CN113503895B - Three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering - Google Patents
Three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering Download PDFInfo
- Publication number
- CN113503895B CN113503895B CN202110650825.8A CN202110650825A CN113503895B CN 113503895 B CN113503895 B CN 113503895B CN 202110650825 A CN202110650825 A CN 202110650825A CN 113503895 B CN113503895 B CN 113503895B
- Authority
- CN
- China
- Prior art keywords
- accelerometer
- inertial navigation
- error
- inertial
- inner frame
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- 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
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Manufacturing & Machinery (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Navigation (AREA)
Abstract
The application provides a three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering, which comprises the following steps: performing coarse alignment on an inertial navigation system; inertial navigation calculation is carried out according to the gyro angular rate and specific force information so as to finish updating of attitude quaternion, position and speed; the inner frame and the outer frame of the inertial navigation system rotate according to a preset rotation sequence and a preset rotation angle, and the gyro angular rate and the accelerometer specific force in the rotation process are obtained; constructing a system error model according to errors of the inertial navigation device, the size of the accelerometer and the inertial navigation resolving result; initializing Kalman filter parameters; and performing inertial device error estimation and accelerometer size estimation by adopting a discrete Kalman filter equation. By applying the technical scheme of the application, the technical problem that the navigation accuracy is affected due to the fact that the inertial device error is coupled with the accelerometer size error and cannot be separated accurately in the prior art can be solved.
Description
Technical Field
The application relates to the technical field of inertial navigation, in particular to a three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering.
Background
In an inertial navigation system, due to mechanical structure and installation reasons, the sensitive mass centers of three accelerometers are not coincident or have larger deviation after being compensated by the measured size of a model. Dimensional effect errors of the accelerometer measurement assembly can be caused when the carrier undergoes vibration or large angular movements. For the three-self inertial measurement unit aligned in a rotating mode, the speed error generated by the size effect error and the equivalent zero error with the meter in the alignment process cannot be ignored, and parameter calibration and compensation are required. In the past, the size of the accelerometer is usually ensured by a model design, when deviation occurs, related parameters are generally identified by utilizing a least square mode through utilizing a speed error excited by angular vibration, and when the device error of an inertial navigation system is not accurately compensated, the inertial device error is coupled with the size error of the accelerometer and cannot be accurately separated.
Disclosure of Invention
The application provides a three-self inertial component accelerometer size estimation method based on Kalman filtering, which can solve the technical problem that the navigation accuracy is affected due to the fact that inertial device errors are coupled with accelerometer size errors and cannot be separated accurately in the prior art.
The application provides a three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering, which comprises the following steps: performing coarse alignment on the inertial navigation system to obtain an inertial navigation initial attitude; inertial navigation calculation is carried out according to the gyro angular rate and specific force information so as to finish updating of attitude quaternion, position and speed; the inner frame and the outer frame of the inertial navigation system rotate according to a preset rotation sequence and a preset rotation angle, and the gyro angular rate and the accelerometer specific force in the rotation process are obtained; constructing a system error model according to errors of the inertial navigation device, the size of the accelerometer and the inertial navigation resolving result; initializing Kalman filter parameters; and (3) performing inertial device error estimation and accelerometer size estimation by adopting a discrete Kalman filter equation according to the gyro angular rate, the acceleration Ji Bi force and the system error model in the rotation process so as to finish three-self inertial group accelerometer size estimation based on Kalman filtering.
Further, the preset rotation sequence and rotation angle of the inner frame and the outer frame of the inertial navigation system are specifically as follows: an inner frame: 0 DEG frame: 0 °, inner frame: 0 DEG frame: 90 °, inner frame: 0 DEG frame: 180 °, inner frame: 0 DEG frame: 270 °, inner frame: 0 DEG frame: 180 °, inner frame: 0 DEG frame: 90 °, inner frame: 0 DEG frame: 0 °, inner frame: 90-degree outer frame: 0 °, inner frame: 90-degree outer frame: 90 °, inner frame: 90-degree outer frame: 180 °, inner frame: 90-degree outer frame: 270 °, inner frame: 90-degree outer frame: 180 °, inner frame: 90-degree outer frame: 90 °, inner frame: 90-degree outer frame: 0 °, inner frame: 180 DEG outer frame: 0 °, inner frame: 270 DEG frame: 0 °, inner frame: 180 DEG outer frame: 0 °, inner frame: 90-degree outer frame: 0 ° and inner frame: 0 DEG frame: 0 deg..
Further, constructing a system error model according to the inertial navigation device error, the accelerometer size and the inertial navigation solution result specifically comprises: constructing a state variable of the inertial navigation system according to the inertial navigation device error and the accelerometer size; and constructing a system error model according to the state variable and the inertial navigation solution result.
Further according toConstructing a state variable of an inertial navigation system, wherein X k State variables representing the k time, δl, δh, and δλ represent the latitude error, the altitude error, and the longitude error, δv, respectively, of the inertial navigation system N 、δV U And δV E Respectively representing north speed error, sky speed error and east speed error of inertial navigation system N 、φ U And phi E Respectively representing misalignment angles of north, sky and east directions in a geographic coordinate system of an inertial navigation system, ++>And->Respectively representing zero errors epsilon of accelerometers in three directions of X, Y and Z in a measurement coordinate system of an inertial navigation system x 、ε y And epsilon z Respectively representing constant drift, k of gyroscopes in X, Y and Z directions in measurement coordinate system of inertial navigation system ax 、k ay And k az Scale factor errors, k, respectively representing an x accelerometer, a y accelerometer and a z accelerometer in a measurement coordinate system of an inertial navigation system ayx 、k azx And k azy K respectively representing the installation error of the x accelerometer relative to the Y direction, the installation error of the x accelerometer relative to the Z direction and the installation error of the Y accelerometer relative to the Z direction in the measurement coordinate system of the inertial navigation system ax2 、k ay2 And k az2 Represent the quadratic coefficient errors, k, of the x accelerometer, the y accelerometer and the z accelerometer in the measurement coordinate system of the inertial navigation system respectively gx 、k gy And k gz Respectively representing scale factor errors, k of an x gyroscope, a y gyroscope and a z gyroscope in a measurement coordinate system of an inertial navigation system gxy 、k gxz 、k gyx 、k gyz 、k gzx And k gzy The measurement system respectively shows the installation error of the Y gyroscope relative to the X direction, the installation error of the Z gyroscope relative to the X direction, the installation error of the X gyroscope relative to the Y direction, the installation error of the Z gyroscope relative to the Y direction, the installation error of the X gyroscope relative to the Z direction and the installation error of the Y gyroscope relative to the Z direction in the inertial navigation system measurement coordinate system.
Further according toConstructing a system error model, wherein phi k.k-1 For the state transition matrix from time k-1 to time k of the system, X k-1 Is the state variable at time k-1, W k-1 Representing system noise at time k-1 of system, Z k For the system observation quantity at k moment, H k For the observation matrix at time k +.>I is an identity matrix, v k Is the observed noise at time k.
Further according toAcquiring a state transition matrix phi k,k-1 Wherein T is n For navigational period, T e For the filtering period A t Is a state transition matrix at the time t,
B 4 ＝0 3×3 ，/>
ω ie for the rotation angular velocity of the earth, V N 、V U And V E North, sky and east speeds of inertial navigation, L and h are latitude and altitude of inertial navigation, R M And R is N Respectively, the radius of the meridian plane and the mortise unitary plane of the earth, < ->Posture conversion matrix for b-series to n-series, < >>And->Gyro output angular rates of an x gyro, a y gyro and a z gyro under an inertial navigation body coordinate system respectively, < >>And->Is an inertial navigation body seatMeter-added output specific force of x accelerometer, y accelerometer and z accelerometer under standard system,/>And->And outputting the angular acceleration of the x gyroscope, the y gyroscope and the z gyroscope, which are obtained by differentiating the angular rate for the gyroscope.
Further, according to Z k ＝[L-L 0 h-h 0 λ-λ 0 V N V U V E ] T Acquiring system observables Z k Wherein λ is the inertial navigation longitude, L 0 、h 0 And lambda (lambda) 0 Initial binding latitude, altitude, and longitude, respectively.
Further, initializing the kalman filter parameters specifically includes: setting an initial covariance matrix P of Kalman filtering 0 System noise variance matrix Q and system error state initial value X 0 And Kalman filtering calculation period T k 。
Further according toP k+1/k ＝Φ k+1,k P k/k Φ T k+1,k +Q k ，K k+1 ＝P k+1/k H T k+1 [H k+1 P k+1/k H T k+1 +R k+1 ] -1 ，P k+1/k+1 ＝[I-K k+1 H k+1 ]P k+1/k ，Performing Kalman filtering, wherein phi k+1,k For the state transition matrix from time k to time k +1,and->The estimated value is respectively the estimated value of the system state quantity at the moment k, the one-step prediction estimated value of the system state quantity at the moment k to the moment k+1 and the estimated value after the measurement and update of the system state quantity at the moment k+1, and P k/k 、P k+1/k And P k+1/k+1 Error covariance values of k time, k to k+1 one-step prediction time and k+1 measurement update time, Z k+1 Represents the systematic observed quantity at time k+1, gamma k Represents the innovation value at time K, K k+1 Representing gain value, Q, during measurement update at time k+1 k And R is k+1 The system noise variance matrix at time k and the measurement noise variance matrix at time k+1 are respectively represented.
By applying the technical scheme of the application, the three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering is provided, and the method realizes the separation of inertial device errors and accelerometer size errors under a proper transposition path by adding the accelerometer size errors into a system error model, simplifies the identification difficulty of the accelerometer size errors and improves the navigation precision of an inertial navigation system. Compared with the prior art, the technical scheme of the application can solve the technical problem that the navigation precision is affected due to the fact that the inertial device error is coupled with the accelerometer size error and cannot be separated accurately in the prior art.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application. It is evident that the drawings in the following description are only some embodiments of the present application and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
FIG. 1 is a flow chart of a method for estimating the size of a three-self inertial measurement unit accelerometer based on Kalman filtering according to a specific embodiment of the application;
FIG. 2 illustrates a three-dimensional coordinate schematic of an accelerometer provided in accordance with a specific embodiment of the application;
fig. 3 illustrates a graph of accelerometer dimensional estimation data provided in accordance with a specific embodiment of the application.
Detailed Description
It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other. The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. The following description of at least one exemplary embodiment is merely exemplary in nature and is in no way intended to limit the application, its application, or uses. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
The relative arrangement of the components and steps, numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present application unless it is specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective parts shown in the drawings are not drawn in actual scale for convenience of description. Techniques, methods, and apparatus known to one of ordinary skill in the relevant art may not be discussed in detail, but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any specific values should be construed as merely illustrative, and not a limitation. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further discussion thereof is necessary in subsequent figures.
As shown in fig. 1, according to a specific embodiment of the present application, there is provided a method for estimating a size of a three-self inertial measurement unit accelerometer based on kalman filtering, the method for estimating a size of a three-self inertial measurement unit accelerometer based on kalman filtering including: performing coarse alignment on the inertial navigation system to obtain an inertial navigation initial attitude; the inner frame and the outer frame of the inertial navigation system rotate according to a preset rotation sequence and a preset rotation angle, and the gyro angular rate and the accelerometer specific force in the rotation process are obtained; constructing a system error model according to the inertial navigation device error and the accelerometer size; initializing Kalman filter parameters; and (3) performing inertial device error estimation and accelerometer size estimation by adopting a discrete Kalman filter equation according to the gyro angular rate, the acceleration Ji Bi force and the system error model in the rotation process so as to finish three-self inertial group accelerometer size estimation based on Kalman filtering.
By applying the configuration mode, the three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering is provided, and the method realizes the separation of inertial device errors and accelerometer size errors under a proper transposition path by adding the accelerometer size errors into a system error model, simplifies the identification difficulty of the accelerometer size errors and improves the navigation precision of an inertial navigation system. Compared with the prior art, the technical scheme of the application can solve the technical problem that the navigation precision is affected due to the fact that the inertial device error is coupled with the accelerometer size error and cannot be separated accurately in the prior art.
Further, in the application, in order to realize the three-self inertial accelerometer size estimation based on Kalman filtering, firstly, the inertial navigation system is subjected to rough alignment to obtain the initial inertial navigation attitude.
As a specific embodiment of the application, the rotating mechanism is in a locking state after the inertial navigation system is started, and the inertial navigation system is stationary at the initial positionAfter a plurality of time periods, sensitive acceleration and angular velocity information, namely angular velocity, are combined by utilizing inertial measurementAnd force information->Coarse alignment is performed and an initial pose is determined. After the initial pose is acquired, the system is unlocked. In this embodiment, the inertial navigation system is stationary for a long period of 30s at the initial position.
In addition, in the application, after rough alignment is completed, inertial navigation calculation is performed according to the gyro angular rate and specific force information to complete updating of attitude quaternion, position and speed.
Further, in the application, after the settlement of inertial navigation is completed, the inner frame and the outer frame of the inertial navigation system rotate according to a preset rotation sequence and a preset rotation angle, and the gyro angular rate and the accelerometer specific force in the rotation process are obtained.
As one embodiment of the application, the inner frame and the outer frame of the indexing mechanism of the inertial navigation system can rotate according to the rotation sequence and the rotation angle shown in the table 1, the stop time at each position is more than or equal to 180s, and the rotation angular speed from one position to the next position is more than or equal to 15 DEG/s.
Table 1 rotation sequence and rotation angle meter of inner frame and outer frame of inertial navigation system
In addition, in the application, after the gyro angular rate and the accelerometer specific force in the rotation process are obtained, a system error model is constructed according to the inertial navigation device error, the accelerometer size and the inertial navigation solution result.
As a specific embodiment of the present application, in the present application, constructing a systematic error model according to inertial navigation device errors, accelerometer dimensions, and inertial navigation solutions specifically includes: constructing a state variable of the inertial navigation system according to the inertial navigation device error and the accelerometer size; and constructing a system error model according to the state variable and the inertial navigation solution result.
In the three-self inertial measurement unit, a rotation center (i.e., a center point where an inner ring axis and an outer ring axis intersect) is generally taken as an origin of a measurement coordinate system, and the size of the accelerometer is a three-dimensional coordinate of a sensitive center of the accelerometer in the measurement coordinate system. As represented by the three cylinders in fig. 2 as accelerometers, the dimensional parameters of the accelerometers are defined as three-dimensional coordinates of the center of sensitivity of the three accelerometers relative to the origin of the measurement coordinate system. The coordinates of the three accelerometers in the measurement coordinate system areWherein Rx, ry and Rz respectively represent three-dimensional coordinates of the x accelerometer, the y accelerometer and the Z accelerometer, rxx, rxy and Rxz respectively represent coordinate values of the relative rotation center of the x accelerometer in the directions X, Y and Z in the measurement coordinate system, ryx, ryy and Ryz respectively represent coordinate values of the relative rotation center of the y accelerometer in the directions X, Y and Z in the measurement coordinate system, and Rzx, rzy and Rzz respectively represent coordinate values of the relative rotation center of the Z accelerometer in the directions X, Y and Z in the measurement coordinate system. Rxx, rxy, rxz, ryx, ryy, ryz, rzx, rzy and Rzz are extended into the inertial navigation system error model.
When the indexing mechanism rotates, the deviation generated by the sensitivity of the accelerometer to the size effect can be obtained,wherein fx, fy and fz respectively represent deviations generated by sensitive dimension effects of an x accelerometer, a y accelerometer and a z accelerometer, ω represents three-dimensional angular velocity obtained by gyro sensitivity, the inertial combination can be regarded as a rigid body, and the angular velocities at any positions on the rigid body are consistent, so that the angular velocity of the acceleration is ω, and the angular velocity of the acceleration is ω>Indicating angular acceleration.
Error of inertial device by combining indexing path and rotation speedAnd the excitation of the accelerometer size error, and the 9-dimensional accelerometer size is expanded into a state variable by combining the navigation error (speed error and attitude error) of the inertial navigation system and the inertial device error. In particular according toConstructing a state variable of an inertial navigation system, wherein X k State variables representing the k time, δl, δh, and δλ represent the latitude error, the altitude error, and the longitude error, δv, respectively, of the inertial navigation system N 、δV U And δV E Respectively representing north speed error, sky speed error and east speed error of inertial navigation system N 、φ U And phi E Respectively representing misalignment angles in north, sky and east directions in a geographic coordinate system of an inertial navigation system x 、▽ y And z respectively representing zero errors epsilon of accelerometers in three directions of X, Y and Z in a measurement coordinate system of an inertial navigation system x 、ε y And epsilon z Respectively representing constant drift, k of gyroscopes in X, Y and Z directions in measurement coordinate system of inertial navigation system ax 、k ay And k az Scale factor errors, k, respectively representing an x accelerometer, a y accelerometer and a z accelerometer in a measurement coordinate system of an inertial navigation system ayx 、k azx And k azy K respectively representing the installation error of the x accelerometer relative to the Y direction, the installation error of the x accelerometer relative to the Z direction and the installation error of the Y accelerometer relative to the Z direction in the measurement coordinate system of the inertial navigation system ax2 、k ay2 And k az2 Represent the quadratic coefficient errors, k, of the x accelerometer, the y accelerometer and the z accelerometer in the measurement coordinate system of the inertial navigation system respectively gx 、k gy And k gz Respectively representing scale factor errors, k of an x gyroscope, a y gyroscope and a z gyroscope in a measurement coordinate system of an inertial navigation system gxy 、k gxz 、k gyx 、k gyz 、k gzx And k gzy Respectively representing the installation error of the Y gyroscope relative to the X direction, the installation error of the z gyroscope relative to the X direction, the installation error of the X gyroscope relative to the Y direction and the installation error of the z gyroscope relative to the Y direction in the measurement coordinate system of the inertial navigation systemThe installation error of the x gyroscope relative to the Z direction and the installation error of the y gyroscope relative to the Z direction.
Further, in the present application, after completion of the construction of the state variables, the method is performed according toConstructing a system error model, wherein phi k.k-1 For the state transition matrix from time k-1 to time k of the system, X k-1 Is the state variable at time k-1, W k-1 Representing system noise at time k-1 of system, Z k For the system observation quantity at k moment, H k As the observation matrix at the time of k,i is an identity matrix, v k Is the observed noise at time k.
In the present application, the state transition matrix Φ k,k-1 Can be according toAcquisition, wherein T n For navigational period, T e Is the filtering period. In this embodiment, T is taken n ＝0.005s，T e ＝1s。A t For the state transition matrix at time t, t=0 at the beginning of each filtering cycle.
B 4 ＝0 3×3 ，/>
Wherein omega ie For the rotation angular velocity of the earth, V N 、V U And V E North, sky and east speeds of inertial navigation, L and h are latitude and altitude of inertial navigation, R M And R is N Respectively, the radius of the meridian plane and the mortise unitary plane of the earth, < ->Posture conversion matrix for b-series to n-series, < >>Andgyro output angular rates of an x gyro, a y gyro and a z gyro under an inertial navigation body coordinate system respectively, < >>And->Output specific force for accelerometer of x accelerometer, y accelerometer and z accelerometer in inertial navigation coordinate system, +.>And->And outputting the angular acceleration of the x gyroscope, the y gyroscope and the z gyroscope, which are obtained by differentiating the angular rate for the gyroscope.
In the present application, the system observance can be based on Z k ＝[L-L 0 h-h 0 λ-λ 0 V N V U V E ] T Acquisition, wherein λ is the inertial longitude, L 0 、h 0 And lambda (lambda) 0 Initial binding latitude, altitude, and longitude, respectively.
In addition, in the present application, in order to reduce the navigation error, the kalman filter parameters are initialized after the construction of the system error model is completed. As one embodiment of the application, an initial covariance matrix P of Kalman filtering is set 0 The parameters of the method can be set according to the magnitude of the initial error; setting a system noise variance matrix Q, wherein the system noise variance matrix Q can be set according to the actual system noise; setting an initial value X of a system error state 0 The dimension is 42×1, and is generally set as a zero matrix; setting a Kalman filtering calculation period T k 。
Further, in the application, after initializing Kalman filter parameters, a discrete Kalman filter equation is adopted to carry out inertial device error estimation and accelerometer size estimation according to the gyro angular rate, acceleration Ji Bi force and a system error model in the rotation process so as to complete three-self inertial accelerometer size estimation based on Kalman filtering.
As a specific embodiment of the application, it is possible toP k+1/k ＝Φ k+1,k P k/k Φ T k+1,k +Q k ，/>K k+1 ＝P k+1/k H T k+1 [H k+1 P k+1/k H T k+1 +R k+1 ] -1 ，P k+1/k+1 ＝[I-K k+ 1 H k+1 ]P k+1/k ，/>Performing Kalman filtering, wherein phi k+1,k State transition matrix from time k to time k+1,>and->The estimated value is respectively the estimated value of the system state quantity at the moment k, the one-step prediction estimated value of the system state quantity at the moment k to the moment k+1 and the estimated value after the measurement and update of the system state quantity at the moment k+1, and P k/k 、P k+1/k And P k+1/k+1 Error covariance values of k time, k to k+1 one-step prediction time and k+1 measurement update time, Z k+1 Represents the systematic observed quantity at time k+1, gamma k Represents the innovation value at time K, K k+1 Representing gain value, Q, during measurement update at time k+1 k And R is k+1 System noise respectively representing k timeAn acoustic variance matrix and a measured noise variance matrix at time k+1.
The application aims to provide a three-self inertial component accelerometer size estimation method based on Kalman filtering, which generally has a self-calibration function for an inertial navigation system with a double-shaft or three-shaft indexing mechanism. The complex process of realizing accelerometer size error separation through random vibration or angular vibration in the traditional scheme is solved, and the identification difficulty of accelerometer size error is greatly simplified. By adopting the algorithm of the scheme, the error estimation of the accelerometer size can be completed only when the system performs self calibration, so that the identification difficulty in engineering application is reduced.
Aiming at an inertial navigation system with a double-shaft or triaxial indexing mechanism, the application adopts a Kalman filtering technology based on 'speed+position' matching, and solves the problem that the acceleration size and the pre-designed size exist in and out due to the mechanical structure and the installation reason; the estimation of the acceleration size is accurately completed in a Kalman filtering estimation mode, the navigation precision of the three-inertial-unit under the vibration condition is improved, and the influence of the sawtooth speed error of the acceleration size error on the north-seeking precision in the single-axis forward and reverse north-seeking process is reduced.
For further understanding of the present application, the three-inertial accelerometer size estimation method based on Kalman filtering of the present application is described in detail below with reference to FIGS. 1 to 3.
In this embodiment, the three accelerometers of the default system are each sized toThe unit is m.
As shown in fig. 1 to 3, according to an embodiment of the present application, there is provided a three-self inertial measurement unit accelerometer size estimation method based on kalman filtering, the method specifically including the following steps.
Step one, starting up an inertial navigation system, enabling a rotating mechanism to be in a locking state, and utilizing angular rateAnd force information->And (5) performing coarse alignment, obtaining an inertial navigation initial posture, and unlocking the system.
And step two, performing inertial navigation calculation according to the gyro angular rate and specific force information to finish updating of the attitude quaternion, the position and the speed.
And thirdly, the indexing mechanism starts to operate according to the indexing path set in the table 1 and a preset rotation speed, and the gyro angular rate and the accelerometer specific force in the rotation process are measured.
Step four, according toEstablishing a system error model, adding the accelerometer size into the system error model, wherein the state variable is as follows
And fifthly, initializing Kalman filter parameters.
And step six, performing inertial device error estimation and accelerometer size estimation by adopting a discrete Kalman filter equation according to the gyro angular rate, the acceleration Ji Bi force and the system error model in the rotation process so as to finish three-self-inertial-group accelerometer size estimation based on Kalman filtering.
And outputting the error of the inertial navigation system device and the size of the accelerometer after the whole rotation period is stopped. The dimensional error estimation of the accelerometer was performed as described above, and the estimated dimensional result and the set dimensional pair are shown in table 2.
TABLE 2 accelerometer size estimation statistics (Unit: m)
From theoretical simulation analysis, the accelerometer size estimation accuracy in table 2 has reached 0.00001, and the accelerometer size set value is basically indistinguishable from the size estimation value; compared with the traditional accelerometer size error estimation, the method estimates the inertial navigation device error at the same time of calibration, separates the accelerometer size error from the inertial navigation system device error, and improves the identification precision of the acceleration size error by identifying the accelerometer size error in a random vibration or angular vibration mode different from the traditional mode using least square.
The coordinate system used in the present application is defined as follows:
s is a measurement coordinate system (ox s y s z s ) The measuring coordinate system is fixedly connected with the inertial measurement unit, and the direction of the coordinate system is consistent with the directions of three sensitive axes of the inertial measurement unit/inertial device of the IMU.
In summary, the application provides a three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering, which is used for realizing separation of inertial device errors and accelerometer size errors under a proper transposition path by adding the accelerometer size errors into a system error model, simplifying the identification difficulty of the accelerometer size errors and improving the navigation precision of an inertial navigation system. Compared with the prior art, the technical scheme of the application can solve the technical problem that the navigation precision is affected due to the fact that the inertial device error is coupled with the accelerometer size error and cannot be separated accurately in the prior art.
Spatially relative terms, such as "above … …," "above … …," "upper surface at … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial location relative to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "above" or "over" other devices or structures would then be oriented "below" or "beneath" the other devices or structures. Thus, the exemplary term "above … …" may include both orientations of "above … …" and "below … …". The device may also be positioned in other different ways (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
In addition, the terms "first", "second", etc. are used to define the components, and are only for convenience of distinguishing the corresponding components, and the terms have no special meaning unless otherwise stated, and therefore should not be construed as limiting the scope of the present application.
The above description is only of the preferred embodiments of the present application and is not intended to limit the present application, but various modifications and variations can be made to the present application by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.
Claims (6)
1. The three-inertial-unit accelerometer size estimation method based on Kalman filtering is characterized by comprising the following steps of:
performing coarse alignment on the inertial navigation system to obtain an inertial navigation initial attitude;
inertial navigation calculation is carried out according to the gyro angular rate and specific force information so as to finish updating of attitude quaternion, position and speed;
the inner frame and the outer frame of the inertial navigation system rotate according to a preset rotation sequence and a preset rotation angle, and the gyro angular rate and the accelerometer specific force in the rotation process are obtained;
constructing a system error model according to errors of inertial navigation devices, sizes of accelerometers and inertial navigation resolving results, and particularly according toConstructing the system error model;
initializing Kalman filter parameters;
according to the gyro angular rate, the accelerometer specific force and the system error model in the rotation process, performing inertial device error estimation and accelerometer size estimation by adopting a discrete Kalman filter equation so as to complete three-self inertial-group accelerometer size estimation based on Kalman filtering;
wherein X is k A state variable representing the moment k,δL, δh and δλ represent latitude error, altitude error and longitude error, δV, respectively, of the inertial navigation system N 、δV U And δV E Respectively representing north speed error, sky speed error and east speed error of inertial navigation system N 、φ U And phi E Respectively representing misalignment angles of north, sky and east directions in a geographic coordinate system of an inertial navigation system, ++>And->Respectively representing zero errors epsilon of accelerometers in three directions of X, Y and Z in a measurement coordinate system of an inertial navigation system x 、ε y And epsilon z Respectively representing constant drift, k of gyroscopes in X, Y and Z directions in measurement coordinate system of inertial navigation system ax 、k ay And k az Scale factor errors, k, respectively representing an x accelerometer, a y accelerometer and a z accelerometer in a measurement coordinate system of an inertial navigation system ayx 、k azx And k azy Respectively representing the relative of the x accelerometer in the measurement coordinate system of the inertial navigation systemMounting error in Y direction, mounting error of x accelerometer relative to Z direction and mounting error of Y accelerometer relative to Z direction, k ax2 、k ay2 And k az2 Represent the quadratic coefficient errors, k, of the x accelerometer, the y accelerometer and the z accelerometer in the measurement coordinate system of the inertial navigation system respectively gx 、k gy And k gz Respectively representing scale factor errors, k of an x gyroscope, a y gyroscope and a z gyroscope in a measurement coordinate system of an inertial navigation system gxy 、k gxz 、k gyx 、k gyz 、k gzx And k gzy The method comprises the steps of respectively representing the installation error of a Y gyroscope relative to an X direction, the installation error of a Z gyroscope relative to the X direction, the installation error of the X gyroscope relative to a Y direction, the installation error of the Z gyroscope relative to the Y direction, the installation error of the X gyroscope relative to the Z direction and the installation error of the Y gyroscope relative to the Z direction in a measurement coordinate system of an inertial navigation system; rxx, rxy and Rxz respectively represent coordinate values of the relative rotation center of the x accelerometer in the three directions X, Y and Z in the measurement coordinate system, ryx, ryy and Ryz respectively represent coordinate values of the relative rotation center of the y accelerometer in the three directions X, Y and Z in the measurement coordinate system, and Rzx, rzy and Rzz respectively represent coordinate values of the relative rotation center of the Z accelerometer in the three directions X, Y and Z in the measurement coordinate system; phi k.k-1 For the state transition matrix from time k-1 to time k of the system,T n for navigational period, T e For the filtering period A t For the state transition matrix at time t, X k-1 Is the state variable at time k-1, W k-1 Representing system noise at time k-1 of system, Z k For the system observation quantity at k moment, H k For the observation matrix at time k +.>I is an identity matrix, v k Is the observed noise at time k.
2. The method for estimating the size of the three-self inertial measurement unit accelerometer based on Kalman filtering according to claim 1, wherein the preset rotation sequence and rotation angle of the inner frame and the outer frame of the inertial navigation system are specifically as follows: an inner frame: 0 DEG frame: 0 °, inner frame: 0 DEG frame: 90 °, inner frame: 0 DEG frame: 180 °, inner frame: 0 DEG frame: 270 °, inner frame: 0 DEG frame: 180 °, inner frame: 0 DEG frame: 90 °, inner frame: 0 DEG frame: 0 °, inner frame: 90-degree outer frame: 0 °, inner frame: 90-degree outer frame: 90 °, inner frame: 90-degree outer frame: 180 °, inner frame: 90-degree outer frame: 270 °, inner frame: 90-degree outer frame: 180 °, inner frame: 90-degree outer frame: 90 °, inner frame: 90-degree outer frame: 0 °, inner frame: 180 DEG outer frame: 0 °, inner frame: 270 DEG frame: 0 °, inner frame: 180 DEG outer frame: 0 °, inner frame: 90-degree outer frame: 0 ° and inner frame: 0 DEG frame: 0 deg..
3. The method for estimating the size of the three-inertial-group accelerometer based on Kalman filtering according to claim 1, wherein,
ω ie for the rotation angular velocity of the earth, V N 、V U And V E North, sky and east speeds of inertial navigation, L and h are latitude and altitude of inertial navigation, R M And R is N Respectively, the radius of the meridian plane and the mortise unitary plane of the earth, < ->Posture conversion matrix for b-series to n-series, < >>And->An x-gyro, a y-gyro and a z-gyro under an inertial navigation body coordinate system respectivelyGyro output angular rate +.>And->Output specific force for accelerometer of x accelerometer, y accelerometer and z accelerometer in inertial navigation coordinate system, +.>And->Outputting angular acceleration of the x-gyro, the y-gyro and the z-gyro obtained by differentiation for the gyro output angular rate, f E 、f U And f N The projections of specific forces in the east, the sky and the north directions of the geographic system, respectively.
4. The method for estimating the size of the three-self inertial measurement unit accelerometer based on Kalman filtering according to claim 1, wherein the method is characterized in that according to Z k ＝[L-L 0 h-h 0 λ-λ 0 V N V U V E ] T Obtaining the system observed quantity Z k Wherein λ is the inertial navigation longitude, L 0 、h 0 And lambda (lambda) 0 Initial binding latitude, altitude, and longitude, respectively.
5. The method for estimating the size of the three-self inertial measurement unit accelerometer based on Kalman filtering according to claim 1, wherein initializing Kalman filter parameters specifically comprises: setting an initial covariance matrix P of Kalman filtering 0 System noise variance matrix Q and system error state initial value X 0 And Kalman filtering calculation period T k 。
6. The kalman filter-based three-self inertial measurement unit (tsm) accelerometer size estimation method according to any one of claims 1 to 5, whereinIn that according toP k+1/k ＝Φ k+1,k P k/k Φ T k+1,k +Q k ，K k+1 ＝P k+1/k H T k+1 [H k+1 P k+1/k H T k+1 +R k+1 ] -1 ，P k+1/k+1 ＝[I-K k+1 H k+1 ]P k+1/k ，Performing Kalman filtering, wherein phi k+1,k For the state transition matrix from time k to time k +1,and->The estimated value is respectively the estimated value of the system state quantity at the moment k, the one-step prediction estimated value of the system state quantity at the moment k to the moment k+1 and the estimated value after the measurement and update of the system state quantity at the moment k+1, and P k/k 、P k+1/k And P k+1/k+1 Error covariance values of k time, k to k+1 one-step prediction time and k+1 measurement update time, Z k+1 Represents the systematic observed quantity at time k+1, gamma k Represents the innovation value at time K, K k+1 Representing gain value, Q, during measurement update at time k+1 k And R is k+1 A system noise variance matrix at k time and a measurement noise variance matrix at k+1 time, H k+1 Is the observation matrix at time k+1.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110650825.8A CN113503895B (en) | 2021-06-10 | 2021-06-10 | Three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110650825.8A CN113503895B (en) | 2021-06-10 | 2021-06-10 | Three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113503895A CN113503895A (en) | 2021-10-15 |
| CN113503895B true CN113503895B (en) | 2023-08-15 |
Family
ID=78009862
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110650825.8A Active CN113503895B (en) | 2021-06-10 | 2021-06-10 | Three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113503895B (en) |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104697553A (en) * | 2015-03-13 | 2015-06-10 | 哈尔滨工程大学 | Method for calibrating inner lever arm of accelerometer of fiber-optic gyroscope strapdown inertial navigation system |
| CN106482746A (en) * | 2016-11-25 | 2017-03-08 | 北京航空航天大学 | In a kind of accelerometer for hybrid inertial navigation system, lever arm is demarcated and compensation method |
| CN107830858A (en) * | 2017-09-30 | 2018-03-23 | 南京航空航天大学 | A kind of mobile phone course estimation method based on gravity auxiliary |
| AU2020101268A4 (en) * | 2020-07-06 | 2020-08-13 | Harbin Engineering University | The initial alignment method for sway base |
-
2021
- 2021-06-10 CN CN202110650825.8A patent/CN113503895B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104697553A (en) * | 2015-03-13 | 2015-06-10 | 哈尔滨工程大学 | Method for calibrating inner lever arm of accelerometer of fiber-optic gyroscope strapdown inertial navigation system |
| CN106482746A (en) * | 2016-11-25 | 2017-03-08 | 北京航空航天大学 | In a kind of accelerometer for hybrid inertial navigation system, lever arm is demarcated and compensation method |
| CN107830858A (en) * | 2017-09-30 | 2018-03-23 | 南京航空航天大学 | A kind of mobile phone course estimation method based on gravity auxiliary |
| AU2020101268A4 (en) * | 2020-07-06 | 2020-08-13 | Harbin Engineering University | The initial alignment method for sway base |
Non-Patent Citations (1)
| Title |
|---|
| 游金川 ; 秦永元 ; 杨鹏翔 ; 严恭敏.捷联惯导加速度计尺寸效应误差建模及其标定.宇航学报.2012,第33卷(第03期),311-317. * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113503895A (en) | 2021-10-15 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107655476B (en) | Pedestrian high-precision foot navigation method based on multi-information fusion compensation | |
| CN109459044B (en) | GNSS dual-antenna assisted vehicle-mounted MEMS inertial navigation combined navigation method | |
| CN107270893B (en) | Lever arm and time asynchronous error estimation and compensation method for real estate measurement | |
| CN111121766B (en) | Astronomical and inertial integrated navigation method based on starlight vector | |
| CN106969783B (en) | Single-axis rotation rapid calibration technology based on fiber-optic gyroscope inertial navigation | |
| CN112629538A (en) | Ship horizontal attitude measurement method based on fusion complementary filtering and Kalman filtering | |
| CN110887507B (en) | Method for quickly estimating all zero offsets of inertial measurement units | |
| CN112595350B (en) | Automatic calibration method and terminal for inertial navigation system | |
| CN106989761B (en) | A kind of spacecraft Guidance instrumentation on-orbit calibration method based on adaptive-filtering | |
| CN112504275B (en) | Water surface ship horizontal attitude measurement method based on cascade Kalman filtering algorithm | |
| CN113503894B (en) | Inertial navigation system error calibration method based on gyro reference coordinate system | |
| CN112857398B (en) | Rapid initial alignment method and device for ship under mooring state | |
| CN108627152B (en) | Navigation method of micro unmanned aerial vehicle based on multi-sensor data fusion | |
| CN114858189B (en) | Gyro drift equivalent compensation method for strapdown inertial navigation system | |
| CN104833375B (en) | A kind of IMU Two position methods by star sensor | |
| CN110296719B (en) | On-orbit calibration method | |
| CN111486870B (en) | System-level calibration method for inclined strapdown inertial measurement unit | |
| CN112902956A (en) | Course initial value acquisition method for handheld GNSS/MEMS-INS receiver, electronic equipment and storage medium | |
| CN112880669A (en) | Spacecraft starlight refraction and uniaxial rotation modulation inertia combined navigation method | |
| CN110849360A (en) | Distributed relative navigation method for multi-machine cooperative formation flight | |
| CN113503895B (en) | Three-self inertial measurement unit accelerometer size estimation method based on Kalman filtering | |
| CN110514201A (en) | A kind of inertial navigation system and the air navigation aid suitable for high revolving speed rotary body | |
| CN111964671B (en) | Inertial astronomical integrated navigation system and method based on double-axis rotation modulation | |
| CN112649001A (en) | Method for resolving attitude and position of small unmanned aerial vehicle | |
| CN110260862B (en) | Rotor helicopter airborne navigation device based on strapdown inertial navigation system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |