CN112505737B - GNSS/INS integrated navigation method - Google Patents
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Abstract
The invention discloses an online learning assisted GNSS/INS integrated navigation method based on an Elman neural network, which comprises the following two parts: (1) Realizing a navigation algorithm based on a conventional GNSS/MEMS-INS combination, designing a Kalman filter to fuse GNSS signals and inertial navigation data, and outputting fused navigation data; (2) The invention predicts the output error of the inertial navigation system under the condition that the GNSS signal of the unmanned aerial vehicle navigation system is lost, and compensates and corrects the output of the inertial navigation system by using the error data so as to realize that the inertial navigation system can output accurate navigation data under the assistance of a neural network algorithm under the condition that the GNSS signal of the navigation system is lost.
Description
Technical Field
The invention belongs to the technical field of integrated navigation methods, and particularly relates to an online learning assisted GNSS/INS integrated navigation method based on an Elman neural network.
Background
In the aspect of navigation technology, the most widely used navigation modes at present are inertial navigation and satellite navigation. The GNSS satellite navigation has the advantages of being global, all-weather and high in long-time positioning accuracy, but has the disadvantage that signals are easy to interfere and shade. The signal quality is poor under the strong electromagnetic environment and when high-rise shielding exists, the output frequency is limited, generally 1-10Hz, the output is discontinuous, and the defects of GNSS satellite navigation are obvious on occasions needing to update information rapidly, such as unmanned aerial vehicle systems with high mobility and real-time requirements. The INS inertial navigation system is a fully autonomous navigation mode, so that the INS inertial navigation system has strong concealment and anti-interference capability, and is continuous in output information and high in positioning accuracy in a short time. However, due to the characteristics of the MEMS-INS device, the gyroscope and the accelerometer have errors such as initial zero offset, random drift and the like, the errors are larger and larger along with the accumulation of time, the long-time positioning accuracy is poor, and finally the gesture and the position information of the unmanned aerial vehicle cannot be accurately reflected.
In order to overcome the defects of two navigation types, the common practice is to combine satellite navigation signals and inertial navigation signals through Kalman filtering, and the respective defects are compensated by utilizing the respective advantages. However, under some special conditions, such as signal blocking areas, satellite signals may be lost in environments with more blocking objects, and the navigation system can only rely on pure inertial navigation, so that errors of navigation data become larger and larger over time. Therefore, a method is needed to replace the function of the GNSS and complete the output of navigation data in cooperation with inertial navigation in the case of GNSS signal loss.
Disclosure of Invention
In order to solve the problems, the invention discloses a GNSS/INS integrated navigation method based on the online learning assistance of an Elman neural network, and provides a method for predicting the output error of an inertial navigation system under the condition that the GNSS signal of an unmanned aerial vehicle navigation system is lost and compensating and correcting the output of the inertial navigation system by using the error data. Under the condition that the GNSS signal is lost, the inertial navigation system can output accurate navigation data under the assistance of a neural network algorithm.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
an GNSS/INS integrated navigation method based on Elman neural network online learning assistance comprises the following steps:
1. realizing a navigation algorithm based on a conventional GNSS/MEMS-INS combination, designing a Kalman filter to fuse GNSS signals and inertial navigation data, and outputting fused navigation data;
2. designing a neural network model on the basis of the step 1, respectively taking the inertial navigation data obtained in the step 1 and the data output by the Kalman filter as sample input and sample output of a training neural network, training the neural network model, predicting inertial navigation output errors by using the trained neural network model when GNSS signals are lost, and compensating and correcting inertial navigation by using the prediction errors.
Furthermore, the GNSS/INS integrated navigation method based on the online learning assistance of the Elman neural network disclosed by the invention specifically comprises the following steps of:
s1, installing an IMU and GNSS equipment, and matching the coordinate axis of the IMU with the axis of the carrier; the method comprises the steps of adopting an LGM851 vehicle-mounted combined navigation positioner based on Beidou satellite communication as a navigation calculation unit, adopting LoRa communication to ensure data safety, connecting a computer with a combined navigation system by using a serial data line, and processing the combined navigation data in real time by using the computer;
s2, calibrating the INS and the GNSS antenna external parameters, calibrating the installation external parameters of the INS and the GNSS receiver antenna by using a total station, and inputting the installation external parameters as initial values into a system;
s3, mounting the combined equipment on a trolley, testing in an experimental field, and starting data acquisition and processing, wherein the method specifically comprises the following steps of:
s3-1 initial alignment of an IMU under GNSS assistance
Initial alignment is accomplished by means of dynamic motion, since the GNSS is able to give the carrier's velocity relative to the local geographic coordinate system, assuming that the GNSS receiver's position under ECEF has been acquired e P GNSS Sum speed of e V GNSS Velocity is calculated by the formulaConversion to the geographic coordinate system n V G ，
The yaw and pitch angles are determined by projecting the velocity in a geographic coordinate system, as follows:
since roll is assigned a value of 0 directly for the vehicle carrier, a larger initial variance is given.
S3-2 inertial navigation solution based on ECEF coordinate system
S3-2-1, in order to initialize the IMU better, firstly, slowly moving the carrier, temporarily not starting the neural network learning part, and starting the neural network learning part after the initialization is finished; reading carrier parameters acquired by an inertial navigation module, including angular velocity informationAcceleration vector->Acquiring position and velocity of a GNSS receiver using a combined system e P k+1,G And e V k+1,G 。
s3-2-2, obtaining a real-time rotation quaternion by solving the following quaternion differential equation e q＝[q 0 q 1 q 2 q 3 ] T ；
e q k+1,INS ＝ e q k,EKF (I+[w × ]) (3)
S3-2-3, the carrier acceleration vector obtained according to step S3-2-1And the gesture quaternion solved in the step S3-2-2>Solving the differential equation of the following formula to obtain speed information of the carrier in three directions under a navigation coordinate system:
wherein V= [ V ] E V N V U ] T The speeds in the middle east, north and sky directions of the geographic coordinate system are respectively,is the rotational angular velocity of the earth, e g is the acceleration of gravity in a geographic coordinate system;
s3-2-4, respectively solving the position parameters of inertial navigation output through the following formulas;
e P k+1,INS ≈ e P k,EKF +( e V k,EKF + e V k+1,INS )Δt/2 (5)
constraint updating with assistance of S3-3 Elman neural network
When the GNSS signals are good, a neural network is connected into the system to predict the output error of inertial navigation and compensate and correct the output of inertial navigation.
S3-3-1 Elman neural network design
The mathematical model of Elman neural network is:
wherein: y (k) is the output of the output layer; x (k-1) is the external input of the input layer; u (u) c (k) Output for the receiving layer; u (k) is the output of the hidden layer; w (w) 1 Connecting weights for the input layer and the hidden layer; w (w) 2 Connecting weights for the receiving layer and the hidden layer; w (w) 3 The weight is connected to the output layer for the hidden layer. The hidden layer of the Elman neural network can adopt a bipolar Sigmoid function shown in formula (7) as an excitation function, and the output layer adopts a Pureline activation function, so that the formula (8) can be obtained:
f(a)＝(1-e -a )/(1+e -a ) (7)
y(k)＝w 3 u(k) (8)
from formulas (6) to (8), it can be deduced that:
u c (k)＝f(w 2 (k-1)u c (k-1)+w 1 (k-2)u c (k-2)) (9)
wherein f (a) is E (-1, 1); w (w) 2 (k-1) and w 1 (k-2) represents the network connection weight at the time of k-1 and k-2, respectively. u (u) c (k) The dynamic recursion characteristic is reflected in relation to the connection weight of the historical time.
The Elman neural network adopts BP algorithm to correct weight, and the learning index function adopts error square sum function:
s3-3-2, performing online learning according to the output of the inertial sensor and the EKF;
s3-3-2-1 corrects the predicted data obtained by the inertial sensor in the step S1 by adopting the position and the speed of GNSS output, and the filtered data can be obtained by Kalman filteringAnd->As in equation (11).
The GNSS measurement state in EKF is updated as follows:
wherein the method comprises the steps ofAnd->Respectively outputting values of inertial sensors; e P k+1,G and e V k+1,G output values of GNSS position and velocity, respectively; />And->Respectively kalman filter solutions.
S3-3-2-2 synchronously trains the neural network model. Designing a neural network model based on the S3-3-2-1 step, and then comparing the relative change value between the inertial navigation data obtained by the S3-3-2-1 step and the epoch of the output data of the Kalman filter, when the number of available satellites of the GNSS is more, comparing the number of available satellites with the number of available satellites of the GNSSAnd->Respectively taking the input and the output of the Elman neural network as input and output of the Elman neural network to be added into a training sample for online learning, so that the network has the capability of predicting the speed and the position variation, then obtaining the position, the rotation quaternion and the speed of the epoch according to the position and the speed of the previous moment, and when the training error meets a certain threshold value, the training model is reliable, and the system can be assisted for forecasting;
in order to ensure the timeliness of the system, a fixed window method is adopted to limit the number of samples, and when the number of samples reaches a certain number, the older samples are removed from the window in order to ensure the timeliness of the samples.
Wherein the method comprises the steps ofThe change quantity between epochs of the output value of the inertial sensor respectively; />The inter-epoch variation of the output value after Kalman filtering; />And->The output values of the inertial sensors at the moment k are respectively; />And->And respectively outputting solutions for the Kalman filtering at the k moment.
S3-3-3, classifying according to satellite signal shielding and non-shielding when online learning meets a threshold value and can be used for predicting;
s3-3-3-1 when GNSS satellite signals are blocked, INS can work normally due to the attribute of the INS; GNSS data at the moment before failure is a filtered initial value which is equivalent to an accurate value, so that the divergence of INS precision caused by long navigation time can be avoided; when GNSS signals are lost, the output error of inertial navigation is predicted by using a trained neural network model, the inertial navigation is compensated and corrected by using the predicted error, and the inertial navigation is obtained by pre-integrating an inertial sensorAs Elman neural network prediction, output neural network prediction data is +.>And->The EKF update is performed as an observation constraint.
Neural network prediction variableAnd->The predicted values of the position, rotation quaternion and speed at the time k+1 are obtained as follows:
the constraint update is:
wherein,and->Respectively outputting state vectors in the step S3-1 according to the inertial sensors; />And->The predicted values of the position, the rotation quaternion and the speed at the time k+1 obtained by the neural network are respectively obtained.
S3-3-3-2 when the GNSS signals are normal, two strategies are available: 1. directly taking the position, the speed and the rotation quaternion of the moment k+1 output by the inertial sensor as the update of the state vector, and then carrying out constraint update by utilizing the position and the speed output by the GNSS (Global navigation satellite System) as the step S3-3-2; 2. inputting the position, the speed and the rotation quaternion variable quantity of the moment k+1 of the inertial sensor output into an Elman neural network, and taking the position, the rotation quaternion and the speed variable quantity of the output of the Elman neural network as pseudo-observation values to update the state vector of the EKF, as shown in a formula (16); and then constraining based on the position and velocity of the GNSS outputNew as in equation (17); finally, the inertial sensor is used for obtainingAnd->Obtained by EKF And->And adding the training program into an online learning system of the neural network to perform real-time learning training.
The EKF state is updated as:
the GNSS measurement state in EKF is updated as follows:
and->The predicted variation of the neural network is respectively +.>And->Pre-determination of position, rotation quaternion and speed at time k+1Measuring a value; e P k+1,G and e V k+1,G the output values of GNSS position and velocity, respectively.
The beneficial effects of the invention are as follows:
the invention discloses an online learning assisted GNSS/INS combined navigation method based on an Elman neural network, which is used for predicting the output error of an inertial navigation system of an unmanned aerial vehicle navigation system under the condition of GNSS signal loss under the condition of a plurality of environments such as a signal blocking area and a plurality of shielding objects or a long shielding time, and compensating and correcting the output of the inertial navigation system by using error data. Under the condition that the GNSS signal is lost, the inertial navigation system can output accurate navigation data under the assistance of a neural network algorithm.
Drawings
FIG. 1 is a flowchart of a GNSS/INS integrated navigation process (with a sufficient number of available GNSS satellites) based on a genetic neural network.
FIG. 2 is a flowchart of GNSS/INS integrated navigation based on a genetic neural network (when the number of GNSS satellites is insufficient).
Fig. 3 is a block diagram of an Elman neural network.
Fig. 4 is a dynamic quasi-resolution diagram.
Fig. 5 is a diagram of a combined navigation apparatus.
Detailed Description
The present invention is further illustrated in the following drawings and detailed description, which are to be understood as being merely illustrative of the invention and not limiting the scope of the invention.
The invention discloses an online learning assisted GNSS/INS integrated navigation method based on an Elman neural network, which specifically comprises the following steps:
s1, installing an IMU and GNSS equipment, and matching the coordinate axis of the IMU with the axis of a carrier as much as possible in order to reduce the lever arm error; FIG. 5 is a block diagram of a GNSS/INS based integrated navigation hardware system. According to the invention, the LGM851 vehicle-mounted combined navigation locator based on the Beidou satellite communication is adopted as a navigation calculation unit, loRa communication is adopted to ensure data safety, a serial data line is used for connecting a computer with a combined navigation system, and the computer is used for processing the combined navigation data in real time.
S2, calibrating the INS and the GNSS antenna external parameters, calibrating the installation external parameters of the INS and the GNSS receiver antenna by using a total station, and inputting the installation external parameters as initial values into a system;
s3, mounting the combined equipment on a trolley, testing in a four-hand building school area experimental field of southeast university, and starting data acquisition and processing, wherein the method specifically comprises the following steps of:
s3-1 initial alignment of an IMU under GNSS assistance
In the GNSS/INS integrated navigation system, initial alignment belongs to a critical step, and the inertial navigation system adopts a dead reckoning algorithm to realize continuous autonomous navigation so as to obtain full navigation parameters (position, speed and gesture information), so that the initial state of the first epoch is particularly critical. Meanwhile, the GNSS can conveniently give the position and the speed (if the receiver can output Doppler frequency shift, the instantaneous speed can be directly obtained through Doppler integration, and if not, the average speed can be obtained through inter-epoch difference of the receiver), so that the key task of initial alignment falls to the determination of the gesture. Thus, the initial alignment of the IMU, mainly referred to as pose initialization, pose accuracy becomes a major factor affecting navigation accuracy. For low-precision MEMSIMU static coarse alignment initialization, the gyroscope measurement precision is low, and the rotation angular velocity of the earth cannot be perceived, so that the coarse alignment can only finish initial alignment by means of dynamic motion. Since GNSS can give the velocity of the carrier relative to the local geographic coordinate system (n-system). Assume that the position of the GNSS receiver under ECEF has been acquired e P GNSS Sum speed of e V GNSS The velocity can be calculated by the formula(can be directly obtained) converted into a geographic coordinate system n V G . As shown in particular in fig. 4.
The yaw and pitch angles are determined by projecting the velocity under the n-series, and the schematic and formula are as follows:
since roll can be assigned a value of 0 directly for the vehicle carrier, a larger initial variance is given.
S3-2 inertial navigation solution based on ECEF coordinate system
S3-2-1, in order to initialize the IMU better, firstly, slowly moving the carrier, temporarily not starting the neural network learning part, and starting the neural network learning part after the initialization is completed. Reading carrier parameters acquired by an inertial navigation module, including angular velocity informationAcceleration vector->Acquiring position and velocity of a GNSS receiver using a combined system e P k+1,G And e V k+1,G 。
s3-2-2, obtaining a real-time rotation quaternion by solving the following quaternion differential equation e q＝[q 0 q 1 q 2 q 3 ] T ；
e q k+1,INS ＝ e q k,EKF (I+[w × ]) (3)
S3-2-3, the carrier acceleration vector obtained according to step S3-2-1And the gesture quaternion solved in the step S3-2-2>Solving the differential equation of the following formula to obtain speed information of the carrier in three directions under a navigation coordinate system:
wherein V= [ V ] E V N V u ] T The speeds in the middle east, north and sky directions of the geographic coordinate system are respectively,is the rotational angular velocity of the earth, e g is the acceleration of gravity in a geographic coordinate system;
s3-2-4, respectively solving the position parameters of the inertial navigation output through the following formula.
e P k+1,INS ≈ e P k,EKF +( e V k,EKF + e V k+1,INS )Δt/2 (5)
Constraint updating with assistance of S3-3 Elman neural network
When the GNSS signals are good, a neural network is connected into the system to predict the output error of inertial navigation and compensate and correct the output of inertial navigation. As in fig. 2.
S3-3-1 Elman neural network design
The Elman neural network is a typical dynamic recurrent neural network, which is characterized in that a receiving layer is added on an implicit layer based on the basic structure of a BP network and is used as a one-step delay operator to achieve the purpose of memorization, so that the system has the capability of adapting to time-varying characteristics, the global stability of the network is enhanced, and the dynamic recurrent neural network has stronger computing capability than a feedforward neural network and can be used for solving the problem of quick optimizing. The Elman neural network structure is shown in fig. 1, and has 4 layers, namely an input layer, an hidden layer, a receiving layer and an output layer. As particularly shown in fig. 3. The mathematical model of Elman neural network is:
wherein: y (k) is the output of the output layer; x (k-1) is the inputExternal input of the layer; u (u) c (k) Output for the receiving layer; u (k) is the output of the hidden layer; w (w) 1 Connecting weights for the input layer and the hidden layer; w (w) 2 Connecting weights for the receiving layer and the hidden layer; w (w) 3 The weight is connected to the output layer for the hidden layer. The hidden layer of the Elman neural network can adopt a bipolar Sigmoid function shown in formula (7) as an excitation function, and the output layer adopts a Pureline activation function, so that the formula (8) can be obtained:
f(a)＝(1-e -a )/(1+e -a ) (7)
y(k)＝w 3 u(k) (8)
from formulas (6) to (8), it can be deduced that:
u c (k)＝f(w 2 (k-1)u c (k-1)+w 1 (k-2)u c (k-2)) (9)
wherein f (a) is E (-1, 1); w (w) 2 (k-1) and w 1 (k-2) represents the network connection weight at the time of k-1 and k-2, respectively. u (u) c (k) The dynamic recursion characteristic is reflected in relation to the connection weight of the historical time.
The Elman neural network adopts BP algorithm to correct weight, and the learning index function adopts error square sum function:
s3-3-2, performing online learning according to the output of the inertial sensor and the EKF;
s3-3-2-1 corrects the predicted data obtained by the inertial sensor in the step S1 by adopting the position and the speed of GNSS output, and the filtered data can be obtained by Kalman filteringAnd->As in equation (11).
The GNSS measurement state in EKF is updated as follows:
wherein the method comprises the steps ofAnd->Respectively outputting values of inertial sensors; e P k+1,G and e V k+1,G output values of GNSS position and velocity, respectively; />And->Respectively kalman filter solutions.
S3-3-2-2 synchronously trains the neural network model. Designing a neural network model on the basis of the S3-3-2-1 step, then obtaining inertial navigation data obtained by the S3-3-2-1 step and the relative change value between the epochs of the output data of the Kalman filter (namely the relative change quantity of the position, the rotation quaternion and the speed between the k and the k+1 epochs), solving the inertial sensor according to the pre-integration, solving the relative change quantity after the Kalman filter according to formulas (12) and (13), and particularly realizing the steps as shown in figure 1, when the number of satellites available in the GNSS is more, obtaining the inertial navigation data by using the inertial navigation sensorAnd->Respectively as input and output of the Elman neural network to be added into training samples for online learning, and the influence of time delay errors between GNSS and INS is not considered in the text once assuming that the lever arm is compensated. The network has the capability of predicting the speed and the position variation, the position, the rotation quaternion and the speed of the epoch are obtained according to the position and the speed of the previous moment, and when the training error meets a certain threshold value, the training is representedThe training model is reliable, and the system can be assisted to forecast;
in order to ensure the timeliness of the system, a fixed window method is adopted to limit the number of samples, and when the number of samples reaches a certain number, the older samples are removed from the window in order to ensure the timeliness of the samples.
Wherein the method comprises the steps ofThe change quantity between epochs of the output value of the inertial sensor respectively; />The inter-epoch variation of the output value after Kalman filtering; />And->The output values of the inertial sensors at the moment k are respectively; />And->And respectively outputting solutions for the Kalman filtering at the k moment.
S3-3-3, classifying according to satellite signal shielding and non-shielding when online learning meets a threshold value and can be used for predicting;
s3-3-3-1 when GNSS satellite signals are blocked, INS can work normally due to the attribute. The GNSS data at the moment before failure is the initial value of the filtering, which is equivalent to the accurate value, becauseThis can avoid divergence of INS accuracy due to long navigation time. When the GNSS signal is lost, the output error of inertial navigation is predicted by using the trained neural network model, and the inertial navigation is compensated and corrected by using the predicted error, and the specific implementation steps are as shown in FIG. 2. First, the inertial sensor is pre-integrated to obtainAs an Elman neural network for prediction, outputting the predicted data of the neural network asAnd->The EKF update is performed as an observation constraint.
Neural network prediction variableAnd->The predicted values of the position, rotation quaternion and speed at the time k+1 are obtained as follows:
the constraint update is:
wherein,and->Respectively outputting state vectors in the step S3-1 according to the inertial sensors; />And->The predicted values of the position, the rotation quaternion and the speed at the time k+1 obtained by the neural network are respectively obtained.
S3-3-3-2 when the GNSS signals are normal, we have two strategies to apply. 1. Directly taking the position, the speed and the rotation quaternion of the moment k+1 output by the inertial sensor as the update of the state vector, and then carrying out constraint update by utilizing the position and the speed output by the GNSS (Global navigation satellite System) as the step S3-3-2; 2. inputting the position, the speed and the rotation quaternion variable quantity of the moment k+1 of the inertial sensor output into an Elman neural network, and taking the position, the rotation quaternion and the speed variable quantity of the output of the Elman neural network as pseudo-observation values to update the state vector of the EKF, as shown in a formula (16); then, constraint updating is carried out according to the position and the speed of GNSS output, as shown in a formula (17); finally, the inertial sensor is used for obtainingAnd->And +.>And->And adding the training program into an online learning system of the neural network to perform real-time learning training. As in fig. 1.
The EKF state is updated as:
the GNSS measurement state in EKF is updated as follows:
and->The predicted variation of the neural network is respectively +.>And->Predicted values of the position, the rotation quaternion and the speed at the moment k+1 are obtained; e P k+1,G and e V k+1,G the output values of GNSS position and velocity, respectively.
The technical means disclosed by the scheme of the invention is not limited to the technical means disclosed by the embodiment, and also comprises the technical scheme formed by any combination of the technical features.
Claims (1)
1. A GNSS/INS integrated navigation method is characterized in that: the method comprises the following steps:
(1) Based on a GNSS/MEMS-INS combined navigation algorithm, a Kalman filter is designed to fuse GNSS signals and inertial navigation data, and fused navigation data is output;
(2) Designing a neural network model on the basis of the step (1), respectively taking the inertial navigation data obtained in the step (1) and the data output by the Kalman filter as sample input and sample output for training the neural network, training the neural network model, predicting an inertial navigation output error by using the trained neural network model when GNSS signals are lost, and compensating and correcting inertial navigation by using the inertial navigation output error;
the method specifically comprises the following steps:
s1, installing an IMU and GNSS receiver equipment, and matching an IMU coordinate axis with a carrier axis; the method comprises the steps of adopting an LGM851 vehicle-mounted combined navigation positioner based on Beidou satellite communication as a navigation calculation unit, adopting LoRa communication to ensure data safety, connecting a computer with a combined navigation system by using a serial data line, and processing the combined navigation data in real time by using the computer;
s2, calibrating the INS and the GNSS receiver antenna external parameters, and calibrating the installation external parameters of the INS and the GNSS receiver antenna by using a total station as initial values and inputting the initial values into a system;
s3, mounting the combined equipment on a trolley, testing in an experimental field, and starting data acquisition and processing, wherein the method specifically comprises the following steps of:
s3-1 initial alignment of IMU under dynamic GNSS assistance
Initial alignment is accomplished by means of dynamic motion, the GNSS gives the velocity of the carrier relative to the local geographic coordinate system, assuming that the position of the GNSS receiver under ECEF has been acquired e P GNSS Sum speed of e V G By the formula (1) e V G Conversion to the geographic coordinate system n V G ，
The yaw and pitch angles are determined by projecting the velocity in a geographic coordinate system, as follows:
since roll is assigned directly to 0 for the vehicle carrier, a large initial variance is given at the same time;
s3-2 inertial navigation solution based on ECEF coordinate system
S3-2-1, in order to initialize the IMU better, firstly, slowly moving the carrier, temporarily not starting the neural network learning part, and starting the neural network learning part after the initialization is finished; reading inertial guideCarrier parameters acquired by the model airplane module, including angular velocity informationAcceleration vector->Acquiring position and velocity of a GNSS receiver using a combined system e P k+1,G And e V k+1,G ，
s3-2-2, obtaining a real-time rotation quaternion by solving the following quaternion differential equation e q＝[q 0 q 1 q 2 q 3 ] T ；
e q k+1,INS ＝ e q k,EKF (I+[w × ]) (3)
S3-2-3, the carrier acceleration vector obtained according to step S3-2-1And a rotation quaternion solved in step S3-2-2 e q solving differential equations of the following formula to obtain speed information of the carrier in three directions under a navigation coordinate system:
in the middle ofIs the rotational angular velocity of the earth, e g is the acceleration of gravity in a geographic coordinate system;
s3-2-4, respectively solving the position parameters of inertial navigation output through the following formulas;
e P k+1,INS ≈ e P k,EKF +( e V k,EKF + e V k+1,INS )Δt/2 (5)
s3-3 constraint updating with assistance of Elman neural network
When GNSS signals are lost, a neural network is connected into the system to predict the output error of inertial navigation and compensate and correct the output of inertial navigation;
s3-3-1, elman neural network design
The mathematical model of Elman neural network is:
wherein: y (k) is the output of the output layer; x (k-1) is the external input of the input layer; u (u) c (k) Output for the receiving layer; u (k) is the output of the hidden layer; w (w) 1 Connecting weights for the input layer and the hidden layer; w (w) 2 Connecting weights for the receiving layer and the hidden layer; w (w) 3 In order to connect weights between the hidden layer and the output layer, the hidden layer of the Elman neural network adopts a bipolar Sigmoid function shown in formula (7) as an excitation function, and the output layer adopts a Pureline activation function to obtain a formula (8):
f(a)＝(1-e -a )/(1+e -a ) (7)
y(k)＝w 3 u(k) (8)
derived from formulas (6) to (8):
u c (k)＝f(w 2 (k-1)u c (k-1)+w 1 (k-2)u c (k-2)) (9)
wherein f (a) is E (-1, 1); w (w) 2 (k-1) and w 1 (k-2) represents the network connection weights at the times k-1 and k-2, respectively, u c (k) The connection weight related to the historical time shows the characteristic of dynamic recursion,
the Elman neural network adopts BP algorithm to correct weight, and the learning index function adopts error square sum function:
s3-3-2, performing online learning according to the output of the inertial sensor and the EKF;
s3-3-2-1, correcting the predicted data obtained by the inertial sensor in the step S1 by adopting the position and the speed of GNSS output, and obtaining a filtered solution by Kalman filteringAnd->As in equation (11),
the GNSS measurement state in EKF is updated as follows:
wherein the method comprises the steps ofAnd->Respectively outputting values of inertial sensors; e P k+1,G and e V k+1,G output values of GNSS position and velocity, respectively;
s3-3-2-2, synchronously training the neural network model, designing the neural network model on the basis of the S3-3-2-1 step, and when the number of available satellites of the GNSS is large, relatively changing values between epochs of inertial navigation data obtained by the S3-3-2-1 and epoch of output data of a Kalman filterRespectively taking the input and the output of the Elman neural network as input and output of the Elman neural network to be added into a training sample for online learning, so that the network has the capability of predicting the speed and the position variation, then obtaining the position, the rotation quaternion and the speed of the epoch according to the position and the speed of the previous moment, and when the training error meets a certain threshold value setting, indicating that the training model is reliable and assisting the system in forecasting;
in order to ensure the timeliness of the system, a fixed window method is adopted to limit the number of samples, when the number of samples reaches a certain number, in order to ensure the timeliness of the samples, older samples are removed from the window,
and->The change quantity between epochs of the output value of the inertial sensor respectively; />And->The inter-epoch variation of the output value after Kalman filtering; />And->The solutions of the position, the attitude and the speed are output by Kalman filtering at the moment k respectively;
s3-3-3, classifying according to satellite signal shielding and non-shielding when online learning meets a threshold value for prediction;
s3-3-3-1, when GNSS satellite signals are shielded, INS can work normally due to the attribute of the INS; the GNSS data at the moment before failure is the initial value of the filtering, which is equivalent to the accurate value, so that I can be avoidedNS accuracy diverges due to long navigation time; when GNSS signals are lost, the output error of inertial navigation is predicted by using a trained neural network model, the inertial navigation is compensated and corrected by using the predicted error, and the inertial navigation is obtained by pre-integrating an inertial sensorThe prediction is carried out as the input of the Elman neural network, and the output neural network prediction data is +.>And->The EKF update is performed as an observation constraint,
predicting variance from neural networksAnd->The predicted values of the position, rotation quaternion and speed at the time k+1 are obtained as follows:
and->The predicted values of the position, the rotation quaternion and the speed at the time k+1 obtained by the neural network are respectively,
the constraint update is:
wherein,and->The state vectors output by the inertial sensor in the step S3-1 are respectively;
s3-3-3-2, when the GNSS signals are normal, two strategies are available: 1. directly using the position, speed and rotation quaternion of the moment k+1 of the inertial sensor output to update the state vector, and then using the position and speed of the GNSS output to update the constraint, as in step S3-3-2; 2. inputting the position, the speed and the rotation quaternion variable quantity of the moment k+1 of the inertial sensor output into an Elman neural network, and taking the position, the rotation quaternion and the speed variable quantity of the output of the Elman neural network as pseudo-observation values to update the state vector of the EKF, as shown in a formula (16); then, constraint updating is carried out according to the position and the speed of GNSS output, as shown in a formula (17); finally, the inertial sensor is used for obtainingAnd->And +.> And->Adding the training program to an online learning system of a neural network to perform real-time learning training,
the EKF state is updated as:
the GNSS measurement state in EKF is updated as follows:
and->The predicted variation of the neural network is respectively +.>And->Predicted values of the position, the rotation quaternion and the speed at the moment k+1 are obtained; e P k+1,G and e V k+1,G the output values of GNSS position and velocity, respectively.
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