CN110186484B - Method for improving drop point precision of inertial guidance spacecraft - Google Patents

Method for improving drop point precision of inertial guidance spacecraft Download PDF

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CN110186484B
CN110186484B CN201910556812.7A CN201910556812A CN110186484B CN 110186484 B CN110186484 B CN 110186484B CN 201910556812 A CN201910556812 A CN 201910556812A CN 110186484 B CN110186484 B CN 110186484B
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inertial
spacecraft
improving
value
guided
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CN110186484A (en
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魏宗康
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Beijing Aerospace Control Instrument Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • 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

Abstract

The invention relates to a method for improving the drop point precision of an inertial guidance spacecraft, belonging to the technical field of inertial navigation. The invention provides a theoretical calculation value of a steady state value of a recursive least square method, and overcomes the defect that the traditional recursive least square method can not provide an accurate theoretical value when a structural matrix is singular; the invention provides the theoretical calculation value of the steady state value of the recursive least square method, which not only covers the condition when the column vectors of the structural matrix are correlated, but also includes the condition when the structural matrix is in a column full rank, and has better application range. The invention provides a theoretical calculation value of the steady state value of the recursive least square method, which is beneficial to analyzing the observability of the system and optimizing the estimated track and the like on the basis, and has better engineering application value.

Description

Method for improving drop point precision of inertial guidance spacecraft
Technical Field
The invention relates to a method for improving the drop point precision of an inertial guidance spacecraft, belonging to the technical field of inertial navigation.
Background
Currently, inertial navigation of an aerospace vehicle mainly adopts a strapdown system or a platform system consisting of a gyroscope and an accelerometer. Before live ammunition flying, error coefficients of a gyroscope and an accelerometer need to be calibrated on the ground, and the use precision of inertial navigation can be effectively improved through error compensation according to a calibration result. At present, in an actual flight navigation test, the inertial device calibrated on the ground still has a large deviation between theoretical values of speed and position calculated according to telemetering data and actual values of flight speed and position obtained by external measurement, and the situation of so-called 'sky and earth inconsistency' occurs. Through analysis, the reason for the occurrence of the 'sky-ground inconsistency' is that the accuracy of the ground calibration method and the data processing method is insufficient, so that errors are accumulated in the actual flight process, and the flight accuracy is deteriorated, so that the error model and the data processing method in the ground calibration process need to be corrected.
Disclosure of Invention
The technical problem of the invention is solved: the method for improving the drop point precision of the inertial guidance spacecraft overcomes the defects of the prior art.
The technical solution of the invention is as follows:
a method for improving the landing accuracy of an inertial guidance spacecraft, wherein an inertial device comprises a gyroscope and an accelerometer, and the method comprises the following steps:
(1) real-time calculation of n sets of error quantities y of inertial devicei；
yi＝x1ui1+x2ui2+…+xmuim＝ciX, i ═ 1,2, …, n, m are the number of state variables;
wherein, ci＝[ui1 ui2 … uim]，
Figure GDA0002977269120000021
Structural matrix C of inertial devicesnIs composed of
Figure GDA0002977269120000022
x1,x2,x3,…,xmIs the error coefficient of the inertial device;
(2) for information matrix
Figure GDA0002977269120000023
Performing eigenvalue decomposition of
Figure GDA0002977269120000024
In the formula, DnIs a diagonal matrix, and each element of the diagonal is
Figure GDA0002977269120000025
Is provided with DnP zeros in the diagonal, and m-p non-zero eigenvalues, expressed as
Figure GDA0002977269120000026
UnIs DnCorresponding orthogonal eigenvector matrix satisfying
Figure GDA0002977269120000027
(3) According to DnCorresponding zero eigenvalue and non-zero eigenvalue in (1), U can be converted intonIs written as
Un＝[U1 U2]
Wherein, U1Set of feature vectors, U, corresponding to zero feature values2A feature vector set corresponding to the non-zero feature value;
(4) by usingCalculating the estimated value of X in the step (1) by using a recursive least square method
Figure GDA0002977269120000028
(5) Obtained according to the step (4)
Figure GDA0002977269120000029
Calculation of X is
Figure GDA00029772691200000210
(6) And (5) according to the error coefficient X of the inertial device obtained in the step (5), carrying out error compensation on the output quantity of the inertial device, and outputting the compensated output quantity of the inertial device to a navigation system for determining the motion state of the spacecraft, so that the landing point precision of inertial guidance is improved.
In the step (4), the estimation value of X in the step (1) is calculated by adopting a recursive least square method
Figure GDA00029772691200000211
Comprises the following steps:
Figure GDA0002977269120000031
wherein the content of the first and second substances,
Figure GDA0002977269120000032
i is an identity matrix;
Pn+1＝Pn-Kn+1cn+1Pn
at n +1 recursion calculations, yn+1Is composed of
yn+1＝cn+1X
When n is set to 0, PnHas an initial value of P0，P0Is a set value;
Figure GDA0002977269120000033
initial value of
Figure GDA0002977269120000034
Is a set value; the number of iterations is n.
Compared with the prior art, the invention has the following beneficial effects
(1) The invention provides a theoretical calculation value of a steady state value of a recursive least square method, and overcomes the defect that the traditional recursive least square method can not provide an accurate theoretical value when a structural matrix is singular;
(2) the invention provides the theoretical calculation value of the steady state value of the recursive least square method, which not only covers the condition when the column vectors of the structural matrix are correlated, but also includes the condition when the structural matrix is in a column full rank, and has better application range.
(3) The invention provides a theoretical calculation value of the steady state value of the recursive least square method, which is beneficial to analyzing the observability of the system and optimizing the estimated track and the like on the basis, and has better engineering application value.
Drawings
FIG. 1 is an output error sequence value of an accelerometer according to a coefficient true value in an embodiment;
fig. 2 is an iterative calculation process given by the recursive least square method in the embodiment.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
examples
A method of determining an error coefficient for an accelerometer, the method comprising the steps of:
(1) calculating 6 groups of error quantities y of accelerometer in real timei；
The orientation of the accelerometer and the components of the gravitational acceleration in that orientation when 6 sets of error quantities are measured in real time are shown in table 1:
serial number x、y、z ax ay az
1 Tiannandong 1 0 0
2 All-grass of south east China 0 0 1
3 Dongtiannan 0 1 0
4 North and West 0 -1 0
5 In the west and north 0 0 -1
6 Northwest of China -1 0 0
The accelerometer output error equation is set as:
Figure GDA0002977269120000041
the structural matrix of the accelerometer is obtained according to table 1 as:
Figure GDA0002977269120000042
in the first position, there are
c1＝[1 1 0 0 f q]
In the second position, there are
c2＝[1 0 0 1 0 0]
In the third position, there are
c3＝[1 0 1 0 0 0]
In the fourth position, there are
c4＝[1 0 -1 0 0 0]
In the fifth position, there are
c5＝[1 0 0 -1 0 0]
In the sixth position, there are
c6＝[1 -1 0 0 -f -q]
The test data at each position were averaged, and 6 test data y were counted for 6 positions1、y2、…、y6。
Taking the state variable as
Figure GDA0002977269120000051
When simulation is carried out, the true value of the error coefficient of the accelerometer is set as k0x＝1.0×10-4、δkx＝-1.0×10-4、kyx＝1.0×10-4、kzx＝-1.0×10-4、kp＝-1.0×10-4、kq＝-1.0×10-4And f-4 and q-2, and substituting the accelerometer output error equation to calculate the accelerometer output error value as shown in fig. 1.
Giving an initial value
Figure GDA0002977269120000052
P0＝107Each error coefficient is estimated by using a recursive least square method, as shown in fig. 2. In the figure, the dotted line represents the true value of each parameter, and the solid line represents the estimated value of each parameter. "k 0 x" in the upper left corner represents "k" in the patent of the present invention0x", dkx in the upper right-hand corner represents" δ k "in the patent of the inventionx", kyx in the left middle figure represents" k "in the patent of the inventionyx", kzx in the right middle figure represents" k "in the patent of the inventionzx", kp in the lower left diagram represents" k "in the patent of the inventionp", kq" in the lower right-hand diagram represents "k" in the patent of the inventionq”。
As can be seen from the figure, there are only three error coefficients k0x、kyx、kzxConverge to the true value, and the remaining three error coefficients δ kx、kp、kqConverge to their respective steady-state values but have a large difference from the true values. The reason why the latter does not converge to the true value is that the three are related, so that the structural matrix is a singular matrix. The steady state value after convergence is
k0x＝9.99999983×10-5、δkx＝4.76190475×10-6、kyx＝9.99999950×10-5、kzx＝-9.99999950×10-5、kp＝-1.90476190×10-5、kq＝-9.52380950×10-6。
Because the recursion process is relatively complex, the algorithm of the invention can be adopted to solve the theoretical calculation value of the parameter, and the specific process is
The structural matrix is
Figure GDA0002977269120000061
The information matrix is
Figure GDA0002977269120000062
Eigenvalue decomposition
Figure GDA0002977269120000063
Figure GDA0002977269120000064
Due to the fact that in D 62 of these feature values are 0, so for U6Is divided into blocks, have
Figure GDA0002977269120000071
Figure GDA0002977269120000072
The theoretical calculation value for finding the steady state value is
k0x＝1.0000000×10-4、δkx＝4.76190476×10-6、kyx＝1.000000×10-5、kzx＝-9.99999999×10-5、kp＝-1.90476190×10-5、kq＝9.52380952×10-6。
It can be seen that the estimate is substantially consistent with the recursive least squares method.
The theoretical calculation value of the error between the steady state value and the true value is calculated as
δk0x＝0、δkx＝1.0476×10-4、δkyx＝0、δkzx＝0、δkp＝8.0952×10-5、δkq＝1.09523×10-4。
(2) And (2) according to the error coefficient X of the inertial device obtained in the step (1), carrying out error compensation on the output quantity of the inertial device, and outputting the compensated output quantity of the inertial device to a navigation system for determining the motion state of the spacecraft, thereby improving the landing point precision of the inertial guidance spacecraft.
The above description is only one embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
The invention has not been described in detail in part of the common general knowledge of those skilled in the art.

Claims (10)

1. A method for improving the landing point precision of an inertial guidance spacecraft is characterized by comprising the following steps:
(1) real-time calculation of n sets of error quantities y of inertial devicei；
yi＝x1ui1+x2ui2+…+xmuim＝ciX, i ═ 1,2, …, n, m are the number of state variables;
wherein, ci＝[ui1 ui2 … uim]，
Figure FDA0002977269110000011
Structural matrix C of inertial devicesnIs composed of
Figure FDA0002977269110000012
x1,x2,x3,…,xmIs the error coefficient of the inertial device;
(2) for information matrix
Figure FDA0002977269110000013
Performing eigenvalue decomposition of
Figure FDA0002977269110000014
In the formula, DnIs a diagonal matrix, and each element of the diagonal is
Figure FDA0002977269110000015
A characteristic root of; u shapenIs DnA corresponding orthogonal eigenvector matrix;
(3) according to DnThe corresponding zero eigenvalue and non-zero eigenvalue in the intermediate table, and UnIs written as
Un＝[U1 U2]
Wherein, U1Set of feature vectors, U, corresponding to zero feature values2A feature vector set corresponding to the non-zero feature value;
(4) calculating the estimated value of X in the step (1) by adopting a recursive least square method
Figure FDA0002977269110000016
(5) Obtained according to the step (4)
Figure FDA0002977269110000017
Calculation of X is
Figure FDA0002977269110000018
(6) And (5) according to the error coefficient X of the inertial device obtained in the step (5), carrying out error compensation on the output quantity of the inertial device, and outputting the compensated output quantity of the inertial device to a navigation system for determining the motion state of the spacecraft, so that the landing point precision of the inertial guidance spacecraft is improved.
2. The method for improving the landing accuracy of an inertial guided spacecraft of claim 1, wherein: the inertial device is a gyroscope.
3. The method for improving the landing accuracy of an inertial guided spacecraft of claim 1, wherein: the inertial device is an accelerometer.
4. The method for improving the landing accuracy of an inertial guided spacecraft of claim 1, wherein: in the step (2), D is setnP zeros in the diagonal, and m-p non-zero eigenvalues, expressed as
Figure FDA0002977269110000021
UnIs DnCorresponding orthogonal eigenvector matrix satisfying
Figure FDA0002977269110000022
dp+1、dp+2、…、dmAre all non-zero eigenvalues.
5. The method for improving the landing accuracy of an inertial guided spacecraft of claim 1, wherein: in the step (4), the estimation value of X is calculated by adopting a recursion least square method
Figure FDA0002977269110000025
The method comprises the following steps:
Figure FDA0002977269110000023
6. the method for improving the landing accuracy of an inertial guided spacecraft of claim 5, wherein:
Figure FDA0002977269110000024
and I is an identity matrix.
7. The method for improving the landing accuracy of an inertial guided spacecraft of claim 6, wherein:
Pn+1＝Pn-Kn+1cn+1Pn。
8. the method for improving the landing accuracy of an inertial guided spacecraft of claim 7, wherein:
at n +1 recursion calculations, yn+1Is composed of
yn+1＝cn+1X。
9. The method for improving the landing accuracy of an inertial guided spacecraft of claim 8, wherein: when n is set to 0, PnHas an initial value of P0，P0Is a set value;
Figure FDA0002977269110000031
initial value of
Figure FDA0002977269110000032
Is a set value.
10. The method for improving the landing accuracy of an inertial guided spacecraft of claim 9, wherein: the number of iterations is n.
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