Disclosure of Invention
In view of the above, the invention provides an acceleration calibration method based on missile-borne inertia/starlight integrated navigation, which can calibrate a horizontal accelerometer so as to improve the performance of the accelerometer.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
an acceleration calibration method based on missile-borne inertia/starlight integrated navigation comprises the following steps:
acquiring an initial posture matrix before carrier emission;
based on the initial gesture matrix and a preset gesture update model, inertial navigation is carried out to obtain a navigation gesture matrix;
performing star observing measurement on the navigation gesture matrix to obtain a star observing gesture matrix;
correcting the navigation gesture matrix through the star-viewing gesture matrix to obtain a corrected gesture matrix;
calculating an attitude error according to the corrected attitude matrix; calculating an initial attitude error provided by an accelerometer in the attitude errors by adopting a Kalman filtering algorithm; and calculating a horizontal meter adding error according to the initial attitude error, and calibrating the accelerometer.
Further, an initial pose matrix of the carrier before being emitted is obtained, comprising,
acquiring output data of a gyroscope and an accelerometer in a navigation self-alignment process;
and carrying out double-vector gesture determination according to the average value of the gyroscope and accelerometer data to obtain an initial gesture matrix.
Further, the outputting data of the gyroscope and the accelerometer in the self-alignment navigation process comprises the following steps:
x-axis direction:
y-axis direction:
z-axis direction:
wherein , and />The three axis output values of the gyroscope and accelerometer, i.e. the angular velocity and acceleration of the carrier system relative to the inertial system, respectively, are represented.
Further, the double-vector attitude determination calculation formula is as follows:
wherein ,
and />Respectively expressed as an earth gravity vector estimated value and an earth rotation vector estimated value, T0 Indicating a self-alignment start time; t (T)1 Indicating the moment when the self-alignment ends.
Further, the gesture update model is as follows:
wherein ,representing a real gesture matrix at a kth moment; />Representation->Is a derivative of (2); />Measurement value provided for a gyro at time k, +.>Is the gesture matrix at time (k-1), +.>Is the projection of the rotation angular velocity of the earth system relative to the inertial system in the navigation system at the moment (k-1), +.>The projection of the rotation angular velocity of the navigation system with respect to the earth system at the time (k-1) is in the navigation system.
Further, the performing star observing measurement on the navigation gesture matrix to obtain a star observing gesture matrix includes:
and recording star coordinates observed by the star sensor and coordinate data of a geocentric equatorial coordinate system stored in a missile-borne navigation star base:
calculating matrix performance indexes by adopting a least square method according to the star-viewing data to obtain an optimal attitude matrix
wherein ,J* Represents the performance index lambdai Is a weighting coefficient;
and calculating a star observing gesture matrix through matrix transmission.
Further, the calculation model for calculating the attitude error is:
εb ＝[εx εy εz ]T ，
wherein Z (t) is an attitude error;the navigation gesture matrix is used for satellite observation measurement; /> and />Three-axis attitude error expressed as star-viewing time; epsilonx 、εy and εz The gyro drift of the triaxial during star observing measurement is expressed; />Andrepresented as a three axis initial posing error.
Further, the calculating, by using a kalman filter algorithm, an initial attitude error provided by an accelerometer from the attitude errors includes:
constructing a combined system state equation:
Z(t)＝XH
wherein ,
m navigation gesture matrixes obtained according to starlight observationAnd combining the system states Z (t), calculating an initial posing error matrix +.>
Further, the calculation formula of the calculation level adding table error is as follows:
wherein ,▽N Representing an equivalent north measurement error, [ V ] of the accelerometerE Representing the equivalent east measurement error of the accelerometer, g representing the earth gravitational acceleration.
The invention has the beneficial effects that:
compared with the prior art, the invention discloses an acceleration calibration method based on missile-borne inertia/starlight combined navigation, which realizes the confirmation of initial gesture through the self-alignment process of the accelerometer, calculates the initial gesture error by combining star observation measurement, and realizes the calibration of the horizontal direction of the accelerometer.
Detailed Description
The following description of the embodiments of the present invention 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 invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Firstly, describing labels in parameters in the invention, wherein i in angle marks in the parameters represents an inertial coordinate system, e in the angle marks represents an earth coordinate system, and n in the angle marks represents a navigation coordinate system;
secondly, the embodiment of the invention discloses an acceleration calibration method based on missile-borne inertia/starlight integrated navigation, which comprises the following steps:
s1: the method for acquiring the initial posture matrix of the carrier before transmission comprises the following steps:
s11: acquiring gyroscope and accelerometer data in a navigation self-alignment process:
confirming a gyro output model and an accelerometer output model through accelerometer self-alignment;
the gyro output model is expressed asWherein epsilon is drift of the gyroscope, omega is true value of the earth rotation vector,representing an estimated value of the earth rotation vector;
accelerometer output model is expressed asWherein, # is zero bias of the accelerometer, f is the true value of the gravity vector, # is the true value of the gravity vector>A gravity vector estimation value;
navigation starts to perform self-alignment work, and output data of the gyroscope and the accelerometer are recorded:
x-axis direction:
y-axis direction:
z-axis direction:
wherein , and />Three-axis output values of the gyroscope and the accelerometer are respectively represented, namely, the angular speed and the acceleration of the carrier system relative to the inertial system;
S13：T0 -T1 self-aligning in time, and calculating a gravity vector estimated value under a b coordinate system according to output data of the gyro output model and the accelerometer output modelAnd the estimated value w of the earth rotation vectori be ：
wherein ,
S14：T1 and after the moment self-alignment is finished, calculating the average value of output data of the gyroscope and the accelerometer in the time period, and carrying out double-vector attitude determination according to the gravity vector and the earth rotation vector to obtain an initial attitude matrix:
wherein , and />Respectively representing a gravity vector estimated value and an earth rotation vector estimated value under an n coordinate system;
s2: based on inertial navigation, a posture updating model after carrier emission is established, and a navigation posture matrix at each moment is obtainedThe method comprises the following steps:
s21: the inertial navigation is from (k-1) moment to the gesture update model of k moment:
wherein ,representing a measurement gesture matrix at a kth moment in a carrier coordinate system; />Representing a measurement gesture matrix at a kth moment in a carrier coordinate system; />Measurement values provided for a gyro at time k in the carrier coordinate system, < >>For the pose matrix measured at time (k-1) under the carrier coordinate system,/for the pose matrix>Is the projection of the rotation angular velocity of the earth system relative to the inertial system in the navigation system at the moment (k-1), +.>The projection of the rotation angular velocity of the navigation system with respect to the earth system at the time (k-1) is in the navigation system.
S3: performing star observation measurement, and obtaining star coordinates observed by a star sensor and coordinate data of a geocentric equatorial coordinate system stored in a missile-borne navigation star base to obtain a star observation posture matrix, wherein the star observation posture matrix comprises the following steps of;
s31: the star coordinates observed by the star sensor and the coordinate data of the geocentric equatorial coordinate system stored in the missile-borne navigation star base are recorded,i＝1,2,3,...n(n≥2)
s32: according to star data, calculating matrix performance indexes by adopting a least square method to obtain an optimal attitude matrix
wherein ,J* Represents the performance index lambdai Is a weighting coefficient;
s33: calculating starlight observation attitude matrix
Since the celestial coordinate system (r-system) is the navigation system (n-system) is the known coordinate system, i.eIs known; then there is a matrix transfer equation
S34: according to the starlight observation attitude matrixNavigation gesture matrix->Correcting to obtain a corrected posture matrix +.>In an auxiliary inertial system, the output signal of the inertial navigation system is compared with independent measurements of the same quantity from an external source, and corrections to the inertial navigation system are then calculated from the differences between these measurements.
S4: according to the attitude update model and the star observing measurement data, calculating a current attitude error, wherein the steps comprise:
establishing an error calculation model:
εb ＝[εx εy εz ]T ，
wherein ；εx 、εy and εz Expressed as gyro drift; and />Represented as a three axis initial posing error.
The method comprises the following specific steps:
calculating an initial attitude error provided by an accelerometer in the current attitude errors by adopting a Kalman filtering algorithm;
the method comprises the following specific steps:
s41: a state equation of the combined system is constructed,
Z(t)＝XH；X＝(HT H)-1 HT Z(t)；
wherein ,
s42: m correction state matrixes obtained according to starlight observationAnd combining the system state Z (t), and establishing an error measurement equation to calculate an initial attitude error matrix ++>
wherein ,t1 -tm For m star measurement moments in the star navigation process,the navigation gesture matrix is used for measuring the time of the m star observation;
s5: calculating a horizontal adding error according to the initial attitude error:
wherein ,▽N Representing an equivalent north measurement error, [ V ] of the accelerometerE Representing an equivalent east measurement error of the accelerometer, g representing earth gravitational acceleration;
performing horizontal calibration on the accelerometer by using a horizontal meter adding error;
assuming an initial pose matrixAnd its true value->There is a small amount of mathematical platform misalignment angle phi between:
wherein I is an identity matrix.
In general, the measurement error of the gyroscope relative to the rotation of the earth is greater than that of the accelerometer relative to the gravity of the earth, i.eAt the time, there are
wherein ,the equivalent east measurement error of the gyro is shown, and L represents the latitude of the carrier.
It can be seen that the alignment accuracy of the horizontal misalignment angle depends on the equivalent horizontal measurement error of the accelerometer, while the alignment accuracy of the azimuth misalignment angle mainly depends on the equivalent east measurement error of the gyro, so that the alignment of the horizontal posture can be performed by using the accelerometer.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.