CN112197767A - Filter design method for improving filtering error on line - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
- G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
- G01S19/47—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial
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Abstract
A filter design method for improving filter error on line, according to the application requirement of inertial navigation system and GPS receiver, adopting indirect closed-loop correction under position and speed loose combination mode to process the filter estimated value obtained by indirect method, then simplifying the design of filter estimated value, substituting the coefficient matrix after simplification into indirect closed-loop, and continuously carrying out on-line estimation or correction on system model parameter, noise statistical characteristic and state gain array, thereby realizing on-line improvement of filter design parameter to reduce actual filter error.
Description
Technical Field
The invention relates to the technical field of filter design, in particular to a filter design method for improving a filtering error on line.
Background
In a GPS/INS integrated navigation system, navigation parameters are estimated by Kalman filtering, and an important prerequisite for the application of a classical Kalman filter is that the statistical characteristics of noise must be accurately known, but because of the instability of components (an accelerometer and a gyroscope) of an actual system, the estimation environment is not constant all the time, such as multipath errors and SA errors of a GPS, the accurate description of system noise and observation noise is difficult.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a filter design method for improving the filtering error on line, so as to solve the above problems in the background art.
The technical problem solved by the invention is realized by adopting the following technical scheme:
a filter design method for improving filter error on line, according to the application requirement of inertial navigation system and GPS receiver, adopting indirect closed-loop correction under position and speed loose combination mode to process the filtering estimated value obtained by indirect method, then simplifying the design of the filtering estimated value, substituting the coefficient matrix after simplification into indirect closed-loop, and continuously carrying out on-line estimation or correction on system model parameter, noise statistical characteristic and state gain array, thereby realizing on-line improvement of filter design parameter, so as to reduce the actual filter error and achieve the purpose of improving the accuracy and reliability of the navigation system; the method comprises the following specific steps:
1) processing an indirect filtering estimated value by indirect closed-loop correction in a position and speed loose combination mode according to the application requirements of an inertial navigation system and a GPS receiver;
selecting a state vector of a system state equation
Selecting 3 position error components, 3 speed error components and 3 attitude angle error components from the state quantities of the position and speed loose combination mode, solving colored noise by adopting a state expansion method, and expanding the errors of a gyroscope and an accelerometer into an error equation as the state quantities:
the system state equation:
calculating to obtain a three-dimensional platform error angle, a three-dimensional speed error and a three-dimensional position error, then taking the three-dimensional platform error angle, the three-dimensional speed error and the three-dimensional position error as state vectors of a system state equation, obtaining respective estimated values by Kalman filtering, and correcting the output of an inertial navigation system through the estimated values, thereby improving the navigation precision;
② selecting system white noise
Taking the white noise drift (omega) of the gyroscopegx、ωgy、ωgz) Accelerometer random white noise drift (omega)ax、ωay、ωaz) And gyroscope first order Markov driven white noise (ω)rx、ωry、ωrz) As system white noise w (t):
W(t)＝[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz]T；
setting system state transfer matrix and system noise coefficient matrix
Assigning values to a system state transition matrix F (t) and a system noise coefficient matrix G (t);
selecting the measurement vector of the system measurement equation
System measurement equation
Wherein the subscript I denotes information of the inertial navigation system, the subscript G denotes information of the GPS,
because the combined mode of position and speed is adopted, two groups of observed values are shared: one group is position observation values, namely longitude and latitude and height information given by an inertial navigation system and corresponding information difference values given by a GPS receiver, and the other group is speed difference values given by the inertial navigation system and the GPS receiver respectively;
taking a speed error in the northeast direction and a position error of the longitude and latitude height of the GPS receiver as measurement white noise;
setting measurement noise coefficient matrix
And assigning a value to the measurement noise coefficient matrix N (t);
2) simplifying the design of the system state transition matrix F (t), the system noise coefficient matrix G (t) and the measurement noise coefficient matrix N (t) according to the engineering state and the requirement
The kalman filter equation is as follows:
wherein,
-a predicted value of the state at time k-1 to time k;
k (k) -the filter gain array at time k;
z (k) -the measured value at time k;
p (k/k-1) -a covariance matrix of the prediction error estimates at time k-1 versus time k;
p (k) -a covariance matrix of error estimates at time k;
q (k) -system noise variance matrix;
r (k) -system observation noise variance matrix;
a) design simplification system state transition matrix phik,k-1
Because the engineering object is generally a continuous system, but the Kalman filtering is commonly used for describing a system by a discretization model, the state transition matrix phi of the system is firstly determinedk,k-1Carrying out discretization treatment:
Φk,k-1＝eFT
wherein, T is a filtering period, and F is a system state transition matrix F (T);
considering that the filter period T is generally short, phik,k-1It can also be simplified as follows:
Φk,k-1＝I+FT+O(T2)≈I+FT(5)
b) designing a simplified process noise variance matrix
The system noise variance required in the filtering calculation is in the form of
Therefore, Q is not generally calculated separatelykInstead, a continuous system of G (t) Q (t) GT(t) direct calculation of
Wherein, G (t) is a system noise coefficient matrix, Q (t) is a variance matrix corresponding to system white noise W (t), Q (t) is a diagonal matrix, and the diagonal elements of the diagonal matrix are the variances of the white noise;
then
The calculation formula of (2) is as follows:
wherein T is the filter period, phik,k-1To simplify the system state transition matrix;
c) design simplification measurement noise error equation matrix Rk
RkFor measuring the variance matrix corresponding to the noise coefficient matrix N (t), and RkIs a diagonal matrix whose diagonal elements are the variance of the process noise;
3) determining an initial state
And the initial error variance matrix P0
Initial state of filtering
Taking different values as required, taking zero vector for convenient calculation, filteringInitial error variance matrix P0The method is characterized in that the diagonal matrix is a diagonal matrix, and diagonal elements of the diagonal matrix are determined according to the range of navigation parameter initial errors, attitude misalignment angle errors, gyro drift errors and accelerometer deviations in combination with engineering;
4) design of Kalman filter using simplified coefficient matrix
The simplified system state transition matrix phi obtained by the processing in the step 2)k,k-1Simplified process noise variance matrix
Simplified measurement noise error equation matrix RkAnd the initial state determined in step 3)
And the initial error variance matrix P0The method substitutes indirect closed loop to carry out correction, and continuously carries out online estimation or correction on unknown or unknown system model parameters, noise statistical characteristics and state gain arrays while carrying out filtering by utilizing observation data, thereby realizing online improvement of filter design parameters, reducing actual filtering errors and achieving the purpose of improving the precision and reliability of a navigation system.
Has the advantages that: the method comprises the steps of processing a filtering estimated value obtained by an indirect method by adopting an indirect method closed loop in a position and speed loose combination mode, then simply designing the filtering estimated value, determining an initial error range by combining engineering experience in the process of developing a missile system, substituting a simplified coefficient matrix and the initial error into the indirect method closed loop, and continuously carrying out online estimation or correction on system model parameters, noise statistical characteristics and a state gain array, thereby realizing online improvement of filter design parameters and reducing the actual filtering error; the filter designed by the invention has a simple structure, is convenient for the concrete realization of actual engineering, is beneficial to the implementation of calculation by a computer, has a good filtering effect, and can effectively improve the filtering precision.
Drawings
FIG. 1 is a schematic diagram of indirect closed loop in the preferred embodiment of the present invention.
FIG. 2 is a schematic diagram of an inertial navigation system according to a preferred embodiment of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further explained below by combining the specific drawings.
A filter design method for improving filter error on line, firstly, according to the application requirements of an inertial navigation system and a GPS receiver, processing the filter estimation value obtained by an indirect method by indirect method closed loop correction under a position and speed loose combination mode, then simplifying the design of the filter estimation value, substituting the coefficient matrix after simplification into the indirect method closed loop, and continuously carrying out on-line estimation or correction on system model parameters, noise statistical characteristics and a state gain array, thereby realizing the on-line improvement of filter design parameters to reduce the actual filter error; the method comprises the following specific steps:
1) according to the application requirements of an inertial navigation system and a GPS receiver, indirect closed-loop correction in a position and speed loose combination mode is adopted to process indirect filtering estimated values, and the principle is shown in figure 1;
selecting a state vector of a system state equation
Selecting 3 position error components, 3 speed error components and 3 attitude angle error components from the state quantities of the position and speed loose combination mode, solving colored noise by adopting a state expansion method, and expanding the errors of a gyroscope and an accelerometer into an error equation as the state quantities:
the system state equation:
calculating to obtain a three-dimensional platform error angle, a three-dimensional speed error and a three-dimensional position error, then taking the three-dimensional platform error angle, the three-dimensional speed error and the three-dimensional position error as state vectors of a system state equation, obtaining respective estimated values by Kalman filtering, and correcting the output of an inertial navigation system through the estimated values, thereby improving the navigation precision;
② selecting system white noise
Taking the white noise drift (omega) of the gyroscopegx、ωgy、ωgz) Accelerometer random white noise drift (omega)ax、ωay、ωaz) And gyroscope first order Markov driven white noise (ω)rx、ωry、ωrz) As system white noise w (t):
W(t)＝[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz]T；
setting system state transfer matrix and system noise coefficient matrix
Assigning values to a system state transition matrix F (t) and a system noise coefficient matrix G (t);
selecting the measurement vector of the system measurement equation
System measurement equation
Wherein the subscript I denotes information of the inertial navigation system, the subscript G denotes information of the GPS,
because this embodiment adopts the position, speed combination mode, so there are two sets of observed values in total: one group is position observation values, namely longitude and latitude and height information given by an inertial navigation system and corresponding information difference values given by a GPS receiver, and the other group is speed difference values given by the inertial navigation system and the GPS receiver respectively;
taking a speed error in the northeast direction and a position error of the longitude and latitude height of the GPS receiver as measurement white noise;
setting measurement noise coefficient matrix
And assigning a value to the measurement noise coefficient matrix N (t);
2) simplifying the design of the system state transition matrix F (t), the system noise coefficient matrix G (t) and the measurement noise coefficient matrix N (t) according to the engineering state and the requirement
The kalman filter equation is designed as follows:
wherein,
-a predicted value of the state at time k-1 to time k;
k (k) -the filter gain array at time k;
z (k) -the measured value at time k;
p (k/k-1) -a covariance matrix of the prediction error estimates at time k-1 versus time k;
p (k) -a covariance matrix of error estimates at time k;
q (k) -system noise variance matrix;
r (k) -system observation noise variance matrix;
a) design simplification system state transition matrix phik,k-1
Because the engineering object is generally a continuous system, but the Kalman filtering is commonly used for describing a system by a discretization model, the state transition matrix phi of the system is firstly determinedk,k-1Carrying out discretization treatment:
Φk,k-1＝eFT
wherein, T is a filtering period, and F is a system state transition matrix F (T);
considering that the filter period T is generally short, phik,k-1It can also be simplified as follows:
Φk,k-1＝I+FT+O(T2)≈I+FT (5)
b) designing a simplified process noise variance matrix
The system noise variance required in the filtering calculation is in the form of
Therefore, Q is not generally calculated separatelykInstead, a continuous system of G (t) Q (t) GT(t) direct calculation of
Wherein, G (t) is a system noise coefficient matrix, Q (t) is a variance matrix corresponding to system white noise W (t), Q (t) is a diagonal matrix, and the diagonal elements of the diagonal matrix are the variances of the white noise;
then
The calculation formula of (2) is as follows:
wherein T is the filter period, phik,k-1To simplify the system state transition matrix;
because the measurement information of the GPS in the SINS/GPS integrated navigation system is provided at the time interval of about 1 second, the measurement equation is discrete, and the discretization processing is not needed;
c) design simplification measurement noise error equation matrixRk
RkFor measuring the variance matrix corresponding to the noise coefficient matrix N (t), and RkIs a diagonal matrix whose diagonal elements are the variance of the process noise;
3) determining an initial state
And the initial error variance matrix P0
Initial state of filtering
Taking different values as required, taking the values as zero vectors for convenient calculation, and taking the initial error variance matrix P of filtering0The method is characterized in that the diagonal matrix is a diagonal matrix, and diagonal elements of the diagonal matrix are determined according to the range of navigation parameter initial errors, attitude misalignment angle errors, gyro drift errors and accelerometer deviations in combination with engineering;
4) design of Kalman filter using simplified coefficient matrix
As shown in fig. 2, the simplified system state transition matrix Φ obtained by the processing in step 2) is usedk,k-1Simplified process noise variance matrix
Simplified measurement noise error equation matrix RkAnd the initial state determined in step 3)
And the initial error variance matrix P0The method substitutes indirect closed loop to carry out correction, and continuously carries out online estimation or correction on unknown or unknown system model parameters, noise statistical characteristics and state gain arrays while carrying out filtering by utilizing observation data, thereby realizing online improvement of filter design parameters, reducing actual filtering errors and achieving the purpose of improving the precision and reliability of a navigation system.
Claims (8)
1. A filter design method for improving filter error on line is characterized in that according to application requirements of an inertial navigation system and a GPS receiver, indirect closed-loop correction under a position and speed loose combination mode is adopted to process filter estimated values obtained by an indirect method, then simplified design is carried out on the filter estimated values, simplified coefficient matrixes are substituted into indirect closed-loop, and on-line estimation or correction is carried out on system model parameters, noise statistical characteristics and state gain matrixes continuously, so that filter design parameters are improved on line, and actual filter errors are reduced.
2. The method for designing the filter for improving the filtering error online according to claim 1, comprising the following steps:
1) processing an indirect filtering estimated value by indirect closed-loop correction in a position and speed loose combination mode according to the application requirements of an inertial navigation system and a GPS receiver;
selecting a state vector of a system state equation
Selecting 3 position error components, 3 speed error components and 3 attitude angle error components from the state quantities of the position and speed loose combination mode, solving colored noise by adopting a state expansion method, and expanding the errors of a gyroscope and an accelerometer into an error equation as the state quantities:
the system state equation:
taking the obtained three-dimensional platform error angle, three-dimensional speed error and three-dimensional position error as state vectors of a system state equation, and obtaining respective estimated values by Kalman filtering;
② selecting system white noise
Taking the white noise drift (omega) of the gyroscopegx、ωgy、ωgz) Accelerometer random white noise drift (omega)ax、ωay、ωaz) And gyroscope first order Markov driven white noise (ω)rx、ωry、ωrz) As system white noise w (t):
W(t)＝[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz]T；
setting system state transfer matrix and system noise coefficient matrix
Assigning values to a system state transition matrix F (t) and a system noise coefficient matrix G (t);
selecting the measurement vector of the system measurement equation
Because of the position and speed combination mode, two groups of observed values are shared: one group is position observation values, namely longitude and latitude and height information given by an inertial navigation system and corresponding information difference values given by a GPS receiver, and the other group is speed difference values given by the inertial navigation system and the GPS receiver respectively;
taking a speed error in the northeast direction and a position error of the longitude and latitude height of the GPS receiver as measurement white noise;
setting measurement noise coefficient matrix
And assigning a value to the measurement noise coefficient matrix N (t);
2) simplifying the system state transition matrix F (t), the system noise coefficient matrix G (t) and the measurement noise coefficient matrix N (t) according to the engineering state and the requirement to obtain a simplified system state transition matrix phik,k-1Simplified process noise variance matrix
Simplified measurement noise error equation matrix Rk；
3) Determining an initial state
And the initial error variance matrix P0
4) Design of Kalman filter using simplified coefficient matrix
The simplified system state transition matrix phi obtained by the processing in the step 2)k,k-1Simplified process noise variance matrix
Simplified measurement noise error equation matrix RkAnd the initial state determined in step 3)
And the initial error variance matrix P0And substituting the closed loop of an indirect method, and continuously carrying out online estimation or correction on unknown or unknown system model parameters, noise statistical characteristics and a state gain array so as to realize online improvement of filter design parameters.
3. The filter design method for improving filtering error online according to claim 2, wherein, in step 1),
the system measurement equation
The subscript I indicates information of the inertial navigation system, and the subscript G indicates information of the GPS.
4. The method for designing the filter for improving the filtering error online according to claim 2, wherein in step 2), the kalman filtering equation is as follows:
wherein,
-a predicted value of the state at time k-1 to time k;
k (k) -the filter gain array at time k;
z (k) -the measured value at time k;
p (k/k-1) -a covariance matrix of the prediction error estimates at time k-1 versus time k;
p (k) -a covariance matrix of error estimates at time k;
q (k) -system noise variance matrix;
r (k) -system observation noise variance matrix;
derived from equation (4): the simplified system state transition matrix phik,k-1：
Φk,k-1＝I+FT+O(T2)≈I+FT (5)
Wherein, T is a filtering period, and F is a system state transition matrix F (T);
the simplified process noise variance matrix
Wherein T is the filter period, phik,k-1To simplify the system state transition matrix.
5. The method as claimed in claim 4, wherein the simplified process noise variance matrix is a simplified process noise variance matrix
Is calculated asThe following:
the system noise variance required in the filtering calculation is in the form of
Therefore, Q is not generally calculated separatelykInstead, a continuous system of G (t) Q (t) GT(t) direct calculation of
Wherein, g (t) is a system noise coefficient matrix, q (t) is a variance matrix corresponding to the system white noise w (t), q (t) is a diagonal matrix, and the diagonal element thereof is the variance of the white noise, and the formula (7) is obtained by simplifying the formula (6).
6. The method as claimed in claim 2, wherein in step 2), the simplified measurement noise error equation matrix R is used for designing the filter for improving the filtering error onlinekThe corresponding variance matrix of the noise coefficient matrix N (t) is measured.
7. The method as claimed in claim 6, wherein the simplified measurement noise error equation matrix R is a simplified measurement noise error equation matrixkIs a diagonal matrix.
8. The method of claim 7, wherein the simplified measurement noise error equation matrix R is used for designing a filter for improving filtering errors on linekThe diagonal element is the variance of the process noise.
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