CN113503895A - Kalman filtering-based three-autonomous inertial measurement unit accelerometer size estimation method - Google Patents

Kalman filtering-based three-autonomous inertial measurement unit accelerometer size estimation method Download PDF

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CN113503895A
CN113503895A CN202110650825.8A CN202110650825A CN113503895A CN 113503895 A CN113503895 A CN 113503895A CN 202110650825 A CN202110650825 A CN 202110650825A CN 113503895 A CN113503895 A CN 113503895A
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accelerometer
inertial navigation
error
inertial
gyro
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CN113503895B (en
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胡奇林
吴亮华
刘玉祝
李瑞贤
高晓波
于杏
危志英
王秋帆
杨槊
张泽
王欣
张吉
盛雪莲
赵彤
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Beijing Automation Control Equipment Institute BACEI
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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
    • 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
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Abstract

The invention provides a Kalman filtering based three-self-inertial-unit accelerometer size estimation method, which comprises the following steps: carrying out coarse alignment on the inertial navigation system; performing inertial navigation calculation according to the angular rate and specific force information of the gyroscope to update the attitude quaternion, the position and the 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 the inertial navigation device error, the accelerometer size and the inertial navigation resolving result; initializing Kalman filter parameters; and (4) performing error estimation of the inertial device and size estimation of the accelerometer by adopting a discrete Kalman filtering equation. By applying the technical scheme of the invention, the technical problem that the navigation precision is influenced because the error of an inertia device is coupled with the dimension error of the accelerometer and the inertia device cannot be accurately separated in the prior art can be solved.

Description

Kalman filtering-based three-autonomous inertial measurement unit accelerometer size estimation method
Technical Field
The invention relates to the technical field of inertial navigation, in particular to a Kalman filtering-based three-self inertial unit accelerometer size estimation method.
Background
In an inertial navigation system, due to a mechanical structure and installation reasons, the centers of mass of the three accelerometers are not coincident or large deviation still exists after compensation is carried out through the size measured by a model. When the carrier is subjected to vibration or large-angle movement, dimension effect errors of the accelerometer measurement assembly are caused. For the three-self-inertia group which is aligned in a rotating mode, a speed error generated by a size effect error and an equivalent zero error of a adding table in the alignment process cannot be ignored, and parameter calibration and compensation are required. The size of the conventional accelerometer is usually ensured through model design, when deviation occurs, related parameters are generally identified through a least square method by utilizing a speed error excited by angular vibration, and when a 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 invention provides a Kalman filtering-based three-self-inertial-unit accelerometer size estimation method, which can solve the technical problem that navigation precision is influenced because inertial device errors and accelerometer size errors are coupled and cannot be accurately separated in the prior art.
The invention provides a Kalman filtering based three-self-inertial-unit accelerometer size estimation method, which comprises the following steps: carrying out coarse alignment on the inertial navigation system to obtain an inertial navigation initial attitude; performing inertial navigation calculation according to the angular rate and specific force information of the gyroscope to update the attitude quaternion, the position and the 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 the inertial navigation device error, the accelerometer size 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 filtering equation according to the gyro angular rate, the accelerometer specific force and the system error model in the rotation process so as to complete Kalman filtering-based three-self inertial group accelerometer size estimation.
Further, the preset rotation order and rotation angle of the inner frame and the outer frame of the inertial navigation system are specifically as follows: inner frame: 0 ° outer frame: 0 °, inner frame: 0 ° outer frame: 90 °, inner frame: 0 ° outer frame: 180 °, inner frame: 0 ° outer frame: 270 °, inner frame: 0 ° outer frame: 180 °, inner frame: 0 ° outer frame: 90 °, inner frame: 0 ° outer frame: 0 °, inner frame: 90 ° outer frame: 0 °, inner frame: 90 ° outer frame: 90 °, inner frame: 90 ° outer frame: 180 °, inner frame: 90 ° outer frame: 270 °, inner frame: 90 ° outer frame: 180 °, inner frame: 90 ° outer frame: 90 °, inner frame: 90 ° outer frame: 0 °, inner frame: 180 ° outer frame: 0 °, inner frame: 270 ° outer frame: 0 °, inner frame: 180 ° outer frame: 0 °, inner frame: 90 ° outer frame: 0 ° and inner frame: 0 ° outer frame: 0 deg.
Further, the step of constructing a system error model according to the inertial navigation device error, the accelerometer size and the inertial navigation resolving 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 variables and the inertial navigation resolving result.
Further in accordance with
Figure BDA0003111093530000021
Constructing state variables of inertial navigation system, wherein XkState variable representing time k, delta L, delta h and delta lambda respectively representing latitude error, altitude error and longitude error of inertial navigation system, and delta VN、δVUAnd δ VERespectively representing north velocity error, sky velocity error and east velocity error of the inertial navigation system, phiN、φUAnd phiERespectively represents the misalignment angles of the north, the sky and the east in the geographic coordinate system of the inertial navigation system,
Figure BDA0003111093530000022
and
Figure BDA0003111093530000023
respectively representing the zero errors of the accelerometer in X, Y and Z directions in a measurement coordinate system of the inertial navigation system, epsilonx、εyAnd εzRespectively representing constant drift of the gyroscope in X, Y and Z directions in a measurement coordinate system of the inertial navigation system, kax、kayAnd kazRespectively representing the scale factor errors, k, of an x accelerometer, a y accelerometer and a z accelerometer in a measurement coordinate system of the inertial navigation systemayx、kazxAnd kazyRespectively representing the installation error of an x accelerometer relative to the Y direction, the installation error of the x accelerometer relative to the Z direction and the installation error of a Y accelerometer relative to the Z direction in a measurement coordinate system of the inertial navigation system, kax2、kay2And kaz2Respectively representing quadratic coefficient errors, k, of an x accelerometer, a y accelerometer and a z accelerometer in a measurement coordinate system of the inertial navigation systemgx、kgyAnd kgzRespectively representing the scale factor errors, k, of an x gyro, a y gyro and a z gyro in a measurement coordinate system of the inertial navigation systemgxy、kgxz、kgyx、kgyz、kgzxAnd kgzyThe mounting error of the Y gyro relative to the X direction, the mounting error of the Z gyro relative to the X direction, the mounting error of the X gyro relative to the Y direction, the mounting error of the Z gyro relative to the Y direction, the mounting error of the X gyro relative to the Z direction and the mounting error of the Y gyro relative to the Z direction in the inertial navigation system measurement coordinate system are respectively shown.
Further in accordance with
Figure BDA0003111093530000031
Constructing a systematic error model, whereink.k-1For the state transition matrix from time k-1 to time k of the system, Xk-1Is a state variable at time k-1, Wk-1Representing the system noise at the moment of system k-1, ZkSystem observations at time k, HkIs the observation matrix at the time k,
Figure BDA0003111093530000032
i is the identity matrix, vkIs the observed noise at time k.
Further in accordance with
Figure BDA0003111093530000033
Obtaining a state transition matrix Φk,k-1Wherein, TnFor navigation period, TeFor the filter period, AtFor the state transition matrix at time t,
Figure BDA0003111093530000034
Figure BDA0003111093530000035
Figure BDA0003111093530000041
Figure BDA0003111093530000042
Figure BDA0003111093530000043
Figure BDA0003111093530000044
Figure BDA0003111093530000045
Figure BDA0003111093530000046
B4＝03×3，
Figure BDA0003111093530000047
Figure BDA0003111093530000051
Figure BDA0003111093530000052
Figure BDA0003111093530000053
Figure BDA0003111093530000054
ωieis the angular velocity of rotation of the earth, VN、VUAnd VENorth, sky and east inertial navigation speeds, L and h inertial navigation latitude and height, RMAnd RNRespectively the meridian plane radius and the unitary plane radius of the earth,
Figure BDA00031110935300000515
for the attitude transformation matrix from b system to n system,
Figure BDA0003111093530000055
and
Figure BDA0003111093530000056
respectively the gyro output angular rates of an x gyro, a y gyro and a z gyro in an inertial navigation body coordinate system,
Figure BDA0003111093530000057
and
Figure BDA0003111093530000058
the specific force is output by adding tables of an x accelerometer, a y accelerometer and a z accelerometer in an inertial navigation body coordinate system,
Figure BDA0003111093530000059
and
Figure BDA00031110935300000510
the angular accelerations of the x gyro, the y gyro and the z gyro obtained by differentiation of the gyro output angular rates.
Further, according to Zk＝[L-L0 h-h0 λ-λ0 VN VU VE]TObtaining a system observation ZkWherein λ is inertial navigation longitude, L0、h0And λ0Initial binding latitude, altitude and longitude, respectively.
Further, initializing kalman filter parameters specifically includes: setting an initial covariance matrix P for Kalman filtering0System noise variance matrix Q and system error state initial value X0And Kalman filter calculation period Tk。
Further in accordance with
Figure BDA00031110935300000511
Pk+1/k＝Φk+1,kPk/kΦT k+1,k+Qk，
Figure BDA00031110935300000512
Kk+1＝Pk+1/kHT k+1[Hk+1Pk+1/kHT k+1+Rk+1]-1，Pk+1/k+1＝[I-Kk+1Hk+1]Pk+1/k，
Figure BDA00031110935300000513
Performing Kalman filtering, whereink+1,kThe state transition matrix from time k to time k +1,
Figure BDA00031110935300000514
and
Figure BDA0003111093530000061
respectively is an estimated value of the system state quantity at the moment k, a one-step prediction estimated value of the system state quantity at the moment k to the moment k +1 and an updated estimated value of the system state quantity at the moment k +1, Pk/k、Pk+1/kAnd Pk+1/k+1Error covariance values, Z, at time k, at one step k to k +1 prediction time and at k +1 measurement update time, respectivelyk+1Representing a systematic observation at time k +1, gammakAn innovation value, K, representing time Kk+1Represents the gain value, Q, in the measurement update process at the time k +1kAnd Rk+1Respectively representing the system noise variance matrix at time k and the measured noise variance matrix at time k + 1.
According to the method, the size error of the accelerometer is added into a system error model, so that the separation of the inertial device error and the size error of the accelerometer is realized under a proper transposition path, the identification difficulty of the size error of the accelerometer is simplified, and the navigation precision of the inertial navigation system is improved. Compared with the prior art, the technical scheme of the invention can solve the technical problem that the navigation precision is influenced because the error of an inertial device is coupled with the dimension error of an accelerometer and the inertial device cannot be accurately separated in the prior art.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a flow chart illustrating a Kalman filtering-based three-autonomous inertial measurement unit accelerometer size estimation method according to an embodiment of the present invention;
FIG. 2 illustrates a three-dimensional coordinate diagram of an accelerometer provided in accordance with a particular embodiment of the invention;
figure 3 illustrates a graph of accelerometer dimension estimation data provided in accordance with a specific embodiment of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
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 example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those 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 particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
As shown in fig. 1, according to an embodiment of the present invention, a kalman filter-based three-self-inertial-unit accelerometer size estimation method is provided, where the kalman filter-based three-self-inertial-unit accelerometer size estimation method includes: carrying out 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 size of the accelerometer; initializing Kalman filter parameters; and performing inertial device error estimation and accelerometer size estimation by adopting a discrete Kalman filtering equation according to the gyro angular rate, the accelerometer specific force and the system error model in the rotation process so as to complete Kalman filtering-based three-self inertial group accelerometer size estimation.
By applying the configuration mode, the method for estimating the size of the three-self inertial measurement unit accelerometer based on Kalman filtering is provided, and the method realizes the separation of the inertial device error and the accelerometer size error under a proper transposition path by adding the accelerometer size error into a system error model, thereby simplifying the identification difficulty of the accelerometer size error and improving the navigation precision of the inertial navigation system. Compared with the prior art, the technical scheme of the invention can solve the technical problem that the navigation precision is influenced because the error of an inertial device is coupled with the dimension error of an accelerometer and the inertial device cannot be accurately separated in the prior art.
Further, in the invention, in order to realize the three-self inertial navigation unit accelerometer size estimation based on the kalman filter, firstly, the inertial navigation system is roughly aligned to obtain the inertial navigation initial attitude.
As a specific embodiment of the invention, after the inertial navigation system is started, the rotating mechanism is in a locking state, and after the inertial navigation system is static at an initial position for a plurality of time periods, the inertial measurement is utilized to combine sensitive acceleration and angular velocity information, namely angular rate
Figure BDA0003111093530000081
And specific force information
Figure BDA0003111093530000082
And performing coarse alignment to determine an initial posture. After the initial pose is obtained, the system unlocks. In this embodiment, the inertial navigation system is stationary at the initial position for a period of no less than 30 seconds.
In addition, in the invention, after the coarse alignment is finished, inertial navigation calculation is carried out according to the gyro angular rate and the specific force information so as to finish the updating of the attitude quaternion, the position and the speed.
Further, in the invention, after the inertial navigation settlement is finished, the inner frame and the outer frame of the inertial navigation system rotate according to the preset rotation sequence and rotation angle, and the gyro angular rate and the accelerometer specific force in the rotation process are obtained.
As an embodiment of the invention, 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 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 order and rotation angle table of inner frame and outer frame of inertial navigation system
Figure BDA0003111093530000091
In addition, in the invention, after the gyro angular rate and the accelerometer specific force in the rotation process are acquired, a system error model is constructed according to the inertial navigation device error, the accelerometer size and the inertial navigation resolving result.
As a specific embodiment of the present invention, in the present invention, constructing a system error model according to an inertial navigation device error, an accelerometer size, and an inertial navigation solution result 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 variables and the inertial navigation resolving result.
In the three-self-inertia set, the rotation center (i.e. the central point where the inner ring axis intersects with the outer ring axis) is usually taken as the origin of the measurement coordinate system, and the dimension of the accelerometer is the three-dimensional coordinate of the sensitive center of the accelerometer in the measurement coordinate system. As in fig. 2, the three cylinders are represented as accelerometers, and the dimension parameter of the accelerometer is defined as the three-dimensional coordinates of the sensitive center of the three accelerometers relative to the origin of the measurement coordinate system. The coordinates of the three accelerometers in the measurement coordinate system are
Figure BDA0003111093530000101
Wherein Rx, Ry and Rz respectively represent the three-dimensional coordinates of the x-accelerometer, the y-accelerometer and the Z-accelerometer, Rxx, Rxy and Rxz respectively represent the coordinate values of the x-accelerometer relative to the rotation center in three directions of X, Y and Z in the measurement coordinate system, Ryx, Ryy and Ryz respectively represent the coordinate values of the y-accelerometer relative to the rotation center in three directions of X, Y and Z in the measurement coordinate system, and Rzx, Rz and Rz respectively represent the coordinate values of the Z-accelerometer relative to the rotation center in three directions of X, Y and Z in the measurement coordinate system. And expanding Rxx, Rxy, Rxz, Ryx, Ryy, Ryz, Rzx, Rzy and Rzz into an inertial navigation system error model.
When the indexing mechanism is rotated, the indexing mechanism,the deviation of the accelerometer sensitivity to size effects can be found,
Figure BDA0003111093530000102
wherein fx, fy and fz respectively represent the deviation generated by the sensitive size effect of the x accelerometer, the y accelerometer and the z accelerometer, ω represents the three-dimensional angular velocity obtained by the gyroscope, the inertial combination can be regarded as a rigid body, the angular velocity is consistent at any position on the rigid body, therefore, the angular velocity of the acceleration is also ω,
Figure BDA0003111093530000111
indicating angular acceleration.
And expanding the dimension of the 9-dimensional accelerometer into a state variable by combining the excitation of the indexing path and the rotation speed on the inertial device error and the dimension error of the accelerometer and combining the navigation error (the velocity error and the attitude error) of the inertial navigation system and the dimension error of the inertial device. In particular, according to
Figure BDA0003111093530000112
Constructing state variables of inertial navigation system, wherein XkState variable representing time k, delta L, delta h and delta lambda respectively representing latitude error, altitude error and longitude error of inertial navigation system, and delta VN、δVUAnd δ VERespectively representing north velocity error, sky velocity error and east velocity error of the inertial navigation system, phiN、φUAnd phiERespectively represents the misalignment angles in the north, the sky and the east in the geographic coordinate system of the inertial navigation system +x、▽yAnd +zRespectively representing the zero errors of the accelerometer in X, Y and Z directions in a measurement coordinate system of the inertial navigation system, epsilonx、εyAnd εzRespectively representing constant drift of the gyroscope in X, Y and Z directions in a measurement coordinate system of the inertial navigation system, kax、kayAnd kazRespectively representing the scale factor errors, k, of an x accelerometer, a y accelerometer and a z accelerometer in a measurement coordinate system of the inertial navigation systemayx、kazxAnd kazyRespectively representing the relative of an x accelerometer in a measurement coordinate system of the inertial navigation systemMounting error in the Y direction, mounting error of the x accelerometer with respect to the Z direction, and mounting error of the Y accelerometer with respect to the Z direction, kax2、kay2And kaz2Respectively representing quadratic coefficient errors, k, of an x accelerometer, a y accelerometer and a z accelerometer in a measurement coordinate system of the inertial navigation systemgx、kgyAnd kgzRespectively representing the scale factor errors, k, of an x gyro, a y gyro and a z gyro in a measurement coordinate system of the inertial navigation systemgxy、kgxz、kgyx、kgyz、kgzxAnd kgzyThe mounting error of the Y gyro relative to the X direction, the mounting error of the Z gyro relative to the X direction, the mounting error of the X gyro relative to the Y direction, the mounting error of the Z gyro relative to the Y direction, the mounting error of the X gyro relative to the Z direction and the mounting error of the Y gyro relative to the Z direction in the inertial navigation system measurement coordinate system are respectively shown.
Further, in the present invention, after the construction of the state variables is completed, the method is based on
Figure BDA0003111093530000121
Constructing a systematic error model, whereink.k-1For the state transition matrix from time k-1 to time k of the system, Xk-1Is a state variable at time k-1, Wk-1Representing the system noise at the moment of system k-1, ZkSystem observations at time k, HkIs the observation matrix at the time k,
Figure BDA0003111093530000122
i is the identity matrix, vkIs the observed noise at time k.
In the present invention, the state transition matrix Φk,k-1Can be based on
Figure BDA0003111093530000123
Obtaining, wherein TnFor navigation period, TeIs the filter period. In this embodiment, T may be takenn＝0.005s，Te＝1s。AtFor the state transition matrix at time t, t is 0 at the beginning of each filtering cycle.
Figure BDA0003111093530000124
Figure BDA0003111093530000125
Figure BDA0003111093530000126
Figure BDA0003111093530000127
Figure BDA0003111093530000131
Figure BDA0003111093530000132
Figure BDA0003111093530000133
Figure BDA0003111093530000134
B4＝03×3，
Figure BDA0003111093530000135
Figure BDA0003111093530000136
Figure BDA0003111093530000137
Figure BDA0003111093530000138
Figure BDA0003111093530000139
Wherein, ω isieIs the angular velocity of rotation of the earth, VN、VUAnd VENorth, sky and east inertial navigation speeds, L and h inertial navigation latitude and height, RMAnd RNRespectively the meridian plane radius and the unitary plane radius of the earth,
Figure BDA0003111093530000141
for the attitude transformation matrix from b system to n system,
Figure BDA0003111093530000142
and
Figure BDA0003111093530000143
respectively the gyro output angular rates of an x gyro, a y gyro and a z gyro in an inertial navigation body coordinate system,
Figure BDA0003111093530000144
and
Figure BDA0003111093530000145
the specific force is output by adding tables of an x accelerometer, a y accelerometer and a z accelerometer in an inertial navigation body coordinate system,
Figure BDA0003111093530000146
and
Figure BDA0003111093530000147
the angular accelerations of the x gyro, the y gyro and the z gyro obtained by differentiation of the gyro output angular rates.
In the present invention, the system observations can be based on Zk＝[L-L0 h-h0 λ-λ0 VN VU VE]TObtaining, wherein λ is inertial navigation longitude, L0、h0And λ0Initial binding latitude, altitude and longitude, respectively.
In addition, in the invention, in order to reduce the navigation error, after the construction of the system error model is completed, the Kalman filter parameters are initialized. As an embodiment of the invention, an initial covariance matrix P of Kalman filtering is set0The parameters 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 the initial value X of the system error state0Dimension 42 × 1, typically set to zero matrix; setting Kalman filtering calculation period Tk。
Further, after initializing Kalman filter parameters, inertial device error estimation and accelerometer size estimation are carried out by adopting a discrete Kalman filtering equation according to a gyro angular rate, an accelerometer specific force and a system error model in the rotation process so as to complete Kalman filtering-based three-autonomous inertial group accelerometer size estimation.
As an embodiment of the present invention, can be made according to
Figure BDA0003111093530000148
Pk+1/k＝Φk+1,kPk/kΦT k+1,k+Qk，
Figure BDA0003111093530000149
Kk+1＝Pk+1/kHT k+1[Hk+1Pk+1/kHT k+1+Rk+1]-1，Pk+1/k+1＝[I-Kk+ 1Hk+1]Pk+1/k，
Figure BDA00031110935300001410
Performing Kalman filtering, whereink+1,kThe state transition matrix from time k to time k +1,
Figure BDA00031110935300001411
and
Figure BDA00031110935300001412
respectively is an estimated value of the system state quantity at the moment k, a one-step prediction estimated value of the system state quantity at the moment k to the moment k +1 and an updated estimated value of the system state quantity at the moment k +1, Pk/k、Pk+1/kAnd Pk+1/k+1Error covariance values, Z, at time k, at one step k to k +1 prediction time and at k +1 measurement update time, respectivelyk+1Representing a systematic observation at time k +1, gammakAn innovation value, K, representing time Kk+1Represents the gain value, Q, in the measurement update process at the time k +1kAnd Rk+1Respectively representing the system noise variance matrix at time k and the measured noise variance matrix at time k + 1.
The invention aims to provide a Kalman filtering-based three-self inertial measurement unit accelerometer size estimation method, which has a self-calibration function for an inertial navigation system with a double-shaft or three-shaft indexing mechanism in general. The method solves the problem that the size error separation of the accelerometer is complex in the traditional scheme through random vibration or angular vibration, and greatly simplifies the identification difficulty of the size error of the accelerometer. By adopting the algorithm of the scheme, the error estimation of the size of the accelerometer can be completed only when the system is self-calibrated, and the identification difficulty in engineering application is reduced.
Aiming at an inertial navigation system with a double-shaft or three-shaft indexing mechanism, the invention adopts a Kalman filtering technology based on 'speed + position' matching, and solves the problem that the acceleration size and the pre-designed size are in and out caused by a mechanical structure and installation reasons; the estimation of the acceleration size is accurately finished in a Kalman filtering estimation mode, the navigation precision of the three-self-inertia unit under the vibration condition is improved, and the influence of a sawtooth speed error on the north-seeking precision in the single-axis positive and negative rotation north-seeking process of the acceleration size error is reduced.
For further understanding of the present invention, the following describes the method for estimating the dimension of the three inertial navigation systems based on kalman filtering according to the present invention with reference to fig. 1 to 3.
In this embodiment, the three accelerometer sizes of the preset system are respectively
Figure BDA0003111093530000151
The unit is m.
As shown in fig. 1 to 3, a method for estimating a dimension of a three-self inertial group accelerometer based on kalman filtering is provided according to an embodiment of the present invention, and the method specifically includes the following steps.
Step one, starting an inertial navigation system, enabling a rotating mechanism to be in a locking state and utilizing angular rate
Figure BDA0003111093530000161
And specific force information
Figure BDA0003111093530000162
And carrying out coarse alignment, obtaining an inertial navigation initial posture, and unlocking the system.
And step two, performing inertial navigation calculation according to the angular rate and specific force information of the gyroscope to complete the updating of the attitude quaternion, the position and the speed.
And step three, the indexing mechanism starts to operate according to the indexing path set in the table 1 and the preset rotating speed, and the gyro angular rate and the accelerometer specific force in the rotating process are measured.
Step four, according to
Figure BDA0003111093530000163
Establishing a system error model, adding the size of the accelerometer into the system error model, and setting the state variable as
Figure BDA0003111093530000164
And step five, initializing Kalman filter parameters.
And sixthly, performing inertial device error estimation and accelerometer size estimation by adopting a discrete Kalman filtering equation according to the gyro angular rate, the accelerometer specific force and the system error model in the rotation process so as to finish the Kalman filtering-based three-self inertial group accelerometer size estimation.
And outputting the device error of the inertial navigation system and the size of the accelerometer after the whole rotation period is stopped. The size error estimation of the accelerometer is carried out according to the steps, and the estimated size result and the set size ratio are shown in table 2.
TABLE 2 accelerometer sizing results statistics (units: m)
Figure BDA0003111093530000165
Figure BDA0003111093530000171
Theoretical simulation analysis shows that the size estimation precision of the accelerometer in the table 2 reaches 0.00001, and the size set value of the accelerometer is basically not different from the size estimation value; compared with the traditional accelerometer dimension error estimation, the method estimates the inertial navigation device error during calibration, separates the accelerometer dimension error from the inertial navigation system device error, and improves the identification precision of the acceleration dimension error by identifying in a random vibration or angular vibration mode in a traditional least square mode.
The coordinate system used in the present invention is defined as follows:
s is a measurement coordinate system (ox)syszs) And the measurement 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 IMU inertial measurement unit/inertial device.
In conclusion, the invention provides a Kalman filtering-based three-self inertial measurement unit accelerometer size estimation method, which 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 invention can solve the technical problem that the navigation precision is influenced because the error of an inertial device is coupled with the dimension error of an accelerometer and the inertial device cannot be accurately separated in the prior art.
Spatially relative terms, such as "above … …," "above … …," "above … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial relationship 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 of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary term "above … …" can include both an orientation of "above … …" and "below … …". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
It should be noted that the terms "first", "second", and the like are used to define the components, and are only used for convenience of distinguishing the corresponding components, and the terms have no special meanings unless otherwise stated, and therefore, the scope of the present invention should not be construed as being limited.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. A Kalman filtering-based three-autonomous-inertial-unit accelerometer size estimation method is characterized by comprising the following steps:
carrying out coarse alignment on the inertial navigation system to obtain an inertial navigation initial attitude;
performing inertial navigation calculation according to the angular rate and specific force information of the gyroscope to update the attitude quaternion, the position and the 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 the inertial navigation device error, the accelerometer size 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 filtering equation according to the gyro angular rate, the accelerometer specific force and the system error model in the rotation process so as to finish three-autonomous inertial group accelerometer size estimation based on Kalman filtering.
2. The Kalman filtering-based three-autonomous inertial measurement unit accelerometer size estimation method of claim 1, wherein the preset rotation order and rotation angle of the inner frame and the outer frame of the inertial navigation system are specifically: inner frame: 0 ° outer frame: 0 °, inner frame: 0 ° outer frame: 90 °, inner frame: 0 ° outer frame: 180 °, inner frame: 0 ° outer frame: 270 °, inner frame: 0 ° outer frame: 180 °, inner frame: 0 ° outer frame: 90 °, inner frame: 0 ° outer frame: 0 °, inner frame: 90 ° outer frame: 0 °, inner frame: 90 ° outer frame: 90 °, inner frame: 90 ° outer frame: 180 °, inner frame: 90 ° outer frame: 270 °, inner frame: 90 ° outer frame: 180 °, inner frame: 90 ° outer frame: 90 °, inner frame: 90 ° outer frame: 0 °, inner frame: 180 ° outer frame: 0 °, inner frame: 270 ° outer frame: 0 °, inner frame: 180 ° outer frame: 0 °, inner frame: 90 ° outer frame: 0 ° and inner frame: 0 ° outer frame: 0 deg.
3. The Kalman filtering-based three-self inertial group accelerometer size estimation method according to claim 1, wherein the building of a system error model according to inertial navigation device errors, accelerometer sizes and inertial navigation solution results specifically comprises:
constructing a state variable of an inertial navigation system according to the inertial navigation device error and the accelerometer size;
and constructing the system error model according to the state variables and the inertial navigation resolving result.
4. The Kalman filtering based three-autonomous-inertial-unit accelerometer size estimation method of claim 3, characterized in that the method is based on
Figure FDA0003111093520000021
Constructing the state variables of the inertial navigation system, wherein XkState variable representing time k, delta L, delta h and delta lambda respectively representing latitude error, altitude error and longitude error of inertial navigation system, and delta VN、δVUAnd δ VERespectively representing north velocity error, sky velocity error and east velocity error of the inertial navigation system, phiN、φUAnd phiERespectively represents the misalignment angles of the north, the sky and the east in the geographic coordinate system of the inertial navigation system,
Figure FDA0003111093520000022
and
Figure FDA0003111093520000023
respectively representing the zero errors of the accelerometer in X, Y and Z directions in a measurement coordinate system of the inertial navigation system, epsilonx、εyAnd εzRespectively representing constant drift of the gyroscope in X, Y and Z directions in a measurement coordinate system of the inertial navigation system, kax、kayAnd kazRespectively representing the scale factor errors, k, of an x accelerometer, a y accelerometer and a z accelerometer in a measurement coordinate system of the inertial navigation systemayx、kazxAnd kazyRespectively represents the installation error of the x accelerometer relative to the Y direction in the measurement coordinate system of the inertial navigation systemDifference, mounting error of x accelerometer with respect to Z direction, and mounting error of y accelerometer with respect to Z direction, kax2、kay2And kaz2Respectively representing quadratic coefficient errors, k, of an x accelerometer, a y accelerometer and a z accelerometer in a measurement coordinate system of the inertial navigation systemgx、kgyAnd kgzRespectively representing the scale factor errors, k, of an x gyro, a y gyro and a z gyro in a measurement coordinate system of the inertial navigation systemgxy、kgxz、kgyx、kgyz、kgzxAnd kgzyThe mounting error of the Y gyro relative to the X direction, the mounting error of the Z gyro relative to the X direction, the mounting error of the X gyro relative to the Y direction, the mounting error of the Z gyro relative to the Y direction, the mounting error of the X gyro relative to the Z direction and the mounting error of the Y gyro relative to the Z direction in the inertial navigation system measurement coordinate system are respectively shown.
5. The Kalman filtering based three-autonomous-inertial-unit accelerometer size estimation method of claim 4, characterized in that the method is based on
Figure FDA0003111093520000031
Constructing the systematic error model, whereink.k-1For the state transition matrix from time k-1 to time k of the system, Xk-1Is a state variable at time k-1, Wk-1Representing the system noise at the moment of system k-1, ZkSystem observations at time k, HkIs the observation matrix at the time k,
Figure FDA0003111093520000032
i is the identity matrix, vkIs the observed noise at time k.
6. The Kalman filtering based three-autonomous-inertial-unit accelerometer size estimation method of claim 5, characterized in that the method is based on
Figure FDA0003111093520000033
Obtaining the state transition matrix phik,k-1Wherein, TnFor navigation period, TeFor the filter period, AtFor the state transition matrix at time t,
Figure FDA0003111093520000034
Figure FDA0003111093520000035
Figure FDA0003111093520000036
Figure FDA0003111093520000037
Figure FDA0003111093520000041
Figure FDA0003111093520000042
Figure FDA0003111093520000043
Figure FDA0003111093520000044
B4＝03×3，
Figure FDA0003111093520000045
Figure FDA0003111093520000046
Figure FDA0003111093520000047
Figure FDA0003111093520000048
Figure FDA0003111093520000049
ωieis the angular velocity of rotation of the earth, VN、VUAnd VENorth, sky and east inertial navigation speeds, L and h inertial navigation latitude and height, RMAnd RNRespectively the meridian plane radius and the unitary plane radius of the earth,
Figure FDA0003111093520000051
for the attitude transformation matrix from b system to n system,
Figure FDA0003111093520000052
and
Figure FDA0003111093520000053
respectively the gyro output angular rates of an x gyro, a y gyro and a z gyro in an inertial navigation body coordinate system,
Figure FDA0003111093520000054
and
Figure FDA0003111093520000055
the specific force is output by adding tables of an x accelerometer, a y accelerometer and a z accelerometer in an inertial navigation body coordinate system,
Figure FDA0003111093520000056
and
Figure FDA0003111093520000057
the angular accelerations of the x gyro, the y gyro and the z gyro obtained by differentiation of the gyro output angular rates.
7. The Kalman filtering based triple inertial set accelerometer size estimation method of claim 5 or 6, characterized in that it is according to Zk＝[L-L0 h-h0 λ-λ0 VN VU VE]TObtaining the system view measurement ZkWherein λ is inertial navigation longitude, L0、h0And λ0Initial binding latitude, altitude and longitude, respectively.
8. The Kalman filtering-based three-autonomous-inertial-unit accelerometer size estimation method of claim 1, characterized in that initializing Kalman filter parameters specifically comprises: setting an initial covariance matrix P for Kalman filtering0System noise variance matrix Q and system error state initial value X0And Kalman filter calculation period Tk。
9. The Kalman filtering based triple inertial group accelerometer size estimation method of any one of claims 1 to 8, according to
Figure FDA0003111093520000058
Pk+1/k＝Φk+1,kPk/kΦT k+1,k+Qk，
Figure FDA0003111093520000059
Kk+1＝Pk+1/kHT k+1[Hk+1Pk+1/kHT k+1+Rk+1]-1，Pk+1/k+1＝[I-Kk+1Hk+1]Pk+1/k，
Figure FDA00031110935200000510
Performing Kalman filtering, whereink+1,kThe state transition matrix from time k to time k +1,
Figure FDA00031110935200000511
and
Figure FDA00031110935200000512
respectively is an estimated value of the system state quantity at the moment k, a one-step prediction estimated value of the system state quantity at the moment k to the moment k +1 and an updated estimated value of the system state quantity at the moment k +1, Pk/k、Pk+1/kAnd Pk+1/k+1Error covariance values, Z, at time k, at one step k to k +1 prediction time and at k +1 measurement update time, respectivelyk+1Representing a systematic observation at time k +1, gammakAn innovation value, K, representing time Kk+1Represents the gain value, Q, in the measurement update process at the time k +1kAnd Rk+1Respectively representing the system noise variance matrix at time k and the measured noise variance matrix at time k + 1.
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