilon represent inertial system accelerometer bias and gyro drift;

prediction stage:

updating:

kalman filter gain K:

the corresponding state quantity updating section:

X _k ＝X _k/k-1 +K _k V _k (23)

a corresponding state covariance update section:

P _k ＝[I-K _k H _k ]P _k/k-1 (24)

from the whole integrated navigation, the optimal estimated solution Z of the current K moment is obtained through EKF _k/k As the error compensation of INS output value, the accurate positioning information is obtained.

4. The CNN-GRU prediction-based GPS/INS kalman filter positioning method according to claim 1, wherein the method is characterized by: in the step 4), the GPS/INS Kalman filtering positioning model predicted by the CNN-GRU is divided into two cases of uninterrupted GPS and uninterrupted GPS, and the specific steps are as follows:

when a GPS signal is available, the system works in a training stage, the angular speed and the specific force provided by the IMU are respectively input into KF by making differences between the position and the speed obtained by mechanization and the position and the speed obtained by the GPS, and then position errors and speed errors are obtained; correcting the resolving result of the strapdown inertial navigation by utilizing the errors to obtain an output value of the integrated navigation system; meanwhile, training a CNN-LSTM model, and finding out the relation between the angular speed and the specific force provided by the IMU and the position error and the speed error output by the Kalman filtering;

when the GPS signal is interrupted and the GNSS is out of lock, the neural network stops training, and a trained CNN-GRU neural network fitting model is utilized to predict a pseudo signal of a position information difference value between the GNSS and the INS according to the instantaneous calculated forward speed of the inertial navigation system INS and the angular speed and specific force obtained by the measurement of the IMU; the false signal value is input into the EKF to be used as an observation value, so that an error value output by the EKF can be obtained; and finally correcting the strapdown inertial navigation by utilizing the error to obtain the output of the integrated navigation.