Summary of the invention
Technical matters to be solved by this invention is, not enough for prior art, and a kind of Ring Laser Gyroscope SINS performance parameter calibration method is provided, and solves existing scaling method and must use high precision turntable, to place and the higher problem of equipment requirement.
For solving the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of Ring Laser Gyroscope SINS performance parameter calibration method, and the method is:
1) Ring Laser Gyroscope SINS is arranged on mould turnover, mould turnover is placed on to flat board upper, and Ring Laser Gyroscope SINS is aimed to local geographic coordinate system;
2) set up the error model of Ring Laser Gyroscope SINS:
δa
bx=α
x+α
xxa
bx+α
xya
by+α
xza
bz
δa
by=α
y+α
yxa
bx+α
yya
by+α
yza
bz
δa
bz=α
z+α
zxa
bx+α
zya
by+α
zza
bz
δω
bx=β
x+β
xxω
bx+β
xyω
by+β
xzω
bz+(β
xyxa
bx+β
xyya
by+β
xyza
bz)ω
by+(β
xzxa
bx+β
xzya
by+β
xzza
bz)ω
bz
δω
by=β
y+β
yxω
bx+β
yyω
by+β
yzω
bz+(β
yxxa
bx+β
yxya
by+β
yxza
bz)ω
bx+(β
yzxa
bx+β
yzya
by+β
yzza
bz)ω
bz
δω
bz=β
z+β
zxω
bx+β
zyω
by+β
zzω
bz+(β
zxxa
bx+β
zxya
by+β
zxza
bz)ω
bx+(β
zyxa
bx+β
zyya
by+β
zyza
bz)ω
by
Wherein, δ a
bi, δ ω
bifor the projection at Ring Laser Gyroscope SINS coordinate system of accelerometer and gyro error; α
ifor accelerometer bias; α
iifor accelerometer scale factor; α
ijfor accelerometer alignment error; a
bifor: the projection of terrestrial gravitation; β
ifor gyroscopic drift; β
iifor gyro scale factor; β
ijfor gyro misalignment; β
ijkthe gyroscopic drift causing for acceleration; ω
bi---the projection of absolute angle speed in Ring Laser Gyroscope SINS coordinate system; I=x, y, z; J=x, y, z; I ≠ j;
3) utilize following formula to demarcate β
iand β
ii:
Wherein, the angle of pitch that θ is Ring Laser Gyroscope SINS, t is for demarcating the test duration (setting rest position time 2~5min, rotation time≤30s before demarcating);
4) utilize following formula to demarcate α
i, α
ii, α
ij:
When the pitching angle theta of rotary laser strapdown inertial navitation system (SINS):
θ=90°:
θ=180°:
When the roll angle γ of rotary laser strapdown inertial navitation system (SINS):
γ=90°:
γ=180°:
When the ψ of the position angle of rotary laser strapdown inertial navitation system (SINS):
ψ=90°:
ψ=180°:
5) demarcate gyro misalignment:
Utilize following formula to estimate β
zxand β
yx:
Wherein,
Utilize following formula to estimate β
zyand β
xy:
Utilize following formula to estimate β
xzand β
yz:
In described step 3), β
iand β
iithe computation process of calibration formula as follows:
1) simplify the error model of Ring Laser Gyroscope SINS, obtain the simplification error model of following Ring Laser Gyroscope SINS:
E-passage:
N-passage:
Wherein,
for inertial navigation east orientation accelerometer output acceleration, δ V
efor Ring Laser Gyroscope SINS east orientation is measured passage output speed, Φ
nfor Ring Laser Gyroscope SINS north orientation is measured passage output rotational angle,
for Ring Laser Gyroscope SINS north orientation, measure passage output rotational angular velocity, R is the radius of gyration,
for Ring Laser Gyroscope SINS north orientation accelerometer output acceleration, δ V
nfor Ring Laser Gyroscope SINS north orientation is measured passage output speed, Φ
efor Ring Laser Gyroscope SINS east orientation is measured passage output rotational angle,
for Ring Laser Gyroscope SINS east orientation is measured passage output rotational angular velocity, δ a
e, δ a
nfor the accelerometer error projection in local geographic coordinate system, δ ω
e, δ ω
nfor the gyro error projection in local geographic coordinate system; G is acceleration of gravity;
2) ignore in above-mentioned simplification error model
with
, obtain new error model:
Wherein, Φ
e(0), Φ
n(0) be horizontal aligument error, and:
3) determine the direction cosine matrix between Ring Laser Gyroscope SINS coordinate system and local geographic coordinate system
c
11=cosγcosψ+sinθsinγsinψ
c
12=cosθsinψ
c
13=sinγcosψ-sinθcosγsinψ
c
21=-cosγsinψ+sinθsinγcosψ
Wherein, c
22=cos θ cos ψ;
c
23=-sinγsinψ-sinθcosγcosψ
c
31=-cosθsinγ
c
32=sinθ
c
33=cosθcosγ
θ, γ, ψ is respectively the angle of pitch of Ring Laser Gyroscope SINS, roll angle and position angle;
4) rotation mould turnover, guarantees that the time of the navigation mode of Ring Laser Gyroscope SINS work is 2~5 minutes, obtains the absolute angle speed omega of Ring Laser Gyroscope SINS in rotary course
b:
Wherein,
for angular velocity of rotation;
5) suppose that the roll angle γ of Ring Laser Gyroscope SINS and position angle ψ keep motionless, the pitching angle theta of rotary laser strapdown inertial navitation system (SINS), obtains the new direction cosine matrix between Ring Laser Gyroscope SINS coordinate system and local geographic coordinate system
6) according to the error model of Ring Laser Gyroscope SINS and absolute angle speed omega
b, obtain:
7) gyro error is transformed into local geographic coordinate system from Ring Laser Gyroscope SINS coordinate system, obtains:
δ ω
upfor the output of rotation axis to responsive gyro;
for absolute angle speed omega
bprojection in Ring Laser Gyroscope SINS coordinate system;
8) by the formula of the formula substitution step 7) of step 6), obtain gyro error being projected as in local geographic coordinate system:
δ ω
efor rotating output, the δ ω of rear east orientation gyro
nfor rotating the output of rear north gyro;
9) the formula integration to step 8), obtains:
Compared with prior art, the beneficial effect that the present invention has is: the calibration facility that the present invention adopts is marble flat board and turnover bracket (also available low precision turntable), characteristic according to Laser strapdown inertial navigation, adopt the output speed of Laser strapdown inertial navigation under navigation mode as observed quantity, a large amount of experimental results show that method of the present invention can be successfully to Laser strapdown inertial navigation demarcate, reduced calibration facility cost and to demarcating the restriction of test site.
Embodiment
The error model of being used to group is as follows:
δa
bx=α
x+α
xxa
bx+α
xya
by+α
xza
bz
δa
by=α
y+α
yxa
bx+α
yya
by+α
yza
bz
δa
bz=α
z+α
zxa
bx+α
zya
by+α
zza
bz
δω
bx=β
x+β
xxω
bx+β
xyω
by+β
xzω
bz+(β
xyxa
bx+β
xyya
by+β
xyza
bz)ω
by+(β
xzxa
bx+β
xzya
by+β
xzza
bz)ω
bz
δω
by=β
y+β
yxω
bx+β
yyω
by+β
yzω
bz+(β
yxxa
bx+β
yxya
by+β
yxza
bz)ω
bx+ (1)(β
yzxa
bx+β
yzya
by+β
yzza
bz)ω
bz
δω
bz=β
z+β
zxω
bx+β
zyω
by+β
zzω
bz+(β
zxxa
bx+β
zxya
by+β
zxza
bz)ω
bx+(β
zyxa
bx+β
zyya
by+β
zyza
bz)ω
by
In formula (1): δ a
bi, δ ω
bi, (i=x, y, z)---accelerometer and gyro error are in the projection of carrier system; α
i: accelerometer bias; α
ii: accelerometer scale factor; α
ij: accelerometer alignment error (i ≠ j); a
bi: the projection of certain force; β
i: gyroscopic drift; β
ii: gyro scale factor; β
ij: gyro misalignment (i ≠ j); β
ijk: the gyroscopic drift that acceleration causes (deflection error); ω
bi: the projection of absolute angle speed in carrier coordinate system.
In demarcating test, generally do not consider gyro deflection error.The object of demarcating is exactly to determine above parameter.
In order to study this scaling method, need to provide the error model that Laser strapdown inertial navigation is simplified.Single channel Laser strapdown ins error model has following form:
E-passage:
N-passage:
δ a wherein
e, δ a
n, δ ω
e, δ ω
nfor the accelerometer in local geographic coordinate system and gyro error projection.
Due to what adopt, be the Laser strapdown ins error model of simplifying, the time that therefore Laser strapdown inertial navigation is operated in navigation mode after each rotation is 2~5 minutes.
Ignore in error model
with
, can again obtain error model as follows:
Φ wherein
e(0), Φ
n(0) be horizontal aligument error, and obtain according to equation (2) and error model (1):
Direction cosine matrix between carrier (being Ring Laser Gyroscope SINS) coordinate system and local geographic coordinate system can be write as following form by pitching, roll and position angle:
Wherein:
c
11=cosγcosψ+sinθsinγsinψ
c
12=cosθsinψ
c
13=sinγcosψ-sinθcosγsinψ
c
21=-cosγsinψ+sinθsinγcosψ
c
22=cosθcosψ
c
23=-sinγsinψ-sinθcosγcosψ
c
31=-cosθsinγ
c
32=sinθ
c
33=cosθcosγ
θ, γ, ψ is respectively the pitching of carrier, roll and position angle.
This scaling method comprises the specific upset order of Laser strapdown inertial navigation different rotation angle under navigation mode.Each is after twice upset, and Laser strapdown inertial navigation need to change to guarantee the navigation time (otherwise error model (2) is by invalid) of navigation mode.
The Laser strapdown inertial navigation of take rotation θ angle is example, and under above-mentioned rotation, navigation error model can be with formal construction below.In rotary course, the absolute angle speed of carrier system has following form:
for angular velocity of rotation.
In equation above with respect to
the projection of big or small earth autobiography angular velocity be left in the basket, consider that carrier coordinate system is with respect to the initial orientation of local geographic coordinate system, direction cosine matrix can obtain at hypothesis ψ, form under γ is enough little, there is no need to require in demarcating for the first time, each axle of carrier strictly to be aimed at, but require carrier coordinate system with respect to local geographic coordinate system initial orientation rough alignment (1-3 °).
Under above-mentioned hypothesis, the transition matrix between carrier and local geographic coordinate system has following form:
With gyroscope error model (1) and carrier angular velocity equation (5), can obtain:
Again gyro error is tied to the conversion of local Department of Geography from carrier as follows:
Bring equation (6) into equation (7), gyro error is projected as local geographic coordinate system:
Above formula is carried out to integration, obtains:
Accelerometer error is adopted to similar method, and in fact, certain force is projected as carrier coordinate system:
The projection form of accelerometer error in carrier coordinate system can be described as:
Acceleration error is projected as local geographic coordinate system:
Bring formula (10) into (11), can obtain:
Aggregative formula (2), (3), (8), (9), (12), velocity survey model can be described as:
When θ=90 °, above-mentioned equation can be changed into:
When θ=180 °
Other rotation angle γ, the velocity survey equation under ψ, also can calculate as stated above.
Rotation γ angle obtains velocity error and measures:
When γ=90 °, above-mentioned equation becomes:
When γ=180 °,
Rotation ψ angular measurement model is:
When ψ=90 °
When ψ=180 °
Gyro misalignment calibration process is as follows:
Suppose that all calibrating parameters, except gyro misalignment, all have demarcated out and compensated, program below can be used for estimating β
ij.
The 1st step rotation θ=90 °
Measurement model:
The 2nd step rotation θ=180 °
Measurement model:
The 3rd step is estimated β
zxand β
yx
The 4th step rotation γ=90 °
Measurement model:
The 5th step rotation γ=180 °
Measurement model:
The 6th step is estimated β
zyand β
xy
The 7th step rotation ψ=180 °
Measurement model:
The 8th step is estimated β
zyand β
xy
Here (15) have been utilized, (16), (18), the measurement model equation that (19) are set up.
What it is emphasized that the equation of definition only describes is the error in rotary course, and total velocity error model comprises:
δV
t=δV
I+δV
II (20)
δ V
i---the velocity error in rotary course, as (13), (14);
δ V
iI---the cumulative velocity error (2-3min) of measurement after rotary course.
Second portion in equation (20) is left in the basket with respect to first, so calibration algorithm utilization is equation (13) and (14).
Scaling method step of the present invention is summarized as follows:
inertial navigation system is arranged on mould turnover and is placed in dull and stereotyped upper (or on low precision turntable), and the local geographic coordinate system of rough alignment;
laser strapdown inertial navigation enters alignment pattern, and after aligning finishes, system enters navigation mode;
system casing rotates different angle (once or twice) in order, and preserves the output speed (2-5min) of Laser strapdown inertial navigation;
system exits (should refer to navigation mode) and gets back to initial position;
said procedure rotates different angles repeatedly to be carried out, and obtains enough measurements export to calibrate each parameter with this;
the velocity survey model of each position is set up, and the speed of storage is carried out to level and smooth (in the short time, speed should be straight line, and its differential should be normal value) in advance;
utilize the speed output of level and smooth mistake and the parameter that measurement model estimates accelerometer and gyro;
estimation routine can adopt traditional least square or Kalman filtering algorithm.
Traditional turntable speed is added to the scaling method of position and this scaling method and respectively same set of Laser strapdown is used to group and demarcates, calibration result is as table 1:
Two kinds of mode comparing results of table 1
From two groups of calibration results, can find out, two kinds of differences of demarcating mode meet index request, prove that scaling method of the present invention is feasible.