CN114018262B - Improved derivative volume Kalman filtering integrated navigation method - Google Patents
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- 238000005259 measurement Methods 0.000 claims abstract description 55
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Classifications
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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
-
- 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
-
- 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
- G01S19/393—Trajectory determination or predictive tracking, e.g. Kalman filtering
-
- 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
Abstract
The invention relates to the technical field of navigation positioning and deep learning, and particularly discloses an improved derivative volume Kalman filtering integrated navigation method. Initializing an SINS and GPS integrated navigation system; in the time updating process, CKF is filtered in the same mode as KF, so that additional calculation caused by volume transformation of a state equation with linear characteristics is avoided, in the measurement updating process, a volume point is adopted to calculate a predicted value and covariance thereof, and cross covariance between the state predicted value and the measured value, excellent characteristics of the CKF for processing nonlinear filtering are ensured, and the redundant calculation problem of a tightly combined system is solved. The invention can improve the filtering precision of the system, the tracking capability of the filter to the system state, the real-time performance of the system state and the robustness of the SINS/GPS integrated navigation system.
Description
Technical Field
The invention relates to the technical field of navigation positioning and deep learning, in particular to an improved derivative volume Kalman filtering combined navigation method.
Background
Modern vehicles place increasing demands on the accuracy and reliability of navigation systems, and single navigation approaches have failed to meet the demands. Therefore, the navigation technology is a necessary trend toward the combination direction. The combined navigation utilizes the complementarity of INS and GPS, and the combined navigation of the INS and the GPS can overcome the defects of the INS and the GPS, and can provide short-time and long-time full navigation parameters with higher precision.
The close-coupled system adopts pseudo-range information to construct a measurement value, and the pseudo-range information is nonlinear in nature, so that a measurement equation of the close-coupled system constructed by the pseudo-range information has nonlinear characteristics, and the traditional processing method is to perform taylor expansion on the pseudo-range, omit high-order terms to perform linearization processing, and then apply a linear algorithm to perform state estimation. However, the measurement model error caused by the linearization and truncation of the pseudo-range measurement will cause the integrated navigation accuracy to be poor or even divergent. Thus, preserving taylor expansion of pseudoranges at or above second order improves filtering performance and reduces positioning errors.
The volume Kalman is derived through a strict mathematical formula based on the rule of solving the volume by a third-order spherical surface and a phase diameter, and for an n-dimensional system, only 2n sampling points are needed to be calculated. CKF can reduce the amount of computation compared to UKF. The weights of all the volume points of the CKF are the same and positive, so that the situation of uncertainty of covariance does not occur in the process of calculation. The taylor expansion of pseudo-range and retention of second-order expansion can lead to increased calculation amount, the dimension of the state vector of the tightly combined system is far higher than that of the measurement vector, the additional calculation load caused by the standard CKF is relatively heavier, in order to reduce the calculation complexity of the standard CKF in the tightly combined system application, a derivative CKF algorithm is provided, in time update, the derivative CKF can avoid the additional calculation caused by volume processing when processing the state equation with linear characteristics, and the excellent characteristic of the nonlinear problem of CKF processing is maintained when the measurement is updated. The derivative CKF effectively solves the problem that the standard CKF has redundant calculation in the application of a tightly combined system, improves the real-time performance of the system, and provides an improved derivative volume Kalman filtering combined navigation method.
Disclosure of Invention
The invention aims to provide an improved derivative volume Kalman filtering integrated navigation method which can improve filtering precision, reduce system calculation complexity, improve filter instantaneity and enhance robustness.
In order to achieve the above purpose, the improved derivative volume Kalman filtering integrated navigation method adopted by the invention comprises the following steps:
Loading actual measurement SINS data and GPS system data;
establishing a SINS/GPS integrated navigation system state space model;
initializing an SINS/GPS integrated navigation system;
Performing time updating and measurement updating of derived volume Kalman at the moment k to obtain an error covariance value of one-step state prediction and a cross covariance value of one-step state prediction;
And measuring and updating by using the error covariance value of the one-step state prediction to obtain the state estimation value and the state error covariance at the time k+1, and finishing the state estimation of the system.
The method for establishing the SINS/GPS integrated navigation system state space model specifically comprises the following steps:
selecting SINS/GPS integrated navigation system state variables:
In a close-coupled GPS navigation error state, two are typically chosen, one being the distance error δt u equivalent to the clock error and the other being the distance error δt ru equivalent to the clock frequency error;
the strapdown inertial navigation coordinate system adopts a geographic coordinate system, and the navigation error states are 15, namely the error angle of the three-dimensional platform Three-dimensional velocity error δv n＝[δvE δvN δvU]T, three-dimensional position error δc= [ δλδlδh ] T; equivalent gyro drift on the geographic system triaxial is epsilon n＝[εE εN εU]T respectively, and equivalent accelerometer errors are V n＝[▽E ▽N ▽U]T respectively;
the state equation is: f (·) is the equation of state; g (t) is a system noise driving matrix; w (t) represents system noise, gaussian white noise, and is derived from noise parts of gyroscopes and accelerometers;
The tightly combined quantity is measured as a pseudo range, and the pseudo range of the GNSS receiver is measured as ρ (i)＝R(i)+bp+v(i); wherein R (i)＝||r-rs I is the geometric distance between the GNSS receiver and the ith satellite; r is the true position vector of the carrier; is the position vector of the ith satellite; b p is the receiver clock error; v (i) is the pseudorange measurement error, typically described by white noise; expanding the expression ρ (i)＝R(i)+bp+v(i) at r ins to a Taylor series and ignoring higher order terms above the second order, we can obtain:
Wherein/> Representing the i-th pseudorange measurement as expanded at r (ins) to the Taylor series,/>The Hessian matrix representing the ith pseudorange measurement at r (ins), note Du＝[J(1)(rins),J(2)(rins),J(3)(rins),J(4)(rins)]T and e= [1, 1] T, let G k(rins)＝[Du e ]; arrange the above materials, have/>
The established nonlinear measurement equation reserves the second-order information of GNSS pseudo-range measurement, and the nonlinear measurement equation of the INS/GNSS tightly combined system is established by performing second-order Taylor expansion on the GNSS pseudo-range measurement:
xk＝Φk/k+1xk-1+ωk；
zk＝h(xk)+vk；
Wherein x k∈Rn and z k∈Rm are the state vector and the measurement vector of the system at the k moment respectively; phi k/k-1 is a discrete state transition matrix; h (·) is a nonlinear function describing the metrology model; omega k and v k are uncorrelated zero-mean Gaussian white noise processes with variance of
Wherein the improved derivative volume Kalman filtering algorithm specifically comprises the following steps:
giving state estimation values and covariance thereof;
Updating time;
Calculating updated state volume points;
a volume point transmitted by the measurement equation;
calculating a measurement predicted value at the moment k+1, and a measurement error covariance matrix and a one-step prediction cross-correlation covariance matrix;
calculating a filter gain matrix at the moment k+1;
calculating a state estimation value at the moment k+1;
And calculating a state error covariance matrix at the moment k+1.
Compared with the prior art, the method has the following advantages:
According to the improved derivative volume Kalman filtering integrated navigation method, a tightly combined system equation is analyzed, the origin of pseudo-range measurement in the system equation is analyzed, the second order term of the pseudo-range Taylor expansion is reserved, the measurement equation is subjected to nonlinearity, and the problems of measurement model errors and integrated navigation precision deterioration and even divergence caused by linearization and truncation of pseudo-range measurement are solved. Meanwhile, a derived volume Kalman filter is provided according to an improved tight combination system equation, redundant calculation of the system is reduced in a state updating stage, excellent characteristics of the volume Kalman processing nonlinear problem are reserved, and instantaneity and robustness of the system are improved.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a block diagram of a mechanical orchestration of strapdown inertial navigation in the present invention.
FIG. 2 is a flow chart of a tight-fitting system according to the present invention.
FIG. 3 is a schematic diagram of an improved derivative volume Kalman filtering integrated navigation method of the present invention.
FIG. 4 is a schematic representation of a simulated three-dimensional trajectory of a carrier in accordance with the present invention.
Fig. 5 is a graph of the northeast-north speed error of the present invention DCKF versus the conventional algorithms UKF, CKF.
Fig. 6 is a graph showing the comparison of the longitude and latitude high position errors of the present invention DCKF and the conventional algorithms UKF, CKF.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention.
Referring to fig. 1 to 6, the present invention provides an improved derivative volume kalman filter integrated navigation method, which includes the following steps:
Step one: loading actual measurement SINS data and GPS system data;
step two: establishing a SINS/GPS integrated navigation system state space model;
step three: initializing an SINS/GPS integrated navigation system;
Step four: performing time updating and measurement updating of derived volume Kalman at the moment k to obtain an error covariance value of one-step state prediction and a cross covariance value of one-step state prediction;
Step five: and measuring and updating by using the error covariance value of the one-step state prediction to obtain the state estimation value and the state error covariance at the time k+1, and finishing the state estimation of the system.
The establishing of the SINS/GPS integrated navigation system state space model specifically comprises the following steps:
selecting SINS/GPS integrated navigation system state variables:
In a close-coupled GPS navigation error state, two are typically chosen, one being the distance error δt u equivalent to the clock error and the other being the distance error δt ru equivalent to the clock frequency error;
the strapdown inertial navigation coordinate system adopts a geographic coordinate system, and the navigation error states are 15, namely the error angle of the three-dimensional platform Three-dimensional velocity error δv n＝[δvE δvN δvU]T, three-dimensional position error δc= [ δλδlδh ] T; equivalent gyro drift on the geographic system triaxial is epsilon n＝[εE εN εU]T respectively, and equivalent accelerometer errors are V n＝[▽E ▽N ▽U]T respectively;
the state equation is: f (·) is the equation of state; g (t) is a system noise driving matrix; w (t) represents system noise, gaussian white noise, and is derived from noise parts of gyroscopes and accelerometers;
The tightly combined quantity is measured as a pseudo range, and the pseudo range of the GNSS receiver is measured as ρ (i)＝R(i)+bp+v(i); wherein R (i)＝||r-rs I is the geometric distance between the GNSS receiver and the ith satellite; r is the true position vector of the carrier; is the position vector of the ith satellite; b p is the receiver clock error; v (i) is the pseudorange measurement error, typically described by white noise; expanding the expression ρ (i)＝R(i)+bp+v(i) at r ins to a Taylor series and ignoring higher order terms above the second order, we can obtain:
Wherein/> Representing the i-th pseudorange measurement as expanded at r (ins) to the Taylor series,/>The Hessian matrix representing the ith pseudorange measurement at r (ins), note Du＝[J(1)(rins),J(2)(rins),J(3)(rins),J(4)(rins)]T and e= [1, 1] T, let G k(rins)＝[Du e ]; arrange the above materials, have/>
The established nonlinear measurement equation reserves the second-order information of GNSS pseudo-range measurement, and can effectively reduce the measurement model error of the INS/GNSS tightly combined system by using the equation, thereby improving the navigation accuracy of the system. By performing second-order Taylor expansion on GNSS pseudo-range measurement, a nonlinear measurement equation of the INS/GNSS tightly combined system is established:
xk＝Φk/k+1xk-1+ωk；
zk＝h(xk)+vk；
Wherein x k∈Rn and z k∈Rm are the state vector and the measurement vector of the system at the k moment respectively; phi k/k-1 is a discrete state transition matrix; h (·) is a nonlinear function describing the metrology model; omega k and v k are uncorrelated zero-mean Gaussian white noise processes with variance of
After a system equation is established, derived volume Kalman is adopted for filtering, and the method specifically comprises the following steps:
(1) Given state estimation values And covariance/>
(2) And (5) updating time. Since the system state equation is linear, the calculation of the state predictor and its covariance is the same as KF, i.e
(3) Calculating updated state volume pointsWherein m is the system state dimension; covariance matrix/>S k+1|k is/>Cholesky decomposition of >/>[1] Represents an n-dimensional unit vector e= [1,0, ], 0 T changing element symbols to perform full arrangement to generate a point set, and the ith column of the [1] i table set [1 ];
Pk+1|k＝Sk+1|k(Sk+1|k)T
(4) Volume point transferred by measurement equation
(5) Calculating a measurement prediction value at time k+1Measurement error covariance matrix P zz,k+1|k and one-step prediction cross-correlation covariance matrix P xz,k+1|k
(6) Calculating a filter gain matrix K at time k+1 k+1
Kk+1＝Pxz,k+1|k(Pzz,k+1|k)-1
(7) Calculating state estimation value at k+1 time
(8) Calculating a state error covariance matrix P at the moment k+1 k+1
In summary, the invention provides an improved derivative volume kalman filtering integrated navigation method, which establishes a state equation and a measurement equation according to a tightly combined model, carries out second-order taylor expansion on pseudo-range measurement, and reduces the measurement model brought by linearization truncation. Initializing an SINS and GPS integrated navigation system; in the time updating process, CKF is filtered in the same mode as KF, so that additional calculation caused by volume transformation of a state equation with linear characteristics is avoided, in the measurement updating process, a volume point is adopted to calculate a predicted value and covariance thereof, and cross covariance between the state predicted value and the measured value, excellent characteristics of the CKF for processing nonlinear filtering are ensured, and the redundant calculation problem of a tightly combined system is solved. The invention can improve the filtering precision of the system, the tracking capability of the filter to the system state, the real-time performance of the system state and the robustness of the SINS/GPS integrated navigation system.
The above disclosure is only a preferred embodiment of the present invention, and it should be understood that the scope of the invention is not limited thereto, and those skilled in the art will appreciate that all or part of the procedures described above can be performed according to the equivalent changes of the claims, and still fall within the scope of the present invention.
Claims (2)
1. An improved derivative volume Kalman filtering integrated navigation method is characterized by comprising the following steps:
Loading actual measurement SINS data and GPS system data;
establishing a SINS/GPS integrated navigation system state space model;
initializing an SINS/GPS integrated navigation system;
Performing time updating and measurement updating of derived volume Kalman at the moment k to obtain an error covariance value of one-step state prediction and a cross covariance value of one-step state prediction;
measuring and updating by using the error covariance value of the one-step state prediction to obtain a state estimation value and a state error covariance at the time k+1, and finishing state estimation of the system;
the establishing of the SINS/GPS integrated navigation system state space model specifically comprises the following steps:
selecting SINS/GPS integrated navigation system state variables:
In the close combination, two GPS navigation error states are selected, one is the distance error delta t u equivalent to the clock error, and the other is the distance error delta t ru equivalent to the clock frequency error;
the strapdown inertial navigation coordinate system adopts a geographic coordinate system, and the navigation error states are 15, namely the error angle of the three-dimensional platform Three-dimensional velocity error δv n＝[δvE δvN δvU]T, three-dimensional position error δc= [ δλδlδh ] T; equivalent gyroscopic drift on the geographic system triaxial is epsilon n＝[εE εN εU]T respectively, and equivalent accelerometer errors are epsilon n＝[εE εN εU]T respectively
The state equation is: f (·) is the equation of state; g (t) is a system noise driving matrix; w (t) represents system noise, gaussian white noise, and is derived from noise parts of gyroscopes and accelerometers;
The tightly combined quantity is measured as a pseudo range, and the pseudo range of the GNSS receiver is measured as ρ (i)＝R(i)+bp+v(i); wherein R (i)＝||r-rs I is the geometric distance between the GNSS receiver and the ith satellite; r is the true position vector of the carrier; Is the position vector of the ith satellite; b p is the receiver clock error; v (i) is the pseudo-range measurement error, described by white noise; expanding the expression ρ (i)＝R(i)+bp+v(i) at r ins to a Taylor series and ignoring higher order terms above the second order, we can obtain:
Wherein/> Representing the i-th pseudorange measurement as expanded at r (ins) to the Taylor series,/>The Hessian matrix representing the ith pseudorange measurement at r (ins), note Du＝[J(1)(rins),J(2)(rins),J(3)(rins),J(4)(rins)]T and e= [1, 1] T, let G k(rins)＝[Du e ]; arrange the above materials, have/>
The established nonlinear measurement equation reserves the second-order information of GNSS pseudo-range measurement, and the nonlinear measurement equation of the INS/GNSS tightly combined system is established by performing second-order Taylor expansion on the GNSS pseudo-range measurement:
xk＝Φk/k+1xk-1+ωk；
zk＝h(xk)+vk；
Wherein x k∈Rn and z k∈Rm are the state vector and the measurement vector of the system at the k moment respectively; phi k/k-1 is a discrete state transition matrix; h (·) is a nonlinear function describing the metrology model; omega k and v k are uncorrelated zero-mean Gaussian white noise processes with variance of
2. The improved derivative volume kalman filter combined navigation method according to claim 1, wherein the improved derivative volume kalman filter algorithm specifically comprises the following steps:
giving state estimation values and covariance thereof;
Updating time;
Calculating updated state volume points;
a volume point transmitted by the measurement equation;
calculating a measurement predicted value at the moment k+1, and a measurement error covariance matrix and a one-step prediction cross-correlation covariance matrix;
calculating a filter gain matrix at the moment k+1;
calculating a state estimation value at the moment k+1;
And calculating a state error covariance matrix at the moment k+1.
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| CN101975956A (en) * | 2010-10-10 | 2011-02-16 | 桂林电子科技大学 | CAPS (China Area Position System) satellite analog signal generator |
| CN102128624A (en) * | 2010-12-28 | 2011-07-20 | 浙江大学 | High dynamic strapdown inertial navigation parallel computing device |
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| CN101975956A (en) * | 2010-10-10 | 2011-02-16 | 桂林电子科技大学 | CAPS (China Area Position System) satellite analog signal generator |
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