CN111351483A - Recursive multi-subsample large dynamic inertial navigation method - Google Patents

Recursive multi-subsample large dynamic inertial navigation method Download PDF

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CN111351483A
CN111351483A CN202010245775.0A CN202010245775A CN111351483A CN 111351483 A CN111351483 A CN 111351483A CN 202010245775 A CN202010245775 A CN 202010245775A CN 111351483 A CN111351483 A CN 111351483A
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李茂登
黄翔宇
郭敏文
徐超
魏春岭
张晓文
胡锦昌
王晓磊
王云鹏
刘旺旺
张琳
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Beijing Institute of Control Engineering
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    • 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
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    • 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
    • G01C21/18—Stabilised platforms, e.g. by gyroscope
    • 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
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Abstract

A recursive multi-subsample large dynamic inertial navigation method belongs to the technical field of autonomous spacecraft navigation and comprises the following steps: s1, carrying out polynomial fitting on the angular velocity of the lander according to the angular increment of the gyroscope of the lander and the continuity characteristics of the angular velocity to obtain an angular velocity polynomial; s2, solving the rotation vector of the lander by using an angular velocity polynomial; s3, constructing a rotation quaternion by using the rotation vector of the lander; s4, calculating to obtain the attitude quaternion of the current time by using the attitude quaternion of the previous time and the rotation quaternion in S3; obtaining the inertial velocity of the current moment by using the inertial velocity of the previous moment, the attitude quaternion of the previous moment and the angle increment of a gyroscope of the lander; and obtaining the inertial position of the current moment by using the inertial position of the previous moment, the inertial speed of the previous moment and the inertial speed of the current moment. The method greatly improves the inertial navigation precision under the large dynamic motion.

Description

Recursive multi-subsample large dynamic inertial navigation method
Technical Field
The invention relates to a recursive multi-subsample large dynamic inertial navigation method, and belongs to the technical field of autonomous navigation of spacecrafts.
Background
The Entry, Landing and Landing segment (EDL) of the mars detection task is the last 6 and 7 minutes of a 7 hundred million kilometer trip of the mars detector, is a key stage of the mars surface detection task, and is the most difficult stage. The EDL technique is also one of the key techniques for the task of Mars surface probing. The Mars detector enters the Mars atmosphere at the speed of 2 ten thousand kilometers per hour, and finally drops on the surface of the Mars in order to ensure safety and accuracy after a series of stages of atmosphere deceleration, parachute dragging, power deceleration and the like. The dynamic of the spark in the descending process is very large, and especially the angular velocity of the parachute section vibrates violently. During which inertial navigation is only possible using the IMU. During navigation calculation, the cone error effect, the paddle error effect and the scroll error caused by large dynamic have serious influence. The existing multi-subsample updating algorithm utilizes IMU speed increment and angle increment of a plurality of subsamples to carry out polynomial fitting in a navigation updating period, and effective compensation of a cone error effect, a paddle error effect and a scroll effect is achieved. However, the existing multi-subsample updating algorithm does not consider the continuity of the angular velocity of adjacent navigation periods, so that the compensation effect is limited.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the defects of the prior art are overcome, and a recursive multi-subsample large dynamic inertial navigation method is provided, which comprises the following steps: s1, carrying out polynomial fitting on the angular velocity of the lander according to the angular increment of the gyroscope of the lander and the continuity characteristics of the angular velocity to obtain an angular velocity polynomial; s2, solving the rotation vector of the lander by using an angular velocity polynomial; s3, constructing a rotation quaternion by using the rotation vector of the lander; s4, calculating to obtain the attitude quaternion of the current time by using the attitude quaternion of the previous time and the rotation quaternion in S3; obtaining the inertial velocity of the current moment by using the inertial velocity of the previous moment, the attitude quaternion of the previous moment and the angle increment of a gyroscope of the lander; and obtaining the inertial position of the current moment by using the inertial position of the previous moment, the inertial speed of the previous moment and the inertial speed of the current moment.
The purpose of the invention is realized by the following technical scheme:
a recursive multi-subsample large dynamic inertial navigation method comprises the following steps:
s1, carrying out polynomial fitting on the angular velocity of the lander according to the angular increment of the gyroscope of the lander and the continuity characteristics of the angular velocity to obtain an angular velocity polynomial;
s2, solving the rotation vector of the lander by using an angular velocity polynomial;
s3, constructing a rotation quaternion by using the rotation vector of the lander;
s4, calculating to obtain the attitude quaternion of the current time by using the attitude quaternion of the previous time and the rotation quaternion in S3;
obtaining the inertial velocity of the current moment by using the inertial velocity of the previous moment, the attitude quaternion of the previous moment and the angle increment of a gyroscope of the lander;
and obtaining the inertial position of the current moment by using the inertial position of the previous moment, the inertial speed of the previous moment and the inertial speed of the current moment.
In the recursive multi-sample large dynamic inertial navigation method, preferably, in S3, a rotation quaternion is constructed using the rotation vector of the lander according to the euler rotation principle.
Preferably, in the recursive multi-sample large dynamic inertial navigation method, the angular velocity polynomial is:
ω(tm+τ)＝am+bmτ+cmτ20≤τ≤ΔT
wherein
Figure BDA0002433938020000021
Figure BDA0002433938020000022
Figure BDA0002433938020000023
In the formula, ω is the inertial angular velocity projected under the IMU body coordinate system, Δ T ═ Tm+1-tmFor navigation update period, am、bm、cmAre each [ tm,tm+1]The coefficient to be fitted for the angular velocity in the time interval, τ being [ t ]m,tm+1]Any time of the interval; the gyro of IMU is at [ t ]m-1,tm]The sub-sample of the navigation period output two angle increments is delta theta1And Δ θ2，θ'1And θ'2Is [ t ]m-1,tm]Two subsamples of gyros within a navigation cycle; a ism-1Is [ t ]m,tm+1]A of the time intervalm。
Preferably, in the recursive multi-subsample large dynamic inertial navigation method, the rotation vector of the lander is as follows:
φm＝αm+βm
in the formula, from tmTime tm+1The rotation vector of the moment is phim；αmIs tmAngular increment of time, βmA cone effect compensation term.
Preferably, in the recursive multi-subsample large dynamic inertial navigation method, the attitude quaternion at the current time is as follows:
Figure BDA0002433938020000031
wherein
Figure BDA0002433938020000032
In the formula,
Figure BDA0002433938020000033
is a quaternion product, qmAnd q ism+1Are each tmAnd tm+1The inertia system at the moment reaches the attitude quaternion of the IMU body coordinate system; from tmTime tm+1The rotation vector of the moment is phim。
Preferably, in the recursive multi-subsample large dynamic inertial navigation method, the inertial velocity at the current time is:
Figure BDA0002433938020000034
wherein
Figure BDA0002433938020000035
Figure BDA0002433938020000036
In the formula, vmAnd vm+1Are each tm,tm+1The inertial velocity at the moment of time is,
Figure BDA0002433938020000037
is tmAttitude transformation matrix from the IMU body coordinate system to the inertial system at time, [ t ]m-1,tm]Is a navigation period, Δ vgVelocity increments due to gravitational acceleration; Δ v1And Δ v2Is [ t ]m,tm+1]Within a regionIMU plus two subsample velocity increment measured by IMU gyro at tm-1,tm]The sub-sample of the navigation period output two angle increments is delta theta1And Δ θ2，amIs [ t ]m,tm+1]Time interval the angular velocity is the coefficient to be fitted.
Preferably, in the recursive multi-subsample large dynamic inertial navigation method, the inertial position at the current time is:
Figure BDA0002433938020000041
in the formula, rm+1Is tm+1Position of the IMU in relation to the central celestial body under the inertial system at the instant rmIs tmPosition of the IMU in relation to the central celestial body under the inertial system at the instant of time vmAnd vm+1Are each tm、tm+1The inertial velocity at a time; Δ T ═ Tm+1-tmFor the navigation update period, [ t ]m-1,tm]Is a navigation cycle.
Preferably, the recursive multi-sample large dynamic inertial navigation method repeats S1 to S4, and continuously obtains the attitude quaternion at the current time, the inertial velocity at the current time, and the inertial position at the current time, thereby completing the inertial navigation of the aircraft.
Compared with the prior art, the invention has the following beneficial effects:
(1) the method has small calculation amount and numerous values for solving and calculating;
(2) the method greatly improves the inertial navigation precision under the large dynamic motion;
(3) the method can reduce IMU sampling frequency and reduce IMU output load;
(4) the method of the invention can increase the navigation updating period and reduce the computational burden of the navigation computer.
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FIG. 1 is a flow chart of the steps of the method of the present invention;
FIG. 2 is a comparison of the navigation error of the method of the present invention with the navigation error of the prior art.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
A recursive multi-subsample large dynamic inertial navigation method, as shown in fig. 1, comprising the steps of:
1) and performing polynomial fitting on the angular velocity of the lander according to the angular increment of the gyroscope of the lander and the continuity characteristic of the angular velocity to obtain an angular velocity polynomial.
Consider [ t ]m,tm+1]Navigation updating in the interval, and performing polynomial fitting on the angular speed in the time interval
ω(tm+τ)＝am+bmτ+cmτ20≤τ≤ΔT (1)
Wherein, omega is the inertia angular velocity projection under the IMU body coordinate system, and delta T is Tm+1-tmFor navigation update period, am,bm,cmAre each [ tm,tm+1]Interval is coefficient to be fitted, tau is [ tm,tm+1]Any time of the interval.
Recording IMU sampling period delta tIFor many subsamples, there is an update algorithm
ΔT＝mΔtI(2)
Wherein m is more than or equal to 1 and is the number of subsamples. Considering 2 sub-cases, m is 2. Thereby to obtain
ΔT＝2ΔtI(3)
Outputting two angle increment sub-samples delta theta by an IMU-recording gyroscope in a navigation period1And Δ θ2. Integrating equation (1) yields:
Figure BDA0002433938020000051
Figure BDA0002433938020000052
the following equations (4) and (1) can be used to obtain:
Figure BDA0002433938020000053
Figure BDA0002433938020000054
from the continuity of the angular velocity it can be derived:
ω(tm)＝ω(tm-1+ΔT) (6)
from the formula (1), in [ tm-1,tm]In the interval of (A), there are
ω(tm-1+τ)＝am-1+bm-1τ+cm-1τ20≤τ≤ΔT (7)
Wherein a ism-1,bm-1,cm-1Is [ t ]m-1,tm]The interval is the coefficient to be fitted to the angular velocity polynomial.
Therefore, there are:
Figure BDA0002433938020000055
wherein theta'1And θ'2Is [ t ]m-1,tm]Two subsamples of gyros within a navigation cycle
And is shown by the formula (1)
ω(tm)＝am(9)
Substituting equations (8) and (9) into (6) can thus yield:
Figure BDA0002433938020000061
note that solving for amA is required to usem-1The value of (c). In actual application, a is set0When 0, a can be solved recursivelym。
2) And solving the rotation vector of the lander by using an angular velocity polynomial.
Remember from tmTime tm+1Rotation of time of dayVector phimCan be written as:
φm＝αm+βm(11)
wherein:
Figure BDA0002433938020000062
where t is time, α (t) is angular increment, αmIs tmAngular increment of time, βmA cone effect compensation term.
The following can be obtained from the formulae (1) and (12):
Figure BDA0002433938020000063
thereby to obtain
Figure BDA0002433938020000064
Substituting formulae (1) and (13) into formula (12) can yield:
Figure BDA0002433938020000065
substituting equations (13) and (15) into equation (11) can yield:
Figure BDA0002433938020000071
then substituting the formula (5) into the formula (16) to obtain
Figure BDA0002433938020000072
3) And according to the Euler rotation principle, constructing a rotation quaternion by using the rotation vector of the lander.
Figure BDA0002433938020000073
4) And calculating to obtain the attitude quaternion of the current moment by using the attitude quaternion of the previous moment and the rotation quaternion in the step 3).
Figure BDA0002433938020000074
Wherein:
Figure BDA0002433938020000075
is a quaternion product, qmAnd q ism+1Are each tmAnd tm+1The inertia at that moment is the attitude quaternion to the IMU body coordinate system.
And 4.1) obtaining the inertial velocity of the current moment by using the inertial velocity of the previous moment, the attitude quaternion of the previous moment and the angle increment of the gyroscope of the lander.
The inertial velocity of IMU is recorded as v, and the differential equation can be written as
Figure BDA0002433938020000076
Wherein f isbIs the projection of the acceleration of non-gravity in the IMU body coordinate system, giIs the projection of the gravitational acceleration under the inertial system,
Figure BDA0002433938020000077
and converting the IMU body coordinate system to the attitude of the inertial system. In the above formula [ tm,tm+1]The updating equation of the inertial navigation speed can be obtained by integrating in the interval:
Figure BDA0002433938020000078
wherein v ismAnd vm+1Are each tm,tm+1The inertial velocity at the moment of time is,
Figure BDA0002433938020000079
is tmOf time of day
Figure BDA00024339380200000710
From tmAttitude quaternion q of timemCalculated as,. DELTA.vgFor the velocity increment caused by gravitational acceleration, the following equation gives
Figure BDA0002433938020000081
Wherein
Figure BDA0002433938020000082
Mu is the gravitational constant of the central celestial body, rmIs tmThe position of the IMU relative to the central celestial body under the inertial system at time. Δ v in formula (21)sfmIs given by
Figure BDA0002433938020000083
Wherein
Figure BDA0002433938020000084
Δv1And Δ v2Is [ t ]m,tm+1]The IMU adds the measured velocity increments for the two subsamples over the interval. Substituting equation (17) into equation (22) yields:
Figure BDA0002433938020000087
wherein,
Figure BDA0002433938020000085
the velocity update is completed by substituting the equations (22) and (24) into the equation (21).
And 4.2) obtaining the inertial position of the current time by using the inertial position of the previous time, the inertial speed of the previous time and the inertial speed of the current time.
The inertial navigation system position update equation can be written as:
Figure BDA0002433938020000086
wherein: r ism+1Is tm+1The position of the IMU relative to the central celestial body under the inertial system at time.
And in conclusion, repeating the steps 1) to 4), and continuously obtaining the attitude quaternion at the current moment, the inertial velocity at the current moment and the inertial position at the current moment, so as to complete the inertial navigation of the aircraft. The applicable dynamic range of the inertial navigation method is as follows: angular acceleration of no more than 8000 DEG/s2. The comparison of the navigation error of the method of the present invention with the navigation error of the method of the prior art is shown in fig. 2, the dotted line in the figure is the method of the prior art, and the solid line is the method of the present invention, so that the method of the present invention has greatly improved navigation position precision, navigation speed precision and navigation attitude precision compared with the prior art, and the navigation error is obviously reduced. The improvement of the inertial navigation precision is beneficial to improving the accuracy, stability and reliability of the landing of the detector, and has important significance and effect on the landing of the detector.
A computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of a recursive multi-subsample large dynamic inertial navigation method.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (10)

1. A recursive multi-subsample large dynamic inertial navigation method is characterized by comprising the following steps:
s1, carrying out polynomial fitting on the angular velocity of the lander according to the angular increment of the gyroscope of the lander and the continuity characteristics of the angular velocity to obtain an angular velocity polynomial;
s2, solving the rotation vector of the lander by using an angular velocity polynomial;
s3, constructing a rotation quaternion by using the rotation vector of the lander;
s4, calculating to obtain the attitude quaternion of the current time by using the attitude quaternion of the previous time and the rotation quaternion in S3;
obtaining the inertial velocity of the current moment by using the inertial velocity of the previous moment, the attitude quaternion of the previous moment and the angle increment of a gyroscope of the lander;
and obtaining the inertial position of the current moment by using the inertial position of the previous moment, the inertial speed of the previous moment and the inertial speed of the current moment.
2. The recursive multi-subsample large dynamic inertial navigation method of claim 1, wherein in S3, a rotation quaternion is constructed using the rotation vector of the lander according to euler rotation principle.
3. The recursive multi-subsample large dynamic inertial navigation method according to any one of claims 1 to 2, wherein the angular velocity polynomial is:
ω(tm+τ)＝am+bmτ+cmτ20≤τ≤ΔT
wherein
Figure FDA0002433938010000011
Figure FDA0002433938010000012
Figure FDA0002433938010000013
In the formula, ω is the inertial angular velocity projected under the IMU body coordinate system, Δ T ═ Tm+1-tmFor navigation update period, am、bm、cmAre each [ tm,tm+1]The coefficient to be fitted for the angular velocity in the time interval, τ being [ t ]m,tm+1]Any time of the interval; the gyro of IMU is at [ t ]m-1,tm]The sub-sample of the navigation period output two angle increments is delta theta1And Δ θ2，θ'1And θ'2Is [ t ]m-1,tm]Gyros within a navigation cycleTwo subsamples of (a); a ism-1Is [ t ]m,tm+1]A of the time intervalm。
4. The recursive multi-subsample large dynamic inertial navigation method according to any one of claims 1 to 2, wherein the rotation vector of the lander is:
φm＝αm+βm
in the formula, from tmTime tm+1The rotation vector of the moment is phim；αmIs tmAngular increment of time, βmA cone effect compensation term.
5. The recursive multi-subsample large dynamic inertial navigation method according to any one of claims 1 to 2, wherein the attitude quaternion at the current time is:
Figure FDA0002433938010000021
wherein
Figure FDA0002433938010000022
In the formula,
Figure FDA0002433938010000023
is a quaternion product, qmAnd q ism+1Are each tmAnd tm+1The inertia system at the moment reaches the attitude quaternion of the IMU body coordinate system; from tmTime tm+1The rotation vector of the moment is phim。
6. The recursive multi-subsample large dynamic inertial navigation method according to any one of claims 1 to 2, wherein the inertial velocity at the current time is:
Figure FDA0002433938010000024
wherein
Figure FDA0002433938010000025
Figure FDA0002433938010000026
In the formula, vmAnd vm+1Are each tm,tm+1The inertial velocity at the moment of time is,
Figure FDA0002433938010000031
is tmAttitude transformation matrix from the IMU body coordinate system to the inertial system at time, [ t ]m-1,tm]Is a navigation period, Δ vgVelocity increments due to gravitational acceleration; Δ v1And Δ v2Is [ t ]m,tm+1]The IMU adds the speed increment of two subsamples measured by a meter in the interval, and the gyro of the IMU is in [ t ]m-1,tm]The sub-sample of the navigation period output two angle increments is delta theta1And Δ θ2，amIs [ t ]m,tm+1]Time interval the angular velocity is the coefficient to be fitted.
7. The recursive multi-subsample large dynamic inertial navigation method according to any one of claims 1 to 2, wherein the inertial position of the current time is:
Figure FDA0002433938010000032
in the formula, rm+1Is tm+1Position of the IMU in relation to the central celestial body under the inertial system at the instant rmIs tmPosition of the IMU in relation to the central celestial body under the inertial system at the instant of time vmAnd vm+1Are each tm、tm+1The inertial velocity at a time; Δ T ═ Tm+1-tmFor the navigation update period, [ t ]m-1,tm]Is a navigation cycle.
8. The recursive multi-sample large dynamic inertial navigation method according to any one of claims 1 to 2, wherein S1 to S4 are repeated to continuously obtain the attitude quaternion at the current time, the inertial velocity at the current time, and the inertial position at the current time, so as to complete inertial navigation of the aircraft.
9. The recursive multi-subsample large dynamic inertial navigation method according to any one of claims 1 to 2, wherein the inertial navigation method is applied to a dynamic range of: angular acceleration of no more than 8000 DEG/s2。
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of one of claims 1 to 9.
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CN113720329A (en) * 2021-09-10 2021-11-30 北京控制工程研究所 Large dynamic inertial navigation method based on lever arm effect algebraic constraint

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