CN102221366A - Quick accurate alignment method based on fuzzy mapping earth spin velocity - Google Patents

Quick accurate alignment method based on fuzzy mapping earth spin velocity Download PDF

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CN102221366A
CN102221366A CN 201110058569 CN201110058569A CN102221366A CN 102221366 A CN102221366 A CN 102221366A CN 201110058569 CN201110058569 CN 201110058569 CN 201110058569 A CN201110058569 A CN 201110058569A CN 102221366 A CN102221366 A CN 102221366A
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alignment
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angular velocity
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CN102221366B (en
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戴晓强
赵琳
史震
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Harbin Engineering University
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Abstract

The invention aims to provide a quick accurate alignment method based on a fuzzy mapping earth spin velocity. The method comprises the following steps of: determining an initial position parameter of a carrier; acquiring outputs of a speedometer and a gyroscope; determining a rough initial attitude matrix; performing Kallman filtering single-step iteration computation according to a computed earth spin velocity; determining accurate alignment time; judging whether accurate alignment is over; if so, adopting a misalignment angle estimated with a Kallman filtering technology and correcting a strapdown attitude matrix of a system by using the misalignment angle to finish accurate initial alignment; and otherwise, returning to correction until accurate alignment is over, adopting the misalignment angle estimated with the Kallman filtering technology and correcting a strapdown attitude matrix of the system by using a misalignment angle to finish accurate initial alignment. In the method, any external observation equipment does not need to be arranged, and an auxiliary position rotary table does not need to be provided, the engineering is easy to realize, and the rapidness of the accurate alignment of a strapdown inertial navigation system is effectively enhanced.

Description

A kind of based on the fuzzy quick fine alignment method that becomes rotational-angular velocity of the earth
Technical field
What the present invention relates to is a kind of alignment methods of navigation field, specifically is used for the definite method of initial attitude of strap down inertial navigation system.
Background technology
The ultimate principle of strapdown inertial navigation system (Strapdown Inertial Navigation System is called for short SINS) is the mechanics law according to the relative inertness space of newton's proposition, utilize the line motion and the angular motion parameter of accelerometer, gyroscope survey carrier inertial space, under given motion starting condition, carry out integral operation by computing machine, position, speed and attitude information are provided continuously, in real time.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 that initial attitude is determined is exactly the initial precision of SINS when entering the navigation duty.That carries out fast accurate initial attitude when therefore, SINS starts working determines it is a crucial step.
Existing strapdown inertial navitation system (SINS) initial attitude determines to be divided into coarse alignment and two stages of fine alignment.Coarse alignment stage is exactly under quiet pedestal condition, and gyroscope and accelerometer output are directly introduced navigational computer, calculates the initial attitude of carrier.When using the method, usually ignore the sum of errors external interference factor of gyroscope and accelerometer, yet these factors can cause error, so the initial attitude computational accuracy is not high.The fine alignment stage is to carry out on the basis of coarse alignment, utilizes the state-space method of modern control theory, and the data of gyroscope and accelerometer output are handled.Calculate navigation coordinate system and the misalignment that true navigation coordinate is, set up initial attitude matrix accurately.Strapdown inertial navigation system requires the alignment precision height, and the aligning time is short.
Poor with velocity error as the observability and the observability degree of the quiet pedestal fine alignment system of observed quantity, be the major reason of its alignment precision of restriction and rapidity, particularly azimuthal observation degree is low, causes the estimation effect of orientation misalignment very poor.About rapid alignment, the conventional thinking of existing document all is how to improve azimuthal observability degree, as increasing aspect sensor or carrying out multiposition aligning etc.Patent of invention as the patent No.: ZL200510130615.7: a kind of any two-position initial alignment method of strapdown inertial navigation system; Patent of invention as the patent No.: ZL200810064146.7: based on the optic fiber gyroscope strapdown inertial navigation system two-position initial alignment method of filtering; Be in alignment procedures, to utilize position turntable to carry out multiposition to aim at ornamental and the considerable degree that improves system,, but need on position turntable, carry out, limited the engineering application though these methods have not needed the precision positions turntable that is difficult to realize.As the patent No.: 200810019357.9 patent of invention: the quick fine alignment method of strapdown inertial navigation system; Be by increasing the ornamental that Magnetic Sensor and obliquity sensor improve strapdown inertial navitation system (SINS), but the aspect sensor of this method utilization generally all is a geomagnetic sensor, this earth magnetism sensing is easy to receive outside interference, when especially carrier is magnetic conductor, the earth magnetism sensing is difficult to operate as normal, is difficult to actual the use.Therefore in practical engineering application, find and a kind ofly can improve the alignment precision of inertial navigation system and the method for reaction capacity, the performance that improves whole strap-down navigation system is had very important military significance and practical value.
Summary of the invention
The object of the present invention is to provide a kind of that practicality is good, precision is high, the aligning time is short based on the fuzzy quick fine alignment method that becomes rotational-angular velocity of the earth.
The object of the present invention is achieved like this:
The present invention is a kind of to be may further comprise the steps based on the fuzzy quick fine alignment method that becomes rotational-angular velocity of the earth:
(1) determines the initial position parameters of carrier by external unit, and it is bound to navigational computer;
(2) the SINS preheating is prepared, and gathers the output of accelerometer and gyroscope;
(3) utilize accelerometer and the gyroscope output that collects, carry out coarse alignment, determine rough initial attitude matrix by the analytical method of standard;
(4) coarse alignment enters the fine alignment stage after finishing, and rotational-angular velocity of the earth is calculated in order
Figure BDA0000049809080000022
Represent true earth rotation speed;
(5) output and the coarse alignment according to accelerometer obtains initial attitude, and calculates rotational-angular velocity of the earth and carry out the calculating of Kalman filtering single-step iteration;
(6) determine fine alignment time t f, make t fValue greater than the convergence time of filtering and the maximum time that can allow less than inertial navigation system.
(7) judge fine alignment t fWhether timing finishes, if fine alignment has finished then to make the calculating rotational-angular velocity of the earth
Figure BDA0000049809080000023
The misalignment that adopts Kalman Filter Technology to estimate, and come the strapdown attitude matrix of update the system with misalignment, finish accurate initial alignment; If fine alignment does not finish, then according to Kalman Filter Estimation error variance P kCalculate two error distances
Figure BDA0000049809080000024
With
Figure BDA0000049809080000025
Wherein
Figure BDA0000049809080000027
Figure BDA0000049809080000028
For east orientation error angle variance of estimaion error,
Figure BDA0000049809080000029
For azimuthal error angle variance of estimaion error,
Figure BDA0000049809080000031
Be azimuthal expectation steady state error, the method by fuzzy reasoning estimates the calculating rotational-angular velocity of the earth
Figure BDA0000049809080000032
Return step (5) and carry out Kalman's iterative computation and finish until fine alignment, rotational-angular velocity of the earth is calculated in order
Figure BDA0000049809080000033
The misalignment that adopts Kalman Filter Technology to estimate, and come the strapdown attitude matrix of update the system with misalignment, finish accurate initial alignment.
Advantage of the present invention is: do not need to increase any External Observation equipment, only need the fine alignment algorithm of strapdown inertial navigation system is upgraded; Need not to provide the aided location turntable, Project Realization is easy; Effectively improved the rapidity of the fine alignment of strapdown inertial navigation system.
Description of drawings
Fig. 1 is the input membership function of fuzzy reasoning;
Fig. 2 is the output membership function of fuzzy reasoning;
Fig. 3 is a strapdown inertial navigation system fine alignment structural drawing;
Fig. 4 is a process flow diagram of the present invention;
The east orientation error angle evaluated error correlation curve of inertial navigation when Fig. 5 is different rotational-angular velocity of the earth;
The north orientation error angle evaluated error correlation curve of inertial navigation when Fig. 6 is different rotational-angular velocity of the earth;
The orientation east orientation error angle evaluated error correlation curve of inertial navigation when Fig. 7 is different rotational-angular velocity of the earth;
Fig. 8 is the east orientation error angle evaluated error correlation curve of fuzzy reasoning inertial navigation when estimating the rotational-angular velocity of the earth that with different rotational-angular velocity of the earth;
Fig. 9 is the north orientation error angle evaluated error correlation curve of fuzzy reasoning inertial navigation when estimating the rotational-angular velocity of the earth that with different rotational-angular velocity of the earth;
Figure 10 is the azimuthal error angle evaluated error correlation curve of fuzzy reasoning inertial navigation when estimating the rotational-angular velocity of the earth that with different rotational-angular velocity of the earth.
Embodiment
For example the present invention is done description in more detail below in conjunction with accompanying drawing:
Embodiment 1:
In conjunction with Fig. 1～10, the present invention includes following steps:
(1) determines the initial position parameters of carrier by external unit, and it is bound to navigational computer;
(2) the SINS preheating is prepared, and gathers the output of accelerometer and gyroscope;
(3) utilize accelerometer and the gyroscope output that collects, carry out coarse alignment, determine rough initial attitude matrix by the analytical method of standard;
(4) coarse alignment enters the fine alignment stage after finishing, and rotational-angular velocity of the earth is calculated in order
Figure BDA0000049809080000041
Figure BDA0000049809080000042
Represent true earth rotation speed;
(5) output and the coarse alignment according to accelerometer obtains initial attitude, and calculates rotational-angular velocity of the earth and carry out the calculating of Kalman filtering single-step iteration;
(6) determine fine alignment time t f, make t fValue greater than the convergence time of filtering and the maximum time that can allow less than inertial navigation system.
(7) judge fine alignment t fWhether timing finishes, if fine alignment has finished then to make the calculating rotational-angular velocity of the earth
Figure BDA0000049809080000043
The misalignment that adopts Kalman Filter Technology to estimate, and come the strapdown attitude matrix of update the system with misalignment, finish accurate initial alignment; If fine alignment does not finish, then according to Kalman Filter Estimation error variance P kCalculate two error distances
Figure BDA0000049809080000044
With
Figure BDA0000049809080000045
Wherein
Figure BDA0000049809080000046
Figure BDA0000049809080000047
Figure BDA0000049809080000048
For east orientation error angle variance of estimaion error,
Figure BDA0000049809080000049
For azimuthal error angle variance of estimaion error,
Figure BDA00000498090800000410
Be azimuthal expectation steady state error, the method by fuzzy reasoning estimates the calculating rotational-angular velocity of the earth
Figure BDA00000498090800000411
Return step (5) and carry out Kalman's iterative computation and finish until fine alignment, rotational-angular velocity of the earth is calculated in order
Figure BDA00000498090800000412
The misalignment that adopts Kalman Filter Technology to estimate, and come the strapdown attitude matrix of update the system with misalignment, finish accurate initial alignment.
The present invention also comprises following feature:
1, system state equation of using in the step 5 and measurement equation
Set up the state equation and the observation equation of fine alignment system
In day coordinate system, obviously have northeastward
Figure BDA00000498090800000413
Wherein
Figure BDA00000498090800000414
Represent true earth rotation speed,
Figure BDA00000498090800000415
The latitude that expression is local,
Figure BDA00000498090800000416
In order to study the initial alignment under the quiet pedestal of strap down inertial navigation system, consider the random deviation of Gyro Random drift error and accelerometer, ignored site error and vertical speed error, according to the inertial error model of revising BaR-iTzhachk and Bermant, the dynamic equation that obtains system is:
Figure BDA00000498090800000418
Figure BDA0000049809080000051
In formula (1), (2), X (t) is the state vector of system, and Z (t) is the observation vector of system; A (t) is the system state transition matrix, and H (t) is the observing matrix of system; W (t), V (t) are respectively the process noise vector sum observation noise vector of system, and its average all is zero white Gaussian noise.
The state vector of system is:
Figure BDA0000049809080000052
The noise vector of system is:
Figure BDA0000049809080000053
In formula (3), (4), δ v E, δ v NThe velocity error of expression system east orientation and north orientation, φ E, φ N, φ DEast orientation, north orientation and the orientation misalignment of expression mathematical platform and navigation platform, O x, O yThe error of the accelerometer of expression x axle and y axle, ε x, ε y, ε zGyrostatic error on the expression xyz axle,
Figure BDA0000049809080000054
The white noise of the velocity error of expression system east orientation and north orientation,
Figure BDA0000049809080000055
The white noise of expression east orientation, north orientation and orientation misalignment.
The state-transition matrix of system is:
Figure BDA0000049809080000056
The observation vector of system is:
The observation noise vector of system is:
Figure BDA0000049809080000061
Formula (5) C IjAttitude matrix for the relative navigation coordinate of carrier coordinate system system
Figure BDA0000049809080000062
The capable and j column element of i, g is local terrestrial gravitation angular velocity.
2, the relation between coarse alignment and the fine alignment
The accuracy of carrying out the attitude matrix that coarse alignment calculates by step 3 is lower, that is to say that the navigation coordinate that actual navigation coordinate system and coarse alignment calculate is not overlap, and has a little deviation, and its cosine matrix is
Figure BDA0000049809080000063
We define through the attitude matrix behind the coarse alignment
Figure BDA0000049809080000064
The direction cosine matrix of so accurate carrier coordinate system and navigation coordinate system is:
Figure BDA0000049809080000065
The middle p of formula (8) represents the mathematical platform behind the coarse alignment.
Coarse alignment has obtained a rough attitude matrix
Figure BDA0000049809080000066
That is to say, if obtain this moment mathematical platform and actual navigation coordinate the cosine matrix of deviation
Figure BDA0000049809080000067
Just can obtain the precision navigation attitude matrix
Figure BDA0000049809080000068
Obtain this moment mathematical platform and actual navigation coordinate the cosine matrix of deviation
Figure BDA0000049809080000069
Just to obtain the misalignment φ of mathematical platform this moment.Because through behind the coarse alignment, each misalignment is a smaller value, so misalignment φ and direction cosine matrix
Figure BDA00000498090800000610
Relation can be expressed as:
Figure BDA00000498090800000611
Can know by top narration,, just can calculate the attitude matrix of carrier coordinate system and navigation coordinate system accurately as long as in the fine alignment process, obtain misalignment φ
Figure BDA00000498090800000612
Therefore the task of fine alignment becomes the rapid and precise misalignment φ that obtains, and can utilize the Kalman filtering state estimation to go out misalignment φ.
3, Kalman filtering state estimation
On the basis of feature 1,2, utilize the kalman filter method of standard to carry out iterative computation, can estimate misalignment φ.Detailed process is as follows:
At first system equation formula (1) and observation equation (2) are carried out discretize, obtain
Figure BDA0000049809080000071
Figure BDA0000049809080000072
X in the formula kBe the status switch of system, Z kObservation sequence for system;
Figure BDA0000049809080000073
Be system state transition matrix, H kObserving matrix for system;
Figure BDA0000049809080000074
V kBe respectively the process noise sequence and the observation noise sequence of system, its average all is zero white Gaussian noise sequence.The systematic procedure noise
Figure BDA0000049809080000075
Variance be Systematic observation noise V kVariance be R k
Carry out Kalman filtering then:
The state one-step prediction:
State estimation:
Figure BDA0000049809080000078
The filter gain matrix:
Figure BDA0000049809080000079
One-step prediction error variance matrix:
Figure BDA00000498090800000710
The estimation error variance matrix:
Figure BDA00000498090800000711
The filtering selection of initial value can be with reference to about finishing the document of initial alignment with standard kalman filtering.
4, in the step 7 according to Kalman Filter Estimation error variance P kCalculate two error distances
Figure BDA00000498090800000712
With
Figure BDA00000498090800000713
The estimation error variance matrix of error angle φ:
Figure BDA00000498090800000714
C represents error angle observing matrix, P in the formula (17) kExpression kalman estimation error variance matrix,
Figure BDA00000498090800000715
So
Figure BDA00000498090800000716
Define two error distances
Figure BDA0000049809080000081
Figure BDA0000049809080000082
Figure BDA0000049809080000083
Expression k is east orientation error angle variance of estimaion error constantly,
Figure BDA0000049809080000084
Expression k is north orientation error angle variance of estimaion error constantly,
Figure BDA0000049809080000085
Expression k is azimuthal error angle variance of estimaion error constantly,
Figure BDA0000049809080000086
Coupling variance of estimaion error between expression lateral error and the azimuthal error,
Figure BDA0000049809080000087
The distance at expression k moment east orientation error angle and azimuthal error angle,
Figure BDA0000049809080000088
The azimuthal error angle is to the distance of steady-state value constantly for expression k, and h represents the weights of azimuthal error angle steady-state error,
Figure BDA0000049809080000089
Be azimuthal steady state error.Because the speed of convergence at lateral error angle is similar to convergence error, so With
Figure BDA00000498090800000811
Also close.
Rotational-angular velocity of the earth is calculated in definition:
Figure BDA00000498090800000812
In the formula (21)
Figure BDA00000498090800000813
Represent true rotational-angular velocity of the earth, n represents to increase the weights of rotational-angular velocity of the earth.
Can basis
Figure BDA00000498090800000814
With
Figure BDA00000498090800000815
Size determine to increase the size of the weights n of rotational-angular velocity of the earth because
Figure BDA00000498090800000816
Relation between the n three is the nonlinear relationship of a complexity, be difficult to express with a relationship, so the present invention according to
Figure BDA00000498090800000817
With Method with fuzzy reasoning estimates weights n.
5, the method by fuzzy reasoning estimates the calculating rotational-angular velocity of the earth
Figure BDA00000498090800000819
At first to two distances
Figure BDA00000498090800000820
With
Figure BDA00000498090800000821
Carry out normalized, obtain two new normalization distances:
Figure BDA00000498090800000822
If quantizating index
Figure BDA00000498090800000823
The domain space be A i(i=1,2).If
Figure BDA00000498090800000824
Have identical domain space, promptly have
Figure BDA00000498090800000825
On domain, define input variable
Figure BDA00000498090800000826
The fuzzy subset is: SP (just little), MP (center), LP (honest), and selected fuzzy subset's subordinate function is the Gaussian function:
Figure BDA00000498090800000827
As shown in Figure 1.In the formula: c and σ, obtain through behind the fuzzy reasoning for the distribution parameter (design parameter) of expression fuzzy inference system quantification input
Figure BDA0000049809080000091
Fuzzy value s jP[0,1].
Equally,, define identical fuzzy subset SP (just little), MP (center), LP (honest), adopt trigonometric function as subordinate function, as shown in Figure 2 at the output region [0,1] of fuzzy inference system.
With above-mentioned carry out obfuscation apart from variable after, adopt following fuzzy reasoning rule to carry out reasoning and release weights
Rule 1:if s 1=SP and s 2=SP then N=SP;
Rule 2:if s 1=SP and s 2=MP then N=MP;
......
Adopt fuzzy reasoning table as shown in table 1 to carry out reasoning according to expertise.
Table 1 fuzzy reasoning table
Figure BDA0000049809080000093
According to above-mentioned fuzzy rule, can obtain the fuzzy value N of k weights constantly, the gelatinization of fuzzy value N reverse is obtained weights The weights of rotational-angular velocity of the earth
Figure BDA0000049809080000095
Figure BDA0000049809080000096
F is that the weights of rotational-angular velocity of the earth allow to change maximum magnitude (can get 100～5000 usually).
The present invention utilize the mode of fuzzy reasoning real-time estimate suitable calculating rotational-angular velocity of the earth, not only accelerated the speed of convergence at azimuthal error angle, and guaranteed the stable state accuracy of lateral error and azimuthal error.The process flow diagram of aiming at as shown in Figure 4, the structural drawing of fine alignment system as shown in Figure 3, this fine alignment method, neither need to increase any sensor, the turntable that does not also need the position, as long as the software that need revise the initial alignment of strapdown inertial navitation system (SINS) just can improve the speed of fine alignment, Project Realization easily greatly.
Now beneficial effect of the present invention is described as follows:
(1) influence of change rotational-angular velocity of the earth
The calculating rotational-angular velocity of the earth is
Figure BDA0000049809080000097
Now get respectively
Figure BDA0000049809080000098
The time, just will calculate rotational-angular velocity of the earth respectively and be increased to 1 times, 100 times, 1000 times, 5000 times.Fig. 5-7 is respectively the calculating rotational-angular velocity of the earth is increased to 1 times, 100 times, 1000 times, east orientation error, north orientation error, azimuthal error analogous diagram (, system noise and observation noise being removed) in the time of 5000 times for the ease of observing the error of calculating rotational-angular velocity of the earth and causing by increasing.Increase with weights n as can be seen, the speed of convergence of lateral error (Fig. 5,6) does not have too many change, but the speed of convergence of azimuthal error (Fig. 7) but improves fast.But work as weights
Figure BDA0000049809080000101
The time, lateral error and azimuthal error all can be vibrated.This explanation raising is calculated rotational-angular velocity of the earth and can be improved the rapidity of initial alignment, but is not to calculate rotational-angular velocity of the earth to be the bigger the better, and when the calculating rotational-angular velocity of the earth arrived to a certain degree greatly, steady-state error vibration can take place and disperses.The present invention that Here it is will estimate the reason of calculating rotational-angular velocity of the earth in real time according to error distance, only in this way could guarantee the stationarity of azimuthal error convergent rapidity and steady-state error.(2) utilize the method for fuzzy reasoning to determine the influence of weights n to speed of convergence.
Calculate rotational-angular velocity of the earth and be increased to how many times on earth, can guarantee that lateral error and azimuthal error can not take place to vibrate or disperse, can simultaneously guarantee the fastest speed of convergence? this problem is difficult to definite answer, system needs different calculating rotational-angular velocity of the earth could guarantee the Optimal error characteristic in the different stages, and the characteristic of different system and different noisinesss, in order to obtain the Optimal error characteristic, also be not quite similar at needed calculating rotational-angular velocity of the earth of different stages.Therefore optimum error characteristics are difficult to obtain, and the calculating rotational-angular velocity of the earth but can estimate by the method for suboptimum.The present invention is by two error distances of definition With
Figure BDA0000049809080000103
, estimate weights n in real time, reasonable this problem that solved according to the mode of these two distances by fuzzy reasoning.Fig. 8-10 be respectively by fuzzy reasoning method estimation weights n and fixedly weights comparison diagram (calculate the error that rotational-angular velocity of the earth causes for the ease of observing, system noise and observation noise are removed) by increasing.From these figure as can be seen, mode by fuzzy reasoning estimates weights n method makes the speed of convergence of lateral error (Fig. 8,9) obviously improve, and the speed of convergence of azimuthal error (Figure 10) is exceedingly fast, and just convergence and steady-state error were steady fully in 45 seconds, do not disperse and vibrates.

Claims (1)

1. one kind based on the fuzzy quick fine alignment method that becomes rotational-angular velocity of the earth, it is characterized in that:
(1) determines the initial position parameters of carrier by external unit, and it is bound to navigational computer;
(2) the SINS preheating is prepared, and gathers the output of accelerometer and gyroscope;
(3) utilize accelerometer and the gyroscope output that collects, carry out coarse alignment, determine rough initial attitude matrix by the analytical method of standard;
(4) coarse alignment enters the fine alignment stage after finishing, and rotational-angular velocity of the earth ω is calculated in order e=Ω e, Ω eRepresent true earth rotation speed;
(5) output and the coarse alignment according to accelerometer obtains initial attitude, and calculates rotational-angular velocity of the earth and carry out the calculating of Kalman filtering single-step iteration;
(6) determine fine alignment time t f, make t fValue greater than the convergence time of filtering and the maximum time that can allow less than inertial navigation system.
(7) judge fine alignment t fWhether timing finishes, if fine alignment has finished then to make calculating rotational-angular velocity of the earth ω e=Ω e, the misalignment that adopts Kalman Filter Technology to estimate, and come the strapdown attitude matrix of update the system with misalignment, finish accurate initial alignment; If fine alignment does not finish, then according to Kalman Filter Estimation error variance P kCalculate two error distances
Figure FDA0000049809070000011
With
Figure FDA0000049809070000012
Wherein
Figure FDA0000049809070000013
For east orientation error angle variance of estimaion error,
Figure FDA0000049809070000016
Be azimuthal error angle variance of estimaion error, h Δ φ DBe azimuthal expectation steady state error, the method by fuzzy reasoning estimates calculates rotational-angular velocity of the earth ω e=n Ω e, to return step (5) and carry out Kalman's iterative computation and finish until fine alignment, rotational-angular velocity of the earth ω is calculated in order e=Ω e, the misalignment that adopts Kalman Filter Technology to estimate, and come the strapdown attitude matrix of update the system with misalignment, finish accurate initial alignment.
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CN110398257A (en) * 2019-07-17 2019-11-01 哈尔滨工程大学 The quick initial alignment on moving base method of SINS system of GPS auxiliary
CN112362083A (en) * 2020-11-17 2021-02-12 中北大学 On-site rapid calibration compensation method for attitude misalignment angle based on Newton iteration method
CN112362083B (en) * 2020-11-17 2022-08-09 中北大学 On-site rapid calibration compensation method for attitude misalignment angle based on Newton iteration method

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