CN1908584A  Method for determining initial status of strapdown inertial navigation system  Google Patents
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Abstract
Description
Technical field
The present invention relates to definite method of a kind of strapdown inertial navigation system (SINS) initial attitude, can be used for various in the initial attitude of highprecision strapdown inertial navigation system determine, be particularly suitable for not having indexing mechanism when airborne SINS installs, or the indexing mechanism precision is not high, the corner condition of limited.
Background technology
The ultimate principle of strapdown inertial navigation system (SINS) is the mechanics law according to the relative inertness space of newton's proposition, utilize the line motion and the angular motion parameter in gyroscope, accelerometer measures carrier relative inertness space, under given motion starting condition, carry out integral operation by computing machine, position, speed and attitude information are provided continuously, in real time.SINS relies on its own inertial sensitive element fully, do not rely on any external information and measure navigational parameter, therefore, it has good concealment, be not subjected to the weather condition restriction, advantage such as no signal is lost, and is interferencefree, be a kind of complete autonomous type, roundtheclock navigational system, be widely used in fields such as Aeronautics and Astronautics, navigation.According to the ultimate principle of SINS, SINS must obtain initial information before navigator fix resolves, comprise initial position, speed and attitude.Initial position and the velocity information of SINS obtain easily than initial attitude, and the precision after initial attitude is determined is exactly the initial precision of SINS when entering the navigation duty.Carry out fast accurate initial attitude when therefore, SINS starts working and determine it is a crucial step.
Existing strapdown inertial navitation system (SINS) initial attitude is determined to be divided into coarse alignment and two stages of fine alignment.Coarse alignment stage is exactly under quiet pedestal condition, with the direct introducing computing machine of the gyroscope of (fixedly two positions or two positions arbitrarily) on single position or two positions and accelerometer output, calculates the initial attitude of carrier.When using the method, usually ignore the error and the external interference factor of gyroscope and accelerometer, yet these factors can cause error, so the initial attitude computational accuracy is not high.Especially, when the gyroscope on adopting fixing two positions and the output of accelerometer are calculated, require SINS around Z axle Rotate 180 degree or 90 degree, this just need be installed in SINS on the indexing mechanism, utilize indexing mechanism to realize the rotation of 180 degree or 90 degree, extremely inconvenient when engineering is used, and also the precision of indexing mechanism is not high, rotational angle also can't accurately be measured, and has reduced the precision that initial attitude is determined.Because the restriction of SINS installation site in the concrete engineering, also exist rotational angle can't satisfy the situation that 180 degree or 90 degree require, at this moment, existing fixed two positions initial attitude determines that method can't use.In addition, when gyroscope on utilizing any two positions and accelerometer output, need to calculate arcsin function, the error of gyroscope and accelerometer itself and measuring error etc. cause the result of calculation instability easily, the imaginary number phenomenon occurs, therefore often need carry out repeatedly the collection and the calculating of gyroscope and accelerometer output on the two positions arbitrarily, result of calculation is selected, after averaging, as the initial attitude of carrier.So, the time that initial attitude is determined will be multiplied, and the precision that initial attitude calculates also can't be guaranteed.
The fine alignment stage is to carry out on the basis of coarse alignment, utilizes the statespace method of modern control theory, and the data of gyroscope and accelerometer output are handled.When the data of single position are handled, the considerable degree of orientation misalignment is poor, speed of convergence is slower, required time is longer, and gyroscope and accelerometer error are unobservable, therefore, can't estimate preferably, do not reach the purpose that improves the initial attitude precision, can not when initial attitude calculates, realize demarcation gyroscope and accelerometer.When the data of fixing two positions are handled, as above to narrate, existing fixed two positions initial attitude determines that there is the restriction of the anglec of rotation in method, and higher to the indexing mechanism accuracy requirement, often can not use in the concrete engineering.
Summary of the invention
Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provide a kind of accurately, initial status of strapdown inertial navigation system is determined method easily.
Technical solution of the present invention is: a kind of initial status of strapdown inertial navigation system is determined method,
Concrete steps are as follows:
(1) the SINS preheating is prepared, and concrete setup time is according to different systems and difference;
(2) SINS ready after, keep SINS in initial position (being called primary importance) transfixion, gather gyroscope output and accelerometer and export;
(3) utilize accelerometer output and the relation of acceleration of gravity and the relation of gyroscope output and earth rotation angular speed, calculate the course angle of primary importance _{1}, pitching angle theta _{1}With roll angle γ _{1}
(4) need not indexing mechanism, SINS is rotated to any one position (being called the second place) from primary importance around the space threedimensional arbitrary axis, keep SINS, gather gyroscope output and accelerometer output in second place transfixion by any means;
(5) adopt Kalman Filter Technology, with _{1}, θ _{1}And γ _{1}As initial parameter, the data of gyroscope and accelerometer output on two positions are handled.Because the change of SINS position, changed the system matrix in the SINS error model, thereby the observability of SINS system improves, filter effect is improved, and the error angle that calculates when better estimating the second place between geographic coordinate system n ' and the true geographic coordinate system n (abbreviates misalignment φ as _{x}, φ _{y}And φ _{z}) and gyroscope constant value drift, accelerometer often be worth biasing;
(6) utilize the φ that estimates _{x}, φ _{y}And φ _{z}Calculate the transition matrix C between true geographic coordinate system n and the calculating geographic coordinate system n ' _{N '} ^{n}According to the angle increment or the angular velocity information of gyroscope output, adopt the hypercomplex number method, calculate the transition matrix C between carrier coordinate system b and the calculating geographic coordinate system n ' _{b} ^{N '}By C _{N '} ^{n}And C _{b} ^{N '}, calculate the transition matrix C between carrier coordinate system b and the true geographic coordinate system n _{b} ^{n}, again by C _{b} ^{n}Calculate the course angle of the second place _{2}, pitching angle theta _{2}With roll angle γ _{2}, with its initial attitude as SINS.
Principle of the present invention is: when SINS kept transfixion in some positions, accelerometer output and acceleration of gravity and gyroscope output had following relation with the earth rotation angular speed:
Wherein, f
_{X1}, f
_{Y1}And f
_{Z1}And ω
_{X1}, ω
_{Y1}And ω
_{Z1}The respectively specific force and the angular speed of Xaxis, Yaxis and the output of Z axle of SINS on the position for this reason; G is an acceleration of gravity; ω
_{Ie}Be the earth rotation angular speed, its in east, north, old name for the Arabian countries in the Middle East make progress be projected as Ω=[0 ω
_{Ie}CosL ω
_{Ie}SinL]; L is a local latitude; C
_{n} ^{b}For navigation coordinate is tied to the transition matrix of carrier coordinate system,
C _{n} ^{b}Can be expressed as this position course angle _{1}, pitching angle theta _{1}With roll angle γ _{1}Expression formula, utilize (1) formula and (2) formula can calculate the of this position _{1}, β _{1}And γ _{1}Computing formula is as follows:
By (1), (2) Shi Kede:
C _{11}＝C _{22}C _{33}C _{23}C _{32}
C _{21}＝C _{12}C _{33}+C _{13}C _{32}
C _{31}＝C _{12}C _{23}C _{13}C _{22}
Course angle _{1}, pitching angle theta _{1}With roll angle γ _{1}The main value computing formula be:
If course angle _{1}, pitching angle theta _{1}With roll angle γ _{1}Span be defined as [0,2 π], [π ,+π], so _{1}, θ _{1}And γ _{1}True value can determine as follows.
θ _{1}=θ _{1 is main}(5)
By the definite of (5) formula _{1}, θ _{1}And γ _{1}Be SINS at this locational course angle, the angle of pitch and roll angle.
Owing to do not consider the measuring error of accelerometer biasing, gyroscopic drift and accelerometer and gyroscope output information in (1) formula and (2) formula, the course angle that tries to achieve _{1}, pitching angle theta _{1}With roll angle γ _{1}Can not the accurate description carrier coordinate system and local geographic coordinate system between true angular relationship.Therefore, should further utilize modern estimation theory that the initial attitude misalignment is estimated from stochastic error and random disturbance on this basis.
Utilize Kalman Filter Technology, with _{1}, θ _{1}And γ _{1}As initial parameter, can estimate the error angle that calculates between geographic coordinate system n ' and the true geographic coordinate system n, proofread and correct C _{b} ^{N '}After, can obtain initial attitude more accurately.But, when Kalman filtering is handled the accelerometer of single position and gyroscope output, the incomplete may observe of system, wherein, two accelerometers and a gyrostatic error are unobservable, so estimation effect is poor, do not reach the purpose that improves the initial attitude precision.The present invention is by rotating to any one position from primary importance around the space threedimensional arbitrary axis with SINS, promptly change the position of SINS, change the system matrix in the SINS error model, thereby improve the observability of SINS system, improve the Kalman filtering effect, estimate the error of misalignment and gyroscope, accelerometer better.The misalignment that utilization estimates is to transition matrix C _{b} ^{N '}Proofread and correct, obtain course angle, the angle of pitch and roll angle more accurately.
The present invention's advantage compared with prior art is:
(1) the present invention broken that conventional fixed two positions initial attitude calculates need be by indexing mechanism with the constraints of SINS around Z axle Rotate 180 degree or 90 degree, but need not to pass through indexing mechanism, SINS is rotated to the optional position around arbitrary axis, is a kind of any twoposition initial attitude computing method of space threedimensional.Avoided because of the indexing mechanism precision is not high, the reduction of the fixedly two positions initial attitude computational accuracy that causes has promptly improved the precision that initial attitude calculates.In addition, SINS being rotated to the optional position around arbitrary axis also greatly facilitates in actual application in engineering.
(2) the present invention utilizes the data of gyroscope and accelerometer output on two positions, improve the observability of SINS system, improve the filter effect of Kalman filter, estimate misalignment and gyroscope constant value drift better, accelerometer often is worth biasing, after the misalignment that utilization estimates is proofreaied and correct attitude matrix, obtain course angle, the angle of pitch and roll angle more accurately.
(3) the present invention can finish to survey when initial attitude calculates and float and the calibration task, has not only improved the precision that system's initial attitude calculates, and calibration precision also is improved, and recompenses at the SINS navigational state, can improve navigation and positioning accuracy effectively.
Description of drawings
Fig. 1 determines the process flow diagram of method for initial attitude of the present invention;
Fig. 2 is the synoptic diagram of course angle , pitching angle theta and roll angle γ, Ox among the figure _{n}y _{n}z _{n}Be navigation coordinate system, i.e. the geographical coordinate system in sky, northeast, Ox _{b}y _{b}z _{b}Be carrier coordinate system.Wherein, Fig. 2 a represents that from navigation coordinate be Ox _{n}y _{n}z _{n}Be rotated counterclockwise and carrier coordinate system Ox around the zn axle _{b}y _{b}z _{b}Overlap, is course angle; Fig. 2 b represents that from navigation coordinate be Ox _{n}y _{n}z _{n}Around x _{n}Axle is rotated counterclockwise θ and carrier coordinate system Ox _{b}y _{b}z _{b}Overlap, θ is the angle of pitch; Fig. 2 c represents that from navigation coordinate be Ox _{n}y _{n}z _{n}Around y _{n}Axle is rotated counterclockwise γ and carrier coordinate system Ox _{b}y _{b}z _{b}Overlap, γ is roll angle.
Embodiment
As shown in Figure 1, specific implementation method of the present invention is as follows:
1, the preparation of strapdown inertial navigation system
After the SINS start, enter standby condition.
2, primary importance data acquisition
SINS is ready, keeps SINS in initial position (being called primary importance) transfixion, gathers gyroscope output in 5 minutes and accelerometer output, if but the lower proper extension of the precision of SINS is adopted several times.
3, primary importance Attitude Calculation
Navigation coordinate system is taken as the geographical coordinate system in sky, northeast, the course angle of primary importance place _{1}, pitching angle theta _{1}With roll angle γ _{1}Definition shown in Fig. 2 a, Fig. 2 b and Fig. 2 c.
Accelerometer output and acceleration of gravity and gyroscope output have following relation with the earth rotation angular speed:
In the formula, f _{X1}, f _{Y1}And f _{Z1}And ω _{X1}, ω _{Y1}And ω _{Z1}Be respectively the specific force and the angular speed of Xaxis, Yaxis and the output of Z axle of SINS on first position; G is an acceleration of gravity; ω _{Ie}Be the earth rotation angular speed, its in east, north, old name for the Arabian countries in the Middle East make progress be projected as Ω=[0 ω _{Ie}CosL ω _{Ie}SinL], L represents local latitude; C _{n} ^{b}For navigation is tied to the transition matrix that carrier is, can be written as:
By (6), (7) Shi Kede:
C _{11}＝C _{22}C _{33}C _{23}C _{32}
C _{21}＝C _{12}C _{33}+C _{13}C _{32}
C _{31}＝C _{12}C _{23}C _{13}C _{22}
Course angle _{1}, pitching angle theta _{1}With roll angle γ _{1}The main value computing formula be:
θ _{1 is main}=arcsin (C _{23}) (9)
If course angle _{1}, pitching angle theta _{1}With roll angle γ _{1}Span be defined as [0,2 π], [π ,+π], so _{1}, θ _{1}And γ _{1}True value can determine as follows.
θ _{1}=θ _{1 is main}(10)
By the definite of (10) formula _{1}, θ _{1}And γ _{1}Be course angle, the angle of pitch and the roll angle of SINS on primary importance.
4, second place data acquisition
By any means SINS is rotated to any one position (being called the second place) from initial position around the space threedimensional arbitrary axis, keep SINS, gather gyroscope output in 5 minutes and accelerometer output in second place transfixion.
5, the data of two positions are carried out Filtering Processing
With _{1}, θ _{1}And γ _{1}As initial parameter, utilize Kalman Filter Technology, the data of gyroscope and accelerometer output on two positions are handled, accurately estimate misalignment φ _{x}, φ _{y}And φ _{z}(under the geographical coordinate system in sky, northeast is φ _{E}, φ _{N}And φ _{U}) and gyroscope constant value drift, accelerometer often be worth biasing.
(1) the SINS initial attitude is determined the foundation of error model
Navigation coordinate system is taken as the geographical coordinate system in sky, northeast, and position and vertical speed error are omitted, and accelerometer and gyrostatic error are considered as setovering at random and add whitenoise process, and this moment, the error model of SINS was:
In the formula, subscript E, N, U represent east, north, sky respectively.Earth rotation angular speed ω _{Ie}In east, north, old name for the Arabian countries in the Middle East make progress be projected as Ω=[0 ω _{Ie}CosL ω _{Ie}SinL]=[0 Ω _{N}Ω _{U}], L represents local latitude; Subscript x, y, z are carrier coordinate system; T _{Ij}(i=1,2,3; J=1,2,3) be attitude matrix C _{b} ^{n}In element,
(2) the SINS initial attitude is determined the foundation of Kalman filter model
For strapdown inertial navitation system (SINS), consider the random deviation of Gyroscope Random Drift Error and accelerometer, equation (11) is modified to following form:
In the formula, W (t) is N (O, white Gaussian noise Q); State variable X
_{a}=[δ V
_{E}δ V
_{N}φ
_{E}φ
_{N}φ
_{U}]
^{T}, X
_{b}=[
_{x}
_{y}ε
_{x}ε
_{y}ε
_{z}]
^{T}The random noise state vector
(12) formula is determined the system equation of Kalman filter model for the strapdown inertial navitation system (SINS) initial attitude.For the application card Thalmann filter carries out the optimal estimation of state vector, also need set up the systematic observation equation.Choosing two horizontal velocity errors is observed quantity, and the systematic observation equation of foundation is
Wherein, η (t) is the systematic observation noise vector, is N (O, white Gaussian noise process R).
(3) foundation of Kalman Filtering for Discrete model
According to said system equation and observation equation, it is as follows to set up the Kalman Filtering for Discrete equation.
Filtering equations:
Gain equation:
Prediction error variance equation:
Filtering error variance equation:
P _{k}＝[IK _{k}H _{k}]P _{k，k1} (17)
In the formula, Φ _{K, k1}Be the statetransition matrix (system matrix) of discretize, Q, R are respectively the covariance matrix of system noise and observation noise.
(4) filtering starting condition
X(0)＝0 _{10×1}；
The value of the corresponding medium accuracy SINS of P (0), Q and R is as follows:
P(0)＝diag{(0.3m/s) ^{2}，(0.3m/s) ^{2}，(30′) ^{2}，(10″) ^{2}，(10″) ^{2}，
(100μg) ^{2}，(100μg) ^{2}，(0.1°) ^{2}，(0.1°) ^{2}，(0.1°) ^{2}}；
Q＝diag{(100μg) ^{2}，(100μg) ^{2}，(0.1°) ^{2}，(0.1°) ^{2}，(0.1°) ^{2}，0，0，0，0，0}；
R＝diag{(0.1m/s) ^{2}，(0.1m/s) ^{2}}。
6, computing gyroscope Random Constant Drift and accelerometer value biasing often at random
The that wave filter estimates _{x}, _{y}Be accelerometer value biasing often at random, ε _{x}, ε _{y}, ε _{z}Be the gyroscope Random Constant Drift.
7, the transition matrix C between calculating carrier coordinate system b and the calculating geographic coordinate system n ' _{b} ^{N '}
Can utilize the angle increment or the angular velocity information of gyroscope output, adopt the hypercomplex number method to calculate C _{b} ^{N '}, calculation procedure is as follows:
(1) utilizes course angle _{1}, pitching angle theta _{1}With roll angle γ _{1}Attitude during first position of initialization is calculated the initial conversion Matrix C _{b} ^{N '}With hypercomplex number q, computing formula is as follows:
Order
Then have:
(2) upgrade hypercomplex number q _{0}, q _{1}, q _{2}, q _{3}With transition matrix C _{b} ^{N '}
Wherein,
Transition matrix C _{b} ^{N '}More new formula as follows:
8, calculate course angle _{2}, pitching angle theta _{2}With roll angle γ _{2}
The φ that utilizes Kalman Filter Estimation to go out _{E}, φ _{N}, φ _{U}Calculate the transition matrix C between true geographic coordinate system n and the calculating geographic coordinate system n ' _{N '} ^{n}According to C _{N '} ^{n}(20) C that calculates of formula _{b} ^{N '}, calculate the transition matrix C between carrier coordinate system b and the true geographic coordinate system n _{b} ^{n}, again by C _{b} ^{n}Calculate the course angle of the second place _{2}, pitching angle theta _{2}With roll angle γ _{2}, with its initial attitude as SINS.Concrete calculation procedure is as follows:
(1) the transition matrix C between true geographic coordinate system n of calculating and the calculating geographic coordinate system n ' _{n} ^{N '}
(2) the transition matrix C between calculating carrier coordinate system b and the true geographic coordinate system n _{b} ^{n}
(3) calculate course angle _{2}, pitching angle theta _{2}With roll angle γ _{2}
Course angle _{2}, pitching angle theta _{2}With roll angle γ _{2}Definition shown in Fig. 2 a, Fig. 2 b and Fig. 2 c.
The C that (22) formula is calculated _{b} ^{n}Be designated as
Again because
Therefore, by (23) formula and (24) formula, can determine course angle _{2}, pitching angle theta _{2}With roll angle γ _{2}Main value, promptly
If course angle _{2}, pitching angle theta _{2}With roll angle γ _{2}Span be defined as respectively [0,2 π], [π ,+π].So, _{2}, θ _{2}And γ _{2}True value can determine by following formula:
θ _{2}=θ _{2 is main}(26)
By the definite of (26) formula _{2}, θ _{2}And γ _{2}Be course angle, the angle of pitch and the roll angle of SINS on the second place, it is entered the initial attitude of navigation duty as SINS.
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CN110006456A (en) *  20190424  20190712  北京星网宇达科技股份有限公司  A kind of detection vehicle alignment methods, device and equipment 
CN110095115A (en) *  20190604  20190806  中国科学院合肥物质科学研究院  A kind of carrier navigation attitude measurement method updated based on Geomagnetism Information 
CN110095115B (en) *  20190604  20201225  中国科学院合肥物质科学研究院  Carrier attitude and heading measurement method based on geomagnetic information update 
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