CN101943585B - Calibration method based on CCD star sensor - Google Patents

Abstract

The invention provides a calibration method based on a CCD star sensor. The method comprises the following steps: (1) acquiring output of the CCD star sensor: attitude information of coordinates of the CCD star sensor relative to a system i; (2) acquiring local position information to obtain a transformation matrix of an earth coordinate system e relative to a navigation coordinate system n; (3) solving a transformation matrix of the system e relative to the system i; (4) resolving the information given in step (1), (2) and (3) to obtain an attitude matrix; (5) performing conversion on the attitude matrix obtained in step (4) to obtain a misalignment angle which is taken as an observational equation and substituted into a Kalman filter for filter estimation; and (6) estimating gyro constant drift and accelerometer zero offset via step (5). The calibration method of the invention can help achieve stable calibration result in short time and estimate the gyro constant drift and the accelerometer zero offset without any maneuverable measure.

Description

A kind of scaling method based on the CCD star sensor

Technical field

What the present invention relates to is a kind of scaling method, particularly relates to a kind of scaling method of strapdown inertial navitation system (SINS).

Background technology

Strapdown inertial navitation system (SINS) is based on the self-aid navigation system of inertial measurement component and navigational computer formation.Generally, no matter be Platform Inertial Navigation System or strapdown inertial navitation system (SINS), before carrying out navigation work, all must carry out the initial alignment of inertial navigation system, initial alignment is divided into two stages, and first stage is a coarse alignment; Second stage is the fine alignment stage.The fine alignment stage, the general Kalman filter that adopts was estimated three misalignments.In the aligning model of quiet pedestal, do not utilize any maneuvering characteristics, Kalman filter can only estimate seven variablees; Under the situation that adopts motor-driven measure, Kalman filter can improve by the number of estimator.After zero of gyroscope constant value drift and accelerometer obtains estimating partially, it is compensated, this measure has very big effect to the precision that improves navigator.

When utilizing the CCD star sensor to carry out initial alignment, owing to its optical axis pointing accuracy can reach in 20 rads, so the alignment precision height, and quick, stable; Three misalignments can be undertaken obtaining after the disposable initial alignment to a certain extent by the CCD star sensor, the misalignment that utilization obtains does not need carrier to do any motor-driven measure and just can estimate gyroscope constant value drift and accelerometer bias as observed quantity.

Summary of the invention

The object of the present invention is to provide a kind of quick, stable scaling method that can effectively improve the navigator navigation accuracy based on the CCD star sensor.

The object of the present invention is achieved like this:

(1) gather the output of CCD star sensor: the coordinate system of CCD star sensor is a attitude information between the i system with respect to inertial coordinates system

(2) gathering local positional information is longitude and latitude, and obtaining terrestrial coordinate system is that e system is the transition matrix of n system with respect to navigation coordinate system

(3) find the solution e system with respect to the transition matrix between the i system

(4) by given information in (1), (2), (3) step, resolve and obtain attitude matrix;

(5) attitude matrix that obtains in the step (4) is obtained misalignment through converting, as observation equation, the substitution Kalman filter is carried out Filtering Estimation with it;

(6) estimate the constant value drift and the accelerometer bias of gyro by step (5).

Method of the present invention has the following advantages:

This method is the scaling method that a kind of attitude sensor that relies on error As time goes on not disperse carries out, can reach stable calibration result in short time, different with scaling method in the past is, it does not need to carry out any motor-driven measure, just can estimate gyroscope constant value drift and accelerometer bias.

The following mode of beneficial effect of the present invention is verified:

Matlab emulation

(1) under following simulated conditions, this method is carried out emulation experiment:

The strapdown attitude system does the three-axis swinging motion.Carrier waves to angle, pitch angle and roll angle with sinusoidal rule deviation from voyage route, and its mathematical model is:

ψ＝ψ _msin(ω _ψ+φ _ψ)+k

θ＝θ _msin(ω _θ+φ _θ)

γ＝γ _msin(ω _γ+φ _γ)

Wherein: ψ, θ, γ represent the angle variables of waving around course angle, pitch angle and roll angle respectively; ψ _m, θ _m, γ _mThe angle amplitude is waved in expression accordingly respectively; ω _ψ, ω _θ, ω _γRepresent corresponding angle of oscillation frequency respectively; φ _ψ, φ _θ, φ _γRepresent corresponding initial phase respectively; And ω _i=2 π/T _i, i=ψ, θ, γ, T _iRepresent corresponding rolling period; K is a true flight path.T _ψ＝20s，T _θ＝25s，T _γ＝26s。

Carrier initial position: 45.7796 ° of north latitude, 126.6705 ° of east longitudes;

The true attitude angle of carrier: ψ=0 °, θ=0 °, γ=30 °;

Equatorial radius: R _e=6378393.0m;

The earth surface acceleration of gravity that can get by universal gravitation: g ₀=9.78049;

Rotational-angular velocity of the earth (radian per second): 7.2921158e-5;

The maximum error of CCD star sensor: η=0.01 °

The gyroscope constant value drift: 0.01 degree/hour;

Gyroscope white noise error: 0.005 degree/hour;

Accelerometer bias: 10 ^-4g ₀

Accelerometer white noise error: 5 * 10 ^-5g ₀:

Constant: π=3.1415926;

Simulation time: t=3600s;

Sample frequency: Hn=0.1;

Utilize the described method of invention to estimate to obtain gyroscope constant value drift as shown in Figure 1; The estimated value of accelerometer bias as shown in Figure 2, three normal value gyroscopic drift estimators are better as seen in Figure 1, the accelerometer bias among Fig. 2 also can estimate preferably.

Description of drawings

Fig. 1 is that x, the y, the z axle that utilize Matlab emulation to obtain often are worth gyroscopic drift estimation curve figure;

Fig. 2 is the curve map of ratio between x, y, z axis accelerometer zero inclined to one side estimated value and the actual value that utilizes Matlab emulation to obtain;

Fig. 3 is the steps flow chart block diagram of invention.

Embodiment

For example the present invention is done description in more detail below in conjunction with accompanying drawing:

(1) output of collection CCD star sensor: the coordinate system of CCD star sensor is with respect to inertial coordinates system (i system: the attitude information celestial coordinate system)

Transition matrix between i system and the boats and ships carrier coordinate system (b system):

$C_i^b=C_s^b{C}_i^s$

(1)

Wherein:

Be the transition matrix between CCD star sensor coordinate system (s system) and the b system, it can accurately obtain by optical laying when navigator is loaded onto ship;

Celestial coordinate system O-UVW according to changeing the w angle counterclockwise around the W axle earlier, is obtained O-U ₁V ₁W ₁Coordinate system is again around U ₁Change the u angle counterclockwise, make W ₁Axle and Z _sOverlap, obtain O-U ₂V ₂W ₂Coordinate system is at last again around W ₂Axle is rotated counterclockwise the v angle, obtains O _s-U _sV _sW _sCoordinate system.

$C_i^s=\left[\begin{array}{ccc}\cos w\cos v-\sin w\sin v\cos u& \sin w\cos v+\cos w\sin v\cos u& \sin v\sin u\\ -\cos w\sin v-\sin w\cos v\cos u& -\sin w\sin v+\cos w\cos v\cos u& \cos v\sin u\\ \sin w\sin u& -\cos w\sin u& \cos u\end{array}\right]---\left(2\right)$

(2) gather local positional information (longitude and latitude), can obtain the transition matrix of terrestrial coordinate system (e system) with respect to navigation coordinate system (n system)

$C_e^n=\left[\begin{array}{ccc}-\sin \mathrm{\λ}& \cos \mathrm{\λ}& 0\\ -\sin \mathrm{\φ}\cos \mathrm{\λ}& -\sin \mathrm{\φ}\sin \mathrm{\λ}& \cos \mathrm{\φ}\\ \cos \mathrm{\φ}\cos \mathrm{\λ}& \cos \mathrm{\φ}\sin \mathrm{\λ}& \sin \mathrm{\φ}\end{array}\right]---\left(3\right)$

(3) find the solution terrestrial coordinate system (e system) with respect to the transition matrix between the i system

$C_i^e=\left[\begin{array}{ccc}\cos (A_j+w_{\mathrm{ie}}\·t)& \sin (A_j+w_{\mathrm{ie}}\·t)& 0\\ -\sin (A_j+w_{\mathrm{ie}}\·t)& \cos (A_j+w_{\mathrm{ie}}\·t)& 0\\ 0& 0& 1\end{array}\right]---\left(4\right)$

w _IeBe rotational-angular velocity of the earth, t is the concrete time that the universal time system provides, A _jBe initial position (longitude and latitude) and the angle between the first point of Aries.

(4) by given information in (1), (2), (3) step, resolve and obtain attitude matrix:

$C_i^b=C_n^b{C}_e^n{C}_i^e---\left(5\right)$

Can calculate attitude information.

(5) attitude matrix that obtains in the step (4) is obtained misalignment through converting, as observation equation, the substitution Kalman filter is carried out Filtering Estimation with it;

Owing to the error of CCD star sensitivity not along with the accumulation of time increases, therefore can think that attitude matrix is real attitude matrix, with the attitude matrix of this matrix and inertial navigation real-time resolving

Combination calculation obtains calculating geographic coordinate system with respect to the attitude transition matrix between the true geographic coordinate system

$C_n^{n^{\′}}=C_b^{n^{\′}}\·C_i^b\·{(C_e^n\·C_i^e)}^{-1}---\left(6\right)$

Then three misalignments are:

φ _x＝C(2，3)

φ _y＝C(3，1)(7)

φ _z＝C(1，2)

Wherein C represents

Amount is measured as:

$Z\left(t\right)=\left[\begin{array}{c}\mathrm{\δV}\left(t\right)\\ \mathrm{\φ}\left(t\right)\end{array}\right]---\left(8\right)$

Wherein:

δ V (t) is the speed of inertial reference calculation and the difference between the real speed;

(6) can estimate the constant value drift and the accelerometer bias of gyro by step (5).

Use first-order linear immediately the differential equation to describe the state error of strapdown attitude system as follows:

$\stackrel{\·}{X}\left(t\right)=F\left(t\right)X\left(t\right)+G\left(t\right)W\left(t\right)---\left(9\right)$

The state vector of etching system when wherein X (t) is t; F (t) and G (t) are respectively system state matrix and noise matrix; W (t) is the noise vector of system;

The state vector of system is:

$X={\left[\begin{array}{cccccccccccc}{\mathrm{\δV}}_E& {\mathrm{\δV}}_N& {\mathrm{\δV}}_U& {\mathrm{\φ}}_x& {\mathrm{\φ}}_y& {\mathrm{\φ}}_z& {\▿}_x& {\▿}_y& {\▿}_z& {\mathrm{\ϵ}}_x& {\mathrm{\ϵ}}_y& {\mathrm{\ϵ}}_z\end{array}\right]}^T---\left(10\right)$

The white noise vector of system is:

$W=\left[\begin{array}{cccccccccccc}{w}_{{\&dtri;}_x}& w_{{\&dtri;}_y}& w_{{\&dtri;}_z}& w_{{\mathrm{\&epsiv;}}_x}& w_{{\mathrm{\&epsiv;}}_y}& w_{{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HSA00000188977900011.png"\; state="\{\{state\}\}">z</figure-callout>}}}& 0& 0& 0& 0& 0& 0\end{array}\right]---\left(11\right)$

δ V wherein _Eδ V _Nδ V _UThe velocity error of representing east orientation, north orientation respectively;

Be respectively the partially zero of X, Y, Z axis accelerometer; ε _xε _yε _zBe respectively the constant value drift of X, Y, Z axle gyro;

Be respectively the white noise error of X, Y-axis accelerometer; Be respectively the white noise error of X, Y, Z axle gyro;

The system noise factor matrix is:

$G\left(t\right)=\left[\begin{array}{ccc}{C}_b^{n^{\&prime;}}& 0_{3\&times;3}& 0_{3\&times;6}\\ 0_{3\&times;3}& -C_b^{n^{\&prime;}}& 0_{3\&times;6}\\ 0_{6\&times;3}& 0_{6\&times;3}& 0_{6\&times;6}\end{array}\right]---\left(12\right)$

The state-transition matrix of system is:

$F\left(t\right)=\left[\begin{array}{c}{F}_s\left(t\right)\\ 0_{6\&times;12}\end{array}\right]---\left(13\right)$

Wherein:

F _s(t)＝[F ₁(t)?F ₂(t)](14)

$F_2\left(t\right)=\left[\begin{array}{cc}{C}_b^{n^{\&prime;}}& 0_{3\&times;3}\\ 0_{3\&times;3}& -C_b^{n^{\&prime;}}\end{array}\right]---\left(16\right)$

ω _IeBe rotational-angular velocity of the earth,

Be local geographic latitude.

Claims (2)

1. scaling method based on the CCD star sensor is characterized in that:

(1) gather the output of CCD star sensor: the coordinate system of CCD star sensor is a attitude information between the i system with respect to inertial coordinates system

The method of the output of described collection CCD star sensor is:

I system and boats and ships carrier coordinate system are that the transition matrix between the b system is

Wherein:

For CCD star sensor coordinate system is transition matrix between s system is with b, when loading onto ship, navigator accurately obtains by optical laying;

Celestial coordinate system O-UVW according to changeing the ω angle counterclockwise around the W axle earlier, is obtained O-U ₁V ₁W ₁Coordinate system is again around U ₁Change the u angle counterclockwise, make W ₁Axle and Z _sOverlap, obtain O-U ₂V ₂W ₂Coordinate system is at last again around W ₂Axle is rotated counterclockwise the v angle, obtains O _s-U _sV _sW _sCoordinate system;

$C_i^s=\left[\begin{array}{ccc}\cos \mathrm{\&omega;}\cos v-\sin \mathrm{\&omega;}\sin v\cos u& \sin \mathrm{\&omega;}\cos v+\cos \mathrm{\&omega;}\sin v\cos u& \sin v\sin u\\ -\cos \mathrm{\&omega;}\sin v-\sin \mathrm{\&omega;}\cos v\cos u& -\sin \mathrm{\&omega;}\sin v+\cos \mathrm{\&omega;}\cos v\cos u& \cos v\sin u\\ \sin \mathrm{\&omega;}\sin u& -\cos \mathrm{\&omega;}\sin u& \cos u\end{array}\right];$

(2) gathering local positional information is longitude and latitude, and obtaining terrestrial coordinate system is that e system is the transition matrix of n system with respect to navigation coordinate system

(3) find the solution e system with respect to the transition matrix between the i system

$C_i^e=\left[\begin{array}{ccc}\cos (A_j+{\mathrm{\&omega;}}_{\mathrm{ie}}\&CenterDot;t)& \sin (A_j+{\mathrm{\&omega;}}_{\mathrm{ie}}\&CenterDot;t)& 0\\ -\sin (A_j+{\mathrm{\&omega;}}_{\mathrm{ie}}\&CenterDot;t)& \cos (A_j+{\mathrm{\&omega;}}_{\mathrm{ie}}\&CenterDot;t)& 0\\ 0& 0& 1\end{array}\right]$

ω _IeBe rotational-angular velocity of the earth, t is the concrete time that the universal time system provides, A _jBe initial position and the angle between the first point of Aries;

(4) by given information in (1), (2), (3) step, resolve and obtain attitude matrix, described attitude matrix For:

$C_n^b=C_i^b\&CenterDot;(C_e^n\&CenterDot;C_i^e{)}^{-1};$

(5) attitude matrix that obtains in the step (4) is obtained misalignment through converting, as observation equation, the substitution Kalman filter is carried out Filtering Estimation with it; Concrete grammar is:

$C_n^{n^{\&prime;}}=C_b^{n^{\&prime;}}\&CenterDot;C_i^b\&CenterDot;{(C_e^n\&CenterDot;C_i^e)}^{-1}$

φ _x＝C(2，3)

φ _y＝C(3，1)

φ _z＝C(1，2)

Wherein C represents

Amount is measured as:

$Z\left(t\right)=\left[\begin{array}{c}\mathrm{\&delta;V}\left(t\right)\\ \mathrm{\&phi;}\left(t\right)\end{array}\right]$

Wherein:

δ V (t) is the speed of inertial reference calculation and the difference between the real speed;

(6) estimate the constant value drift and the accelerometer bias of gyro by step (5).

2. a kind of scaling method based on the CCD star sensor according to claim 1 is characterized in that describedly estimating the constant value drift of gyro and the method for accelerometer bias is:

Use the first-order linear stochastic differential equation to describe the state error of strapdown attitude system:

$\stackrel{\&CenterDot;}{X}\left(t\right)=F\left(t\right)X\left(t\right)+G\left(t\right)W\left(t\right)$

The state vector of etching system when wherein X (t) is t; F (t) and G (t) are respectively system state matrix and noise matrix; W (t) is the noise vector of system;

The state vector of system is:

$X={\left[\begin{array}{cccccccccccc}\mathrm{\&delta;}{V}_E& \mathrm{\&delta;}{V}_N& \mathrm{\&delta;}{V}_U& {\mathrm{\&phi;}}_x& {\mathrm{\&phi;}}_y& {\mathrm{\&phi;}}_z& {\&dtri;}_x& {\&dtri;}_y& {\&dtri;}_z& {\mathrm{\&epsiv;}}_x& {\mathrm{\&epsiv;}}_y& {\mathrm{\&epsiv;}}_z\end{array}\right]}^T$

The white noise vector of system is:

$W=\left[\begin{array}{cccccccccccc}{w}_{{\&dtri;}_x}& w_{{\&dtri;}_y}& w_{{\&dtri;}_z}& w_{{\mathrm{\&epsiv;}}_x}& w_{{\mathrm{\&epsiv;}}_y}& w_{{\mathrm{\&epsiv;}}_z}& 0& 0& 0& 0& 0& 0\end{array}\right]$

δ V wherein _Eδ V _Nδ V _UThe velocity error of representing east orientation, north orientation respectively;

Be respectively the partially zero of X, Y, Z axis accelerometer; ε _xε _yε _zBe respectively the constant value drift of X, Y, Z axle gyro; Be respectively the white noise error of X, Y-axis accelerometer;

Be respectively the white noise error of X, Y, Z axle gyro;

The system noise factor matrix is:

$G\left(t\right)=\left[\begin{array}{ccc}{C}_b^{n^{\&prime;}}& 0_{3\&times;3}& 0_{3\&times;6}\\ 0_{3\&times;3}& -C_b^{n^{\&prime;}}& 0_{3\&times;6}\\ 0_{6\&times;3}& 0_{6\&times;3}& 0_{6\&times;6}\end{array}\right]$

The state-transition matrix of system is:

$F\left(t\right)=\left[\begin{array}{c}{F}_s\left(t\right)\\ 0_{6\&times;12}\end{array}\right]$

Wherein: F _s(t)=[F ₁(t) F ₂(t)],

$F_2\left(t\right)=\left[\begin{array}{cc}{C}_b^{n^{\&prime;}}& 0_{3\&times;3}\\ 0_{3\&times;3}& -C_b^{n^{\&prime;}}\end{array}\right]$

ω _IeBe rotational-angular velocity of the earth,

Be local geographic latitude.

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