CN107990910A - A kind of naval vessel Large azimuth angle Transfer Alignment based on volume Kalman filtering - Google Patents

A kind of naval vessel Large azimuth angle Transfer Alignment based on volume Kalman filtering Download PDF

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CN107990910A
CN107990910A CN201711078693.6A CN201711078693A CN107990910A CN 107990910 A CN107990910 A CN 107990910A CN 201711078693 A CN201711078693 A CN 201711078693A CN 107990910 A CN107990910 A CN 107990910A
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inertial navigation
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CN107990910B (en
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高伟
王凯
张亚
王岩岩
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Harbin Institute of Technology
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    • 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
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Abstract

The invention discloses a kind of naval vessel Large azimuth angle Transfer Alignment based on volume Kalman filtering.First, the specific force output of sub- inertial navigation accelerometer is transformed into navigational coordinate system, processing is filtered to it using Butterworth wave digital lowpass filter；Secondly, main and sub inertial navigation carries out inertial reference calculation respectively, and speed, posture and the angular velocity information of main inertial navigation are transferred to the navigational computer of sub- inertial navigation, and measurement is constructed using the velocity error between main and sub inertial navigation system, attitude error and angular speed error；Then, the matching way of angular speed is added using speed plus posture, establishes state equation and measurement equation in the case of Large azimuth angle；Finally, established state equation and measurement equation are utilized, carries out volume Kalman filtering resolving, estimates the fix error angle between sub- inertial navigation system and main inertial navigation system, completes Transfer Alignment.The present invention solves quick high accuracy alignment issues of the naval vessel under Large azimuth angle and big lever arm error condition.

Description

A kind of naval vessel Large azimuth angle Transfer Alignment based on volume Kalman filtering
Technical field
It is generous more particularly to a kind of naval vessel based on volume Kalman filtering the present invention relates to inertial navigation technical field Position misalignment Transfer Alignment.
Background technology
Inertial navigation system is a kind of autonomic navigation system based on principle of inertia.Strapdown Inertial Navigation System is by gyro and adds The angular movement and line movable information that speedometer is directly connected on carrier to measure carrier, fortune is extrapolated by integral operation Carrier is relative to the speed of the earth, position and posture and course information.Initial alignment is a key of Strapdown Inertial Navigation System Technology, the precision of alignment directly influences the precision of navigation system, and the time for completing alignment then directly influences the fast of system Fast respond.Transfer Alignment is that a kind of initial alignment of sub- inertial navigation is directed at using the output information of main inertial navigation, alignment Speed is fast, and to the motor-driven without restriction of carrier.
Can be influenced since naval vessel rides the sea be subject to wave, especially sea situation it is bad in the case of, based on big orientation lose The nonlinear model at quasi- angle can more describe real system exactly.For large ship, the main inertial navigation on naval vessel is often Installed in its swing center, and the installation site of the sub- inertial navigation on on-board equipment has very long a distance with main inertial navigation, works as carrier There are during angular movement, main and sub inertial navigation accelerometer sensitive can arrive different acceleration, so as to cause to exist between main and sub inertial navigation Lever arm speed difference, here it is the lever arm effect phenomenon in Transfer Alignment.Lever arm effect can seriously affect Transfer Alignment precision and Convergence rate, it is necessary to compensate.
Gao Wei et al. exists《The error analysis and compensation of Transfer Alignment Caused by Lever Arm Effect》(it is published in periodical《Instrument and meter Report》, volume 34,03 phase in 2013) in a text, proposed for the nonlinear system under the conditions of Large azimuth angle a kind of straight The compensation method of calculating is connect, azimuthal misalignment angle can converge to 0.381 ° in 120s.Yellow Hunan it is remote et al.《Dropped based on CKF/ is simplified The non-linear alignment technical research of Victoria C KF mixed filterings》(it is published in periodical《Play arrow and guidance journal》, 2015, volume 35, 01 phase) in a text, it is proposed that based on the non-linear alignment method for simplifying CKF/ dimensionality reduction CKF mixed filterings, substantially reduce calculating Amount, horizontal aligument precision reach below 1 ', and alignment of orientation precision reaches below 5 '.Xu Xiao Soviet Unions et al. exist《Based on modified CKF's SINS Initial Alignment Methods》In (Central China University of Science and Technology's journal (natural science edition), 2016, volume 44,01 phase) text, propose A kind of modified CKF methods are used for the Transfer Alignment under the conditions of Large azimuth angle, and alignment of orientation precision reaches below 3 '.This Invention devises a kind of speed based on volume Kalman filtering and adds posture to add angular speed Transfer Alignment, is deposited available for naval vessel In Large azimuth angle and the situation of big lever arm error, the speed and ratio of precision existing method of alignment, which have, significantly to be carried It is high.
The content of the invention
Can be applied to naval vessel it is an object of the invention to provide one kind, there are Large azimuth angle and big lever arm error feelings Quick high accuracy Transfer Alignment under condition.
The technical solution for realizing the object of the invention is：A kind of naval vessel Large azimuth angle based on volume Kalman filtering passes Alignment methods are passed, are comprised the following steps：
Step 1：Complete the startup of sub- inertial navigation system, preheating prepares；
Step 2：The specific force output of sub- inertial navigation accelerometer is transformed into navigational coordinate system, it is low using Butterworth numeral Bandpass filter is filtered it processing, is influenced with achieving the purpose that to eliminate lever arm effect error；
Step 3：Main and sub inertial navigation system carries out inertial reference calculation respectively, and speed, posture and the angular velocity information of main inertial navigation pass The defeated navigational computer to sub- inertial navigation；
Step 4：In the case where naval vessel is there are Large azimuth angle, the match party of angular speed is added using speed plus posture Formula, it is believed that main and sub inertial navigation carrier coordinate system is different and navigational coordinate system is identical, and the speed chosen between main and sub inertial navigation system is missed Difference, attitude error and angular speed error establish the state equation and measurement equation of system as measurement；
Step 5：Established state equation and measurement equation are utilized, carries out volume Kalman filtering resolving, estimates that son is used Fix error angle between guiding systems and main inertial navigation system, completes Transfer Alignment.
In step 2, the technical requirements of Butterworth wave digital lowpass filter are：
Cut-off frequecy of passband is fp=0.01Hz, passband ripple αp=2dB, stopband cutoff frequency are fs=0.15Hz, resistance Band decays to αs=40dB.
The discrete transfer function for designing second order Butterworth digital filter is：
Then the state equation of wave filter is：
Output equation is：
Wherein, u (n) represents the input of wave filter,C= [0.00166 0.70710], d=5.53551e-06.
In step 3, the speed of foundation adds posture to add angular rate matching Transfer Alignment mathematical model as follows：
Ignore vertical passage, the state variable of selection is：
System state equation is：
Wherein, n is navigational coordinate system；M systems are main inertial navigation carrier coordinate system；S systems are sub- inertial navigation carrier coordinate system；For son Inertial navigation calculates carrier coordinate system；δVnFor velocity error navigational coordinate system projection；It is used to son for main inertial navigation carrier coordinate system Lead the direction cosine matrix of carrier coordinate system；More than main inertial navigation carrier coordinate system to the direction of sub- inertial navigation calculating carrier coordinate system String matrix；For the direction cosine matrix of main inertial navigation carrier coordinate system to navigational coordinate system；Specific force for sub- inertial navigation measurement exists The projection of its carrier coordinate system；For rotational-angular velocity of the earth navigational coordinate system projection；Sat for n systems relative to the earth Mark projection of the angular speed in n systems of system；For the fix error angle between s systems and m systems；ForMeasurement between system and m systems is lost Quasi- angle；For main inertial navigation relative to navigational coordinate system angular speed m systems projection；For accelerometer constant value drift；wvFor Accelerometer random drift；εsFor gyroscope constant value drift；For Modelling of Random Drift of Gyroscopes.
Add the matching way of angular speed using speed plus posture, by the velocity error δ V between main and sub inertial navigationn, measure misalignment AngleAnd angular speed errorAs observed quantity：
Measurement equation is：
Z=h (X)+V
Wherein, V is the measurement noise of system.
Ask volume regular using Three Degree Of Freedom Spherical-Radial, wait the volume point of weights to design using one group 2n Nonlinear filtering algorithm, that is, volume Kalman filtering, it is specific as follows：
For such as next Continuous Nonlinear Systems：
System model is carried out by discretization using 4 rank Runge Kuttas (Runge Kutta) method, obtains a Discrete Nonlinear System：
Wherein, XkFor system state vector；ZkFor measurement vector；WkFor system noise vector, VkTo measure noise vector, Both at the Gaussian sequence of zero-mean, and it is orthogonal, that is, meet：
Wherein, QkFor the variance matrix of system noise sequence；RkTo measure the variance matrix of noise sequence；δkjFor Kronecker letter Number.
The specific implementation step of volume Kalman filtering is as follows：
A. the time updates
Assuming that the state x at k-1 momentk-1Statistical property it is known that first to Pk-1Do Cholesky decomposition：
Calculate volume point：
Calculate the volume point after system state equation transmits：
Estimate the status predication value at k moment：
Estimate the status predication covariance matrix at k moment：
B. renewal is measured
To Pk/k-1Do Cholesky decomposition：
Calculate volume point：
Calculate the volume point after the transmission of system measurements equation：
Zi,k/k-1=h (Xi,k/k-1) i=1,2 ..., 2n
Estimate the measurement predictor at k moment：
Estimate the measurement prediction covariance matrix at k moment：
Estimate the one-step prediction cross-correlation covariance matrix at k moment：
Estimate the filtering gain at k moment：
Ask for the state estimation at k moment：
Ask for the state error covariance matrix at k moment：
Add posture to add the state equation and measurement equation of angular rate matching Transfer Alignment according to the speed of foundation, carry out volume Kalman filtering resolves, and estimates the fix error angle between sub- inertial navigation system and main inertial navigation system, completes Transfer Alignment.
Compared with prior art, the beneficial effects of the invention are as follows：
System is thought of as nonlinear model, and design by the present invention in the case where naval vessel is there are Large azimuth angle Output of the Butterworth wave digital lowpass filter to sub- inertial navigation accelerometer is filtered processing, adds angle fast using speed plus posture The matching way of degree, establishes Filtering Model, carries out volume Kalman filtering resolving, effectively eliminates the influence of lever arm effect, Alignment speed and precision of the naval vessel under Large azimuth angle and big lever arm error condition has been significantly increased.
Brief description of the drawings
Fig. 1 is the basic procedure block diagram of the present invention；
Fig. 2 is the frequency spectrum of lever arm acceleration；
Fig. 3 is the fix error angle evaluated error curve emulated using Matlab.
Embodiment
The present invention is further described below in conjunction with the accompanying drawings.
It is generous to the naval vessel based on volume Kalman filtering of design using Matlab in order to verify effectiveness of the invention Transfer Alignment nonlinear model during the misalignment of position is emulated.
Naval vessel can be subject to Lidar Equation in marine navigation, produce three-axis swinging movement, its mathematical model is：
In formula, ψ, θ, γ represent course angle, pitch angle and roll angle respectively；ψm, θm, γmTo wave angular amplitude；ωy, ωp, ωrTo wave angular frequency；Ti=2 π/ωi, (i=y, p, r) is rolling period；For initial attitude angle；K is first Initial course.
Simulation parameter sets as follows：
Wave angular amplitude：ψm=5 °, θm=15 °, γm=10 °；
Rolling period：Ty=8s, Tp=12s, Tr=6s；
Initial attitude angle：
Initial heading：K=30 °；
Initial latitudeInitial longitude λ=126.6705 °；
Error angle is：
Gyroscope constant value drift is εx=εy=εz=0.01 °/h, random drift is 0.001 °/h；
The random constant value of accelerometer is biased to 10-4G, accelerometer random drift are 10-5g；
At the uniform velocity sailed through to the speed of 5m/s on naval vessel；
Filtering cycle：0.05s；
Lever arm length：rs=[8 25 2]T(m)。
Design Butterworth wave digital lowpass filter handles the output of sub- inertial navigation accelerometer, comprises the following steps that：
The vibration of sub- inertial navigation system is the vibration based on Schuler cycle and earth rotation period, is in low frequency range, its frequency Spectral structure is in f=2 × 10-4Below Hz.According to the frequency spectrum of lever arm effect acceleration, it may be determined that the skill of Butterworth LPF Art requirement：
Cut-off frequecy of passband fp=0.01Hz, passband ripple αp=2dB, stopband cutoff frequency fs=0.15Hz, stopband attenuation αs=40dB.The exponent number N of wave filter is determined by following formula first.
In formula, Substitution can obtain N=1.80, take N=2.
3dB cutoff frequencies are：
The normalization prototype system letter of second-order low-pass filter can be obtained by Butterworth normalization low-pass filter parameter list Number：
By Ga(p) go to normalize, obtain the system function of simulation low-pass filter：
Sampling interval T=0.05s, is changed using Bilinear transformation method, obtains the system function of wave digital lowpass filter：
The state equation of wave filter is：
Output equation is：
Wherein, u (n) represents the input of wave filter,C= [0.00166 0.70710], d=5.53551e-06.
Establishing speed adds posture to add angular rate matching Transfer Alignment mathematical model, comprises the following steps that：
Speed adds posture to add the starting point of angular rate matching Transfer Alignment mathematical modeling to be that the carrier for thinking main and sub inertial navigation is sat Mark system is different, and navigational coordinate system is identical.If the navigational coordinate system of main and sub inertial navigation is n systems, the carrier coordinate system of main and sub inertial navigation Represented respectively with m and s, then fix error angle of the amount to be estimated between m systems and s systemsDue to right Before standard, sub- inertial navigation can not obtain strap-down matrix of the sub- inertial navigation carrier coordinate system s relative to navigational coordinate system n, therefore first define Sub- inertial navigation calculates carrier coordinate systemWillError angle between m is known as measuring misalignment, is expressed as
According to specific force equation, have to main and sub inertial navigation：
In formula,WithRespectively the specific force of main and sub inertial navigation measurement respective carrier coordinate system projection,WithFor Projection of the speed of main and sub inertial navigation in navigational coordinate system；For the direction cosines of main inertial navigation carrier coordinate system to navigational coordinate system Matrix；For the direction cosine matrix of sub- inertial navigation carrier coordinate system to navigational coordinate system；Navigating for rotational-angular velocity of the earth The projection of coordinate system；For n systems relative to terrestrial coordinate system angular speed n systems projection；WithIt is respectively main and sub used Lead the acceleration of gravity of position.
Two formulas are subtracted each other：
Without considering lever arm effect error, main and sub inertial navigation output specific force relation is as follows：
In formula,For sub- inertial navigation accelerometer error；For main inertial navigation carrier coordinate system to sub- inertial navigation carrier coordinate system Direction cosine matrix.ThinkIt can obtain：
Above formula is that speed adds posture to add the velocity error differential equation of angular rate matching Transfer Alignment.
The differential for measuring misalignment is that s ' is the projection for being in s ' relative to the angular speed of m systems, i.e.,：
Without considering deflection deformation, main and sub inertial navigation Output speed relation is as follows：
Therefore have：
Since main and sub inertial navigation is connected on carrier, therefore think fix error angleFor constant value, therefore：
Above-mentioned two formula is that speed adds posture to add the measurement misalignment differential equation and the installation of angular rate matching Transfer Alignment The error angle differential equation.
The main error source of inertia device has gyroscopic drift ε and accelerometer biasGyroscopic drift is mainly floated by constant value Move εc, associated drift εr, random white noise drift wgFormed etc. three parts.The correlation time of associated drift be generally higher than 1 it is small when, Can approximation be considered as constant value drift, and the 1-2 order of magnitude smaller than constant value drift, therefore gyroscope error model can be reduced to：
Similar, accelerometer bias can also be reduced to constant value drift, i.e.,：
Ignore vertical passage, the state variable of selection is：
System state equation is：
Choose velocity error between main and sub inertial navigation, measure misalignment and angular speed error as observed quantity, i.e.,：
Wherein, speed observed quantity is δ Vn, attitude observation isAngular speed observed quantity is
Measurement equation is：
Z=h (X)+V
Wherein, V is the measurement noise of system.
Volume Kalman filtering resolving is carried out, its algorithm flow is as follows：
A. the time updates
Assuming that the state x at k-1 momentk-1Statistical property it is known that first to Pk-1Do Cholesky decomposition：
Calculate volume point：
Calculate the volume point after system state equation transmits：
Estimate the status predication value at k moment：
Estimate the status predication covariance matrix at k moment：
B. renewal is measured
To Pk/k-1Do Cholesky decomposition：
Calculate volume point：
Calculate the volume point after the transmission of system measurements equation：
Zi,k/k-1=h (Xi,k/k-1) i=1,2 ..., 2n
Estimate the measurement predictor at k moment：
Estimate the measurement prediction covariance matrix at k moment：
Estimate the one-step prediction cross-correlation covariance matrix at k moment：
Estimate the filtering gain at k moment：
Ask for the state estimation at k moment：
Ask for the state error covariance matrix at k moment：
Volume Kalman filter primary condition, including state estimation covariance battle array P0, system noise variance matrix Q0And measure Noise variance matrix R0, set as follows：
P0=diag { (0.1m/s)2,(0.1m/s)2,(0.2°)2,(0.2°)2,(10°)2,(0.2°)2,(0.2°)2, (10°)2,
(1×10-4g0)2,(1×10-4g0)2,(0.01°/h)2,(0.01°/h)2,(0.01°/h)2}
Q0=diag { (1 × 10-5g0)2,(1×10-5g0)2,(0.001°/h)2,(0.001°/h)2,(0.001°/h)2}
R0=diag { (0.1m/s)2,(0.1m/s)2,(0.001°)2,(0.001°)2,(0.001°)2,(0.5°/h)2, (0.5°/h)2,(0.5°/h)2}
Simulation result：
With above-mentioned simulated conditions, the result arrived of emulation is as shown in table 1, Fig. 3.
Fix error angle evaluated error in the case of 1 Large azimuth angle of table
, longitudinally, laterally can be in 1s rapidly with course estimation error using the method for the present invention it can be seen from table 1 and Fig. 3 Less than 2 jiaos points are dropped to, 5s reaches less than 0.1 jiao point, and evaluated error reaches less than 0.01 jiao point after 20s.It is in conclusion of the invention The method of offer, can effectively eliminate the influence of lever arm effect, can on naval vessel, there are Large azimuth angle and big lever arm to miss Realize that quick high accuracy is aligned in the case of difference.

Claims (3)

  1. A kind of 1. naval vessel Large azimuth angle Transfer Alignment based on volume Kalman filtering, it is characterised in that including with Lower step：
    Step 1：Complete the startup of sub- inertial navigation system, preheating prepares；
    Step 2：The specific force output of sub- inertial navigation accelerometer is transformed into navigational coordinate system, is filtered using Butterworth digital lowpass Ripple device is filtered it processing, is influenced with achieving the purpose that to eliminate lever arm effect error；
    Step 3：Main and sub inertial navigation system carries out inertial reference calculation respectively, and speed, posture and the angular velocity information of main inertial navigation are transferred to The navigational computer of sub- inertial navigation；
    Step 4：In the case where naval vessel is there are Large azimuth angle, the matching way of angular speed is added using speed plus posture, is recognized For main and sub inertial navigation carrier coordinate system difference, navigational coordinate system is identical, chooses velocity error, appearance between main and sub inertial navigation system State error and angular speed error establish the state equation and measurement equation of system as observed quantity；
    Step 5：Established state equation and measurement equation are utilized, volume Kalman filtering resolving is carried out, estimates sub- inertial navigation system Fix error angle between system and main inertial navigation system, completes Transfer Alignment.
  2. A kind of 2. naval vessel Large azimuth angle Transfer Alignment side based on volume Kalman filtering according to claim 1 Method, it is characterised in that the vibration of sub- inertial navigation system is the vibration based on Schuler cycle and earth rotation period, is in low frequency Area, its spectrum distribution is in f=2 × 10-4Below Hz.According to the frequency spectrum of lever arm effect acceleration, it may be determined that Butterworth low pass The technical requirements of ripple device：
    Cut-off frequecy of passband fp=0.01Hz, passband ripple αp=2dB, stopband cutoff frequency fs=0.15Hz, stopband attenuation αs= 40dB.The exponent number N of wave filter is determined by following formula first.
    <mrow> <mi>N</mi> <mo>=</mo> <mfrac> <mrow> <mi>lg</mi> <mi> </mi> <msub> <mi>k</mi> <mrow> <mi>s</mi> <mi>p</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>lg&amp;lambda;</mi> <mrow> <mi>s</mi> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> </mrow>
    In formula,Substitution can obtain N=1.80, take N=2.
    3dB cutoff frequencies are：
    The normalization prototype system function of second-order low-pass filter can be obtained by Butterworth normalization low-pass filter parameter list：
    <mrow> <msub> <mi>G</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mi>p</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>1.4142</mn> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow>
    By Ga(p) go to normalize, obtain the system function of simulation low-pass filter：
    <mrow> <msub> <mi>H</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>G</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mi>p</mi> <mo>=</mo> <mfrac> <mi>s</mi> <msub> <mi>Q</mi> <mi>c</mi> </msub> </mfrac> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>112.57908</mn> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>15.00512</mn> <mi>s</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow>
    Sampling interval T=0.05s, is changed using Bilinear transformation method, obtains the system function of wave digital lowpass filter：
    <mrow> <mi>H</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>H</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mi>s</mi> <mo>=</mo> <mfrac> <mn>2</mn> <mi>T</mi> </mfrac> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>5.5682</mn> <mo>&amp;times;</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> <mo>+</mo> <mn>1.1136</mn> <mo>&amp;times;</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mn>5.5682</mn> <mo>&amp;times;</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mn>1.9963</mn> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mn>0.9963</mn> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow>
    The state equation of wave filter is：
    <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>a</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mi>b</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow>
    Output equation is：
    <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>c</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mi>d</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow>
    Wherein, u (n) represents the input of wave filter,C= [0.00166 0.70710], d=5.53551e-06.
  3. A kind of 3. naval vessel Large azimuth angle Transfer Alignment side based on volume Kalman filtering according to claim 1 Method, it is characterised in that ignore vertical passage, the state variable of selection is：
    System state equation is：
    Wherein, n is navigational coordinate system；M systems are main inertial navigation carrier coordinate system；S systems are sub- inertial navigation carrier coordinate system；For sub- inertial navigation Calculate carrier coordinate system；δVnFor velocity error navigational coordinate system projection；Carried for main inertial navigation carrier coordinate system to sub- inertial navigation The direction cosine matrix of body coordinate system；The direction cosines square of carrier coordinate system is calculated for main inertial navigation carrier coordinate system to sub- inertial navigation Battle array；For the direction cosine matrix of main inertial navigation carrier coordinate system to navigational coordinate system；Specific force for sub- inertial navigation measurement is carried at it The projection of body coordinate system；For rotational-angular velocity of the earth navigational coordinate system projection；It is n systems relative to terrestrial coordinate system Angular speed n systems projection；For the fix error angle between s systems and m systems；ForMeasurement misalignment between system and m systems Angle；For main inertial navigation relative to navigational coordinate system angular speed m systems projection；▽sFor accelerometer constant value drift；wvTo add Speedometer random drift；εsFor gyroscope constant value drift；For Modelling of Random Drift of Gyroscopes.
    Add the matching way of angular speed using speed plus posture, by the velocity error δ V between main and sub inertial navigationn, measure misalignment And angular speed errorAs observed quantity：
    Measurement equation is：
    Z=h (X)+V
    Wherein, V is the measurement noise of system.
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