CN103364842A - Error separation method of strapdown airborne gravitometer - Google Patents

Abstract

The invention discloses an error separation method of a strapdown airborne gravitometer. The error separation method comprises the following steps: (1) pre-treating original data of the strapdown airborne gravitometer: converting original pulse signals of an accelerometer and a spinning top, which are obtained by the strapdown airborne gravitometer, into normal measurement information through equivalents; (2) determining a posture error generated by the strapdown airborne gravitometer in a flight measurement process; and (3) correcting a measured result of the strapdown airborne gravitometer through the posture error determined by the step (2) to realize the separation of errors. The error separation method disclosed by the invention has the advantages of simple principle, simplicity and convenience in operation, high separation precision, easiness of being popularized and used and the like.

Description

A kind of strapdown airborne gravimeter error separating method

Technical field

The present invention is mainly concerned with strapdown airborne gravimeter field, refers in particular to a kind of strapdown airborne gravimeter error separating method.

Background technology

Accelerometer and gyro are Primary Components in the strapdown airborne gravimeter.Because accelerometer and gyro exist deviation and drift, the precision of accelerometer and gyro just is restricted, especially the precision of gyro can have influence on the attitude of the gravity meter that finally estimates, so that there is larger attitude error in the attitude that estimates, will in the final measurement result of strapdown airborne gravimeter, cause measuring error like this.

At present, for the separation of attitude error full ripe way not, there is the scholar to propose the methods such as wavelet de-noising, wave number correlation filtering, engineer's scale correction abroad and carries out error and separate.These methods all are the skills aspect some data processing of afterwards process adopting at numerical value, fundamentally attitude error is not estimated, an obtainable effect neither be very desirable.So, the method for estimation of just must design a kind of brand-new attitude error of the error separation problem that wants to solve the strapdown airborne gravimeter.

Summary of the invention

The technical problem to be solved in the present invention just is: the technical matters for prior art exists the invention provides the strapdown airborne gravimeter error separating method that a kind of principle is simple, easy and simple to handle, separation accuracy is high, easily promote the use of.

For solving the problems of the technologies described above, the present invention by the following technical solutions:

A kind of strapdown airborne gravimeter error separating method the steps include:

(1), the pre-service of strapdown airborne gravimeter raw data: the accelerometer that the strapdown airborne gravimeter is obtained and the original burst signal of gyro convert normal metrical information to by equivalent;

(2), determine the attitude error that the strapdown airborne gravimeter produces in the flight measurement process;

(3), the attitude error of determining by step (2) is revised the separation of realization error to the measurement result of strapdown gravity meter.

As a further improvement on the present invention: described step (1) is: the original pulse data that the calibrating parameters that demarcation obtains according to the strapdown airborne gravimeter obtains gravity meter are carried out the equivalent conversion, to obtain normal metrical information;

f=K _a·N _a+B _a (1)

w=K _g·(N _g-B _g) (2)

Wherein, K _aAnd B _aRepresent respectively the calibration factor and zero of accelerometer partially; K _gAnd B _gRepresent respectively the calibration factor and zero of gyro partially; N _aAnd N _gThe original pulse data that represent respectively accelerometer and gyro; F and w represent respectively the metrical information after the equivalent conversion.

As a further improvement on the present invention: in the described step (2), obtain by step (1) after the normal metrical information of strapdown airborne gravimeter, minute following three steps are determined the attitude error of strapdown airborne gravimeter:

(2.1), the error dynamics equation of strapdown airborne gravimeter is in local geographic coordinate system:

$\mathrm{\δ}\stackrel{.}{p}=\mathrm{\δv}---\left(3\right)$

$\mathrm{\δ}\stackrel{.}{v}=[f^n\×]\mathrm{\ψ}+C_b^n\mathrm{\δ}{f}^b-({2\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n)\×\mathrm{\δv}$

(4)

$-(2\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{ie}}^n+\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{en}}^n)\×v-\mathrm{\δ}{g}^n$

$\stackrel{.}{\mathrm{\ψ}}=-{\mathrm{\ω}}_{\mathrm{in}}^n\×\mathrm{\ψ}+\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{in}}^n-C_b^n\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{ib}}^b---\left(5\right)$

Wherein, δ p, δ v and ψ represent respectively site error, velocity error, the attitude error of strapdown airborne gravimeter; f ⁿBe illustrated in the accelerometer specific force value under the local geographic coordinate system;

Expression is tied to the transition matrix of local geographic coordinate system from coordinate; δ f ^bWith

The measuring error that represents respectively accelerometer and gyro; The expression terrestrial coordinate system is with respect to the projection of velocity of rotation in local geographic coordinate system of inertial coordinates system;

Represent that local geographic coordinate system is with respect to the projection of velocity of rotation under local geographic coordinate system of terrestrial coordinate system; δ g ⁿRepresent the gravity disturbance under the local geographic coordinate system;

Chosen position error, velocity error and attitude error are state variable, can obtain the state equation of Kalman filtering:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}\mathrm{\δp}\\ \mathrm{\δv}\\ \mathrm{\ψ}\end{array}\right]=F\left[\begin{array}{c}\mathrm{\δp}\\ \mathrm{\δv}\\ \mathrm{\ψ}\end{array}\right]+\mathrm{Gu}---\left(6\right)$

(2.2), utilize kalman filter method to carry out the forward estimation of state variable X, a Kalman filtering process of finishing can be expressed as follows:

X _k+1/k=φ _kX _k/k (10)

$P_{k+1/k}={\mathrm{\φ}}_k{P}_{k/k}{\mathrm{\φ}}_k^T+Q_k---\left(11\right)$

X _k+1/k+1=X _k+1/k-K _k+1(H _k+1X _k+1/k-z _k+1) (12)

$P_{k+1/k+1}=(I-K_{k+1}{H}_{k+1})P_{k+1/k}{(I-K_{k+1}{H}_{k+1})}^T-K_{k+1}{\mathrm{PK}}_{k+1}^T---\left(13\right)$

Wherein,

$K_{k+1}=P_{k+1/k}{H}_{k+1}^T(H_{k+1}{P}_{k+1/k}{H}_{k+1}^T+R)---\left(14\right)$

(2.3), utilize forward estimation obtains in the one-period state variable oppositely to recover to obtain the final estimated value of the state variable at this starting point place, attitude error wherein in cycle

It is exactly the attitude error that finally estimates; That oppositely recovers is calculated as follows:

X _0/0=φ _0,NX _N/N (15)

Wherein, X _N/NRepresent a forward estimation-oppositely the recover state estimation value of computation period destination county; X _0/0Represent a forward estimation-oppositely the recover state estimation value at computation period starting point place; φ _{0, N}Represent that a forward estimation-oppositely recover computation period terminal point is to the transition matrix of starting point.

As a further improvement on the present invention: described step (3) is carried out the separation of error by following formula:

$d\tilde{g}=\mathrm{dg}+\mathrm{\δ}{f}^n---\left(16\right)$

$\mathrm{\δ}{f}^n=f^n\×\widetilde{\mathrm{\ψ}}---\left(17\right)$

Wherein,

The gravity disturbance that obtains after the expression error is separated; Dg represents the front gravity disturbance measurement result of error separation; δ f ⁿExpression is because the size of the measuring error that attitude error causes.

Compared with prior art, the invention has the advantages that:

(1) strapdown airborne gravimeter error separating method theoretical foundation of the present invention is strong.The present invention has estimated the error source of this strapdown airborne gravimeter measuring error of attitude error to cause the former in starting point of strapdown airborne gravimeter measuring error, and the result that error is separated more can be accurate, has more directive significance.

(2) strapdown airborne gravimeter error separating method separation accuracy of the present invention is high.Specific aim of the present invention is very strong, only carries out error for the source that causes strapdown airborne gravimeter measuring error and separates, and has avoided the mistake of effective information to separate.Compare with original method, such error is separated the situation that more is close to reality, and the as a result precision after error is separated is also higher.

(3) strapdown airborne gravimeter error separating method of the present invention is realized easy.The present invention only need to get final product according to reversely restoring process of filtering convergence situation design in the forward estimation process of Kalman filtering, and algorithm realizes that required additional workload is less.

Description of drawings

Fig. 1 is the schematic flow sheet of the inventive method.

Fig. 2 is the principle schematic that adopts forward estimation-reverse restoration methods among the present invention.

Fig. 3 is the schematic flow sheet of restoration methods in application example of the forward estimation that adopts among the present invention-oppositely.

Embodiment

Below with reference to Figure of description and specific embodiment the present invention is described in further details.

Strapdown airborne gravimeter error separating method of the present invention is a kind of forward estimation of separating based on the strapdown airborne gravimeter error of Kalman filtering-reverse restoration methods, and such as Fig. 1, Fig. 2 and shown in Figure 3, its concrete steps are:

(1), the pre-service of strapdown airborne gravimeter raw data: the accelerometer that the strapdown airborne gravimeter obtains and the raw data of gyro all are pulse signals, need to just can convert normal metrical information to by the equivalent conversion.

The original pulse data that the calibrating parameters that demarcation obtains according to the strapdown airborne gravimeter obtains gravity meter are carried out the equivalent conversion, to obtain normal metrical information;

f=K _a·N _a+B _a (1)

w=K _g·(N _g-B _g) (2)

Wherein, K _aAnd B _aRepresent respectively the calibration factor and zero of accelerometer partially; K _gAnd B _gRepresent respectively the calibration factor and zero of gyro partially; N _aAnd N _gThe original pulse data that represent respectively accelerometer and gyro; F and w represent respectively the metrical information after the equivalent conversion.

(2), determine the attitude error that the strapdown airborne gravimeter produces in the flight measurement process: obtain by step (1) after the normal metrical information of strapdown airborne gravimeter, minute following three steps are determined the attitude error of strapdown airborne gravimeter:

(2.1), the error dynamics equation of strapdown airborne gravimeter is in local geographic coordinate system:

$\mathrm{\δ}\stackrel{.}{p}=\mathrm{\δv}---\left(3\right)$

$\mathrm{\δ}\stackrel{.}{v}=[f^n\×]\mathrm{\ψ}+C_b^n\mathrm{\δ}{f}^b-({2\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n)\×\mathrm{\δv}$

(4)

$-(2\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{ie}}^n+\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{en}}^n)\×v-\mathrm{\δ}{g}^n$

$\stackrel{.}{\mathrm{\ψ}}=-{\mathrm{\ω}}_{\mathrm{in}}^n\×\mathrm{\ψ}+\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{in}}^n-C_b^n\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{ib}}^b---\left(5\right)$

Wherein, δ p, δ v and ψ represent respectively site error, velocity error, the attitude error of strapdown airborne gravimeter; f ⁿBe illustrated in the accelerometer specific force value under the local geographic coordinate system;

Expression is tied to the transition matrix of local geographic coordinate system from coordinate; δ f ^bWith The measuring error that represents respectively accelerometer and gyro;

The expression terrestrial coordinate system is with respect to the projection of velocity of rotation in local geographic coordinate system of inertial coordinates system;

Represent that local geographic coordinate system is with respect to the projection of velocity of rotation under local geographic coordinate system of terrestrial coordinate system; δ g ⁿRepresent the gravity disturbance under the local geographic coordinate system.

Chosen position error, velocity error and attitude error are state variable, can obtain the state equation of Kalman filtering:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}\mathrm{\δp}\\ \mathrm{\δv}\\ \mathrm{\ψ}\end{array}\right]=F\left[\begin{array}{c}\mathrm{\δp}\\ \mathrm{\δv}\\ \mathrm{\ψ}\end{array}\right]+\mathrm{Gu}---\left(6\right)$

Observation equation is:

$y=H\left[\begin{array}{c}\mathrm{\δp}\\ \mathrm{\δv}\\ \mathrm{\ψ}\end{array}\right]---\left(7\right)$

Wherein:

$H=\left[\begin{array}{ccc}I& 0& 0\\ 0& I& 0\end{array}\right]---\left(8\right)$

Observed quantity is:

$Z=\left[\begin{array}{c}\mathrm{\δp}\\ \mathrm{\δv}\end{array}\right]=\left[\begin{array}{c}{p}_{\mathrm{GPS}}^n-p_{\mathrm{INS}}^n\\ v_{\mathrm{GPS}}^n-v_{\mathrm{INS}}^n\end{array}\right]\·---\left(9\right)$

Wherein,

Gravity meter position in the local geographic coordinate system that expression is recorded by GPS;

The gravity meter position that expression is obtained by the accelerometer in the gravity meter and gyro; Gravity meter speed in the local geographic coordinate system that expression is recorded by GPS;

The gravity meter speed that expression is obtained by the accelerometer in the gravity meter and gyro.

(2.2), utilize kalman filter method to carry out the forward estimation of state variable X, a Kalman filtering process of finishing can be expressed as follows:

X _k+1/k=φ _kX _k/k (10)

$P_{k+1/k}={\mathrm{\φ}}_k{P}_{k/k}{\mathrm{\φ}}_k^T+Q_k---\left(11\right)$

X _k+1/k+1=X _k+1/k-K _k+1(H _k+1X _k+1/k-z _k+1) (12)

$P_{k+1/k+1}=(I-K_{k+1}{H}_{k+1})P_{k+1/k}{(I-K_{k+1}{H}_{k+1})}^T-K_{k+1}{\mathrm{PK}}_{k+1}^T---\left(13\right)$

Wherein,

$K_{k+1}=P_{k+1/k}{H}_{k+1}^T(H_{k+1}{P}_{k+1/k}{H}_{k+1}^T+R)---\left(14\right)$

(2.3), utilize forward estimation obtains in the one-period state variable oppositely to recover to obtain the final estimated value of the state variable at this starting point place, attitude error wherein in cycle

It is exactly the attitude error that finally estimates.That oppositely recovers is calculated as follows:

X _0/0=φ _0,NX _N/N (15)

Wherein, X _N/NRepresent a forward estimation-oppositely the recover state estimation value of computation period destination county; X _0/0Represent a forward estimation-oppositely the recover state estimation value at computation period starting point place; φ _{0, N}Represent that a forward estimation-oppositely recover computation period terminal point is to the transition matrix of starting point.

(3), the attitude error determined by step (2) revises the measurement result of strapdown gravity meter, thereby realize the separation of error:

$d\tilde{g}=\mathrm{dg}+\mathrm{\δ}{f}^n---\left(16\right)$

$\mathrm{\δ}{f}^n=f^n\×\widetilde{\mathrm{\ψ}}---\left(17\right)$

Wherein,

The gravity disturbance that obtains after the expression error is separated; Dg represents the front gravity disturbance measurement result of error separation; δ f ⁿExpression is because the size of the measuring error that attitude error causes.

Below only be preferred implementation of the present invention, protection scope of the present invention also not only is confined to above-described embodiment, and all technical schemes that belongs under the thinking of the present invention all belong to protection scope of the present invention.Should be pointed out that for those skilled in the art the some improvements and modifications not breaking away under the principle of the invention prerequisite should be considered as protection scope of the present invention.

Claims (4)

1. strapdown airborne gravimeter error separating method is characterized in that step is:

(1), the pre-service of strapdown airborne gravimeter raw data: the accelerometer that the strapdown airborne gravimeter is obtained and the original burst signal of gyro convert normal metrical information to by equivalent;

(2), determine the attitude error that the strapdown airborne gravimeter produces in the flight measurement process;

(3), the attitude error of determining by step (2) is revised the separation of realization error to the measurement result of strapdown gravity meter.

2. strapdown airborne gravimeter error separating method according to claim 1, it is characterized in that, described step (1) is: the original pulse data that the calibrating parameters that demarcation obtains according to the strapdown airborne gravimeter obtains gravity meter are carried out the equivalent conversion, to obtain normal metrical information;

f=K _a·N _a+B _a (1)

w=K _g·(N _g-B _g) (2)

Wherein, K _aAnd B _aRepresent respectively the calibration factor and zero of accelerometer partially; K _gAnd B _gRepresent respectively the calibration factor and zero of gyro partially; N _aAnd N _gThe original pulse data that represent respectively accelerometer and gyro; F and w represent respectively the metrical information after the equivalent conversion.

3. strapdown airborne gravimeter error separating method according to claim 1, it is characterized in that, in the described step (2), obtain by step (1) after the normal metrical information of strapdown airborne gravimeter, minute following three steps are determined the attitude error of strapdown airborne gravimeter:

(2.1), the error dynamics equation of strapdown airborne gravimeter is in local geographic coordinate system:

$\mathrm{\δ}\stackrel{.}{p}=\mathrm{\δv}---\left(3\right)$

$\mathrm{\δ}\stackrel{.}{v}=[f^n\×]\mathrm{\ψ}+C_b^n\mathrm{\δ}{f}^b-({2\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n)\×\mathrm{\δv}$

(4)

$-(2\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{ie}}^n+\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{en}}^n)\×v-\mathrm{\δ}{g}^n$

$\stackrel{.}{\mathrm{\ψ}}=-{\mathrm{\ω}}_{\mathrm{in}}^n\×\mathrm{\ψ}+\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{in}}^n-C_b^n\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{ib}}^b---\left(5\right)$

Wherein, δ p, δ v and ψ represent respectively site error, velocity error, the attitude error of strapdown airborne gravimeter; f ⁿBe illustrated in the accelerometer specific force value under the local geographic coordinate system;

Expression is tied to the transition matrix of local geographic coordinate system from coordinate; δ f ^bWith

The measuring error that represents respectively accelerometer and gyro;

The expression terrestrial coordinate system is with respect to the projection of velocity of rotation in local geographic coordinate system of inertial coordinates system;

Represent that local geographic coordinate system is with respect to the projection of velocity of rotation under local geographic coordinate system of terrestrial coordinate system; δ g ⁿRepresent the gravity disturbance under the local geographic coordinate system;

Chosen position error, velocity error and attitude error are state variable, can obtain the state equation of Kalman filtering:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}\mathrm{\δp}\\ \mathrm{\δv}\\ \mathrm{\ψ}\end{array}\right]=F\left[\begin{array}{c}\mathrm{\δp}\\ \mathrm{\δv}\\ \mathrm{\ψ}\end{array}\right]+\mathrm{Gu}---\left(6\right)$

(2.2), utilize kalman filter method to carry out the forward estimation of state variable X, a Kalman filtering process of finishing is expressed as follows:

X _k+1/k=φ _kX _k/k (10)

$P_{k+1/k}={\mathrm{\φ}}_k{P}_{k/k}{\mathrm{\φ}}_k^T+Q_k---\left(11\right)$

X _k+1/k+1=X _k+1/k-K _k+1(H _k+1X _k+1/k-z _k+1) (12)

$P_{k+1/k+1}=(I-K_{k+1}{H}_{k+1})P_{k+1/k}{(I-K_{k+1}{H}_{k+1})}^T-K_{k+1}{\mathrm{PK}}_{k+1}^T---\left(13\right)$

Wherein,

$K_{k+1}=P_{k+1/k}{H}_{k+1}^T(H_{k+1}{P}_{k+1/k}{H}_{k+1}^T+R)---\left(14\right)$

(2.3), utilize forward estimation obtains in the one-period state variable oppositely to recover to obtain the final estimated value of the state variable at this starting point place, attitude error wherein in cycle

It is exactly the attitude error that finally estimates; That oppositely recovers is calculated as follows:

X _0/0=φ _0,NX _N/N (15)

Wherein, X _N/NRepresent a forward estimation-oppositely the recover state estimation value of computation period destination county; X _0/0Represent a forward estimation-oppositely the recover state estimation value at computation period starting point place; φ _{0, N}Represent that a forward estimation-oppositely recover computation period terminal point is to the transition matrix of starting point.

4. strapdown airborne gravimeter error separating method according to claim 1 is characterized in that, described step (3) is carried out the separation of error by following formula:

$d\tilde{g}=\mathrm{dg}+\mathrm{\δ}{f}^n---\left(16\right)$

$\mathrm{\δ}{f}^n=f^n\×\widetilde{\mathrm{\ψ}}---\left(17\right)$

Wherein, The gravity disturbance that obtains after the expression error is separated; Dg represents the front gravity disturbance measurement result of error separation; δ f ⁿExpression is because the size of the measuring error that attitude error causes.

Images