CN106767928A - A kind of self adaptation fast transfer alignment method - Google Patents

A kind of self adaptation fast transfer alignment method Download PDF

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Publication number
CN106767928A
CN106767928A CN201710023543.9A CN201710023543A CN106767928A CN 106767928 A CN106767928 A CN 106767928A CN 201710023543 A CN201710023543 A CN 201710023543A CN 106767928 A CN106767928 A CN 106767928A
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inertial navigation
error
sub
delta
filtering
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刘义亭
谢斌
王晓璇
李婷婷
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CETC 28 Research Institute
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CETC 28 Research Institute
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices

Abstract

The invention discloses a kind of self adaptation fast transfer alignment method, comprise the following steps:(1) set up " speed+attitude " Matching Model of main inertial navigation and sub- inertial navigation system, using the deflection deformation between main inertial navigation and sub- inertial navigation as finite energy measurement noise;(2) H of the design based on adaptive weighted algorithm2/HFiltering algorithm, completes the Transfer Alignment of main inertial navigation and sub- inertial navigation.The method can automatically adjust H in the case of unknown deflection deformation according to deformation quantity size2Filtering and HThe weighted operator of filtering gain battle array;Increase H when deflection deformation is bigThe weighted operator of filtering gain battle array, reduces H2The weighted operator of filtering gain battle array;Deflection deformation hour increases H2The weighted operator of filtering gain battle array, reduces HThe weighted operator of filtering gain battle array;Filtering accuracy is effectively improved, boss's inertial navigation fast transfer alignment of unknown deflection deformation is realized.

Description

A kind of self adaptation fast transfer alignment method
Technical field
The self adaptation in the case of field, more particularly to a kind of unknown deflection deformation is initially directed at the invention belongs to inertial navigation Fast transfer alignment method.
Background technology
Transfer Alignment process is that the sub- inertial navigation system being not yet aligned is calibrated using precision main inertial navigation system higher, transmission Technique of alignment can not only reduce the requirement to inertia device, and can greatly improve the speed of alignment.At present, Transfer Alignment Technology is widely used in various occasions such as carrier-borne, airborne and mobile unit.Different applied environments has different spies Point, for on-board equipment, can be subject to come from wave, fitful wind, the ocean temperature change in the external world when being navigated by water in water due to naval vessel Deng influence, while the naval vessel influence such as engine, load, deadweight in itself is also subject to, so that hull deforms, so being arranged on warship Inevitably there is attitude error with main inertial navigation system in the sub- inertial navigation system in load equipment.Attitude error comprising alignment error and Deflection deformation.
Initial alignment will not only estimate alignment error, and the deflection deformation of hull is also estimated in real time.In inertial navigation system In system, deflection deformation, lever arm effect and information transfer time delay are three principal elements for influenceing system accuracy.Wherein, rigid rod The lever arm effect that arm causes can accurately be compensated by physical method, and the time delayses of information transfer can be by extrapolation etc. Algorithm is compensated.But the deflection deformation of hull is changed, thing of having no idea as hull is changed by external influence First obtain accurate deflection.
Research shows that the deformation of hull can reach tens jiaos points, part to hull rolling, pitching, the influence in course Angle point, a few angles grade, and this magnitude can be more far longer than in the case where sea situation is severe.Therefore, deflection deformation angle is measured in real time There is highly important meaning to improving Transfer Alignment precision.
At present, the research to deflection deformation in Transfer Alignment is divided into three aspects:1st, there is much information in Transfer Alignment Matching way, different matching ways require difference to the maneuver mode of hull, and the time of alignment and effect are also different;2 bases The characteristics of deflection deformation, sets up the error model of inertial navigation;3 wave filters of the design with certain robustness.
Naval vessel environment during navigation is complicated, and the influence to naval vessel can not be carried out completely by single Disturbance Model Estimation., based on linear model, when hull is influenceed by wave etc., attitude error angle is no longer for traditional kalman filtering techniques When meeting the situation at small angle, there is larger model error in traditional error model, and being filtered using linear kalman may make filter Ripple result dissipates.Use H merelyAlthough filtering can increase the robustness of system, in the case of stormy waves is less, H's Filtering accuracy filters low than kalman.
The content of the invention
Goal of the invention:For problem above, the present invention proposes a kind of self adaptation fast transfer alignment method.
Technical scheme:To realize the purpose of the present invention, the technical solution adopted in the present invention is:A kind of self adaptation is quickly passed Alignment methods are passed, is comprised the following steps:
(1) " speed+attitude " Matching Model of main inertial navigation and sub- inertial navigation system is set up, by between main inertial navigation and sub- inertial navigation Deflection deformation as finite energy measurement noise;
(2) H of the design based on adaptive weighted algorithm2/HFiltering algorithm, the transmission for completing main inertial navigation and sub- inertial navigation is right It is accurate.
Step (1) is specifically included:
Step 1.1:Set up SYSTEM ERROR MODEL:
Wherein, Xk∈Rn×1For the n of system ties up state vector;Fk,k-1∈Rn×nFor n × n ties up step status predication battle array;Wk∈ Rn×1It is the process noise of system;Γk,k-1It is systematic procedure noise inputs matrix;Yk∈Rm×1It is the observed quantity of m dimensions;Hk∈Rm×n It is observing matrix;Vk∈Rm×1It is system measurements noise.
Step 1.2:The state vector X of 15 dimensions is set:
Wherein, δ VE、δVN、δVUThe east of respectively sub- inertial navigation, north, day to velocity error;φE、φN、φUIt is respectively sub The pitching of inertial navigation, rolling, course attitude error;δ λ, δ L, δ h are respectively longitude, latitude, the height error of sub- inertial navigation;εE、εN、εU The three axis accelerometer drift of respectively sub- inertial navigation;Three axles of respectively sub- inertial navigation add table zero inclined.
Step 1.3:Set up velocity error equation:
Wherein, φ is the attitude error of sub- inertial navigation, and f represents specific force, and δ V are the velocity errors of sub- inertial navigation, and V is sub- inertial navigation Speed,It is that sub- inertial navigation plus table zero are inclined;N, i, e are respectively navigation system, inertial system and terrestrial coordinate system, Respectively Projection and its error of the earth rotation in n systems,Represent rotational angular velocity and its error of the n systems with respect to e systems;Subscript N represents the projection in n systems;"×" represents backslash battle array.
Step 1.4:Set up systematic error equation:
Attitude error equations:
Site error equation:
Wherein, ε is the gyroscopic drift of sub- inertial navigation,Represent rotational angular velocity and its error of the n systems with respect to i systems, R It is earth radius, L is the latitude of sub- inertial navigation, VEThe speed of sub- inertial navigation east orientation.
The gyroscopic drift single order Markov equation inclined with table zero is added:
Step 1.5:Set up system measurements equation;
Calculate measuring value Y:
Y=[VE-VME VN-VMN VU-VMU φEME φNMN φUMU] 7
Wherein, VME、VMN、VMURepresent east orientation, north orientation, the sky orientation speed of main inertial navigation, φME、φMN、φMURepresent main inertial navigation Attitude angle;
Calculate and measure matrix H:
H=[I6×6 06×9] 8
Wherein, I6×6It is the unit matrix of 6 × 6 dimensions, 06×9It is 0 matrix of 6 × 9 dimensions.
Step (2) is specifically included:
Step 2.1:Calculate weight coefficient d:
Wherein, the mark of tr () representing matrix;P(2)(k)、P(∞)K () represents previous kalman filtering and H respectivelyFilter The estimation error variance of ripple;D is real constant, 0≤d≤1.
Step 2.2:Calculate previous H2/HFilter gain K (k):
K (k)=dK(2)(k)+(1-d)K(∞)(k) 10
Wherein, K(2)K () is previous kalman filtering gains, K(∞)K () is previous HFiltering gain.
Step 2.3:Calculate this state estimation
Wherein,It is previous state estimation, y (k+1) is Current observation value, Fk+1kIt is next state transfer Battle array, Hk+1It is current state observing matrix.
Step 2.4:Calculate this HFiltering gain K(∞)And estimation error variance P (k+1)(∞)(k+1):
Wherein, L (k) ∈ R are the given matrix of appropriate dimension, and I is unit matrix, and δ is real coefficient, according to engineering practice To determine, when stability requirement is high, δ takes smaller, and when required precision is high, then δ takes greatly.
OrderMeasure across subjects { Y is being given in expression0,Y1,…YkUnder the conditions of to YkEstimation, definition such as Lower filtering error:
If Tk(Ff) represent uncertain interferenceMap to filtering error { ekTransmission function, HSuboptimal filtering problem can be described as:Given positive number γ>0, find suboptimum HEstimateSo that | | Tk (Ff)||<γ, and meet
Wherein, P0It is the evaluated error of zero moment state vector, WkAnd VkThe respectively system noise sequence and amount at k moment Survey noise sequence.
Step 2.5:Calculate this kalman filtering gain K(2)And estimation error variance P (k+1)(2)(k+1):
P(2)(k+1)=A (k) ((P(2)(k))-1+CT(k)C(k))-1AT(k)+B(k)BT(k) 17
K(2)(k+1)=P(2)(k+1)CT(k+1)(I+C(k+1)P(2)(k+1)CT(k+1))-1 18
Step 2.6:Step 2.1 is returned to, continues to iterate to calculate.
Beneficial effect:Self adaptation fast transfer alignment method of the invention has used the H based on adaptive weighted algorithm2/ HFiltering algorithm, algorithm can automatically adjust H according to the size of the flexural deformations between master/sub- inertial navigation2Filtering gain and HFiltering The weighted operator of gain;Increase H when deflection deformation is bigThe weighted operator of filtering gain battle array, reduces H2The weighting of filtering gain battle array Operator;Deflection deformation hour increases H2The weighted operator of filtering gain battle array, reduces HThe weighted operator of filtering gain battle array.The method H can be automatically adjusted according to deformation quantity size in the case of unknown deflection deformation2Filtering and HThe weighting of filtering gain battle array is calculated Son, effectively improves filtering accuracy, realizes boss's inertial navigation fast transfer alignment of unknown deflection deformation.
Brief description of the drawings
Fig. 1 is the relative installation of boss's inertial navigation, and when 1a is without deflection deformation, boss's inertial navigation is mounted opposite position Put;1b is the relative installation of boss's inertial navigation when having deflection deformation;
H when Fig. 2 is in the absence of deflection deformationThe pitching of filtering, rolling and course attitude error;
Adaptive H when Fig. 3 is in the absence of deflection deformationThe pitching of filtering, rolling and course attitude error;
H of the invention when Fig. 4 is in the absence of deflection deformation2/HThe pitching of filtering, rolling and course attitude error;
Fig. 5 is H when there is deflection deformationThe pitching of filtering, rolling and course attitude error;
Fig. 6 is adaptive H when there is deflection deformationThe pitching of filtering, rolling and course attitude error;
Fig. 7 is H of the invention when there is deflection deformation2/HThe pitching of filtering, rolling and course attitude error.
Specific embodiment
Technical scheme is further described with reference to the accompanying drawings and examples.
Self adaptation fast transfer alignment method of the present invention, comprises the following steps:
S1. set up master/sub- inertial navigation system " speed+attitude " Matching Model, using deflection deformation as finite energy amount Survey noise VkProcessed.Specifically include following steps:
Step 1.1:Set up the error model of system:
Wherein, Xk∈Rn×1For the n of system ties up state vector;Fk,k-1∈Rn×nFor n × n ties up step status predication battle array;Wk∈ Rn×1It is the process noise of system;Γk,k-1It is systematic procedure noise inputs matrix;Yk∈Rm×1It is the observed quantity of m dimensions;Hk∈Rm×n It is observing matrix;Vk∈Rm×1It is system measurements noise.
Step 1.2:The state vector of the dimension of selecting system 15 is as follows:
Wherein, δ VE、δVN、δVUThe east of respectively sub- inertial navigation, north, day to velocity error;φE、φN、φUIt is respectively sub The pitching of inertial navigation, rolling, course attitude error;δ λ, δ L, δ h are respectively longitude, latitude, the height error of sub- inertial navigation;εE、εN、εU The three axis accelerometer drift of respectively sub- inertial navigation;Three axles of respectively sub- inertial navigation add table zero inclined.
Step 1.3:Set up velocity error equation:
Wherein, φ is the attitude error of sub- inertial navigation, and f represents specific force, and δ V are the velocity errors of sub- inertial navigation, and V is sub- inertial navigation Speed,It is that sub- inertial navigation plus table zero are inclined;N, i, e are respectively navigation system, inertial system and terrestrial coordinate system, Respectively Projection and its error of the earth rotation in n systems,Represent rotational angular velocity and its error of the n systems with respect to e systems;Subscript N represents the projection in n systems;"×" represents backslash battle array.
Step 1.4:Set up the error equation of system;
Attitude error equations:
Site error equation:
Wherein, ε is the gyroscopic drift of sub- inertial navigation,Represent rotational angular velocity and its error of the n systems with respect to i systems;R It is earth radius, L is the latitude of sub- inertial navigation, VEThe speed of sub- inertial navigation east orientation.
Assuming that gyroscopic drift and add table zero partially all be one order Markovian process, then have:
Step 1.5:Set up system measurements equation;
The speed of main and sub inertial navigation and attitude are subtracted each other as measuring value Y:
Y=[VE-VME VN-VMN VU-VMU φEME φNMN φUMU] 7
Wherein, VME、VMN、VMURepresent east orientation, north orientation, the sky orientation speed of main inertial navigation, φME、φMN、φMURepresent main inertial navigation Attitude angle.
Measurement matrix H is:
H=[I6×6 06×9] 8
Wherein, I6×6It is the unit matrix of 6 × 6 dimensions, 06×9It is 0 matrix of 6 × 9 dimensions.
Because deck deflection deformation is present, noise V will be measuredkProcessed as the noise of finite energy.
S2. design is based on the H of adaptive weighted algorithm2/HFiltering algorithm, the master/son for completing " speed+attitude " matching is used to Lead Transfer Alignment.Specifically include following steps:
Step 2.1:Seek weight coefficient d;
Wherein, the mark of tr () representing matrix, P(2)(k)、P(∞)K () represents previous kalman filtering and H respectivelyFilter The estimation error variance of ripple, d is real constant, 0≤d≤1.
Step 2.2:Calculate previous H2/HFilter gain K (k), H2/HFilter gain is that kalman filtering increases Benefit and HThe weighted sum of filtering gain;
K (k)=dK(2)(k)+(1-d)K(∞)(k) 10
Wherein, K(2)K () is previous kalman filtering gains, K(∞)K () is previous HFiltering gain.
Step 2.3:Calculate this state estimation
Wherein,It is previous state estimation, y (k+1) is Current observation value, Fk+1,kIt is next state transfer Battle array, Hk+1It is current state observing matrix.
Step 2.4:Calculate this HFiltering gain K(∞)And estimation error variance P (k+1)(∞)(k+1):
Wherein, L (k) ∈ R are the given matrix of appropriate dimension, and I is unit matrix, and δ is real coefficient, according to engineering practice To determine, when stability requirement is high, δ takes smaller, and when required precision is high, then δ takes greatly.
OrderMeasure across subjects { Y is being given in expression0,Y1,…YkUnder the conditions of to YkEstimation, definition such as Lower filtering error:
If Tk(Ff) represent uncertain interferenceMap to filtering error { ekTransmission function, HSuboptimal filtering problem can be described as:Given positive number γ>0, find suboptimum HEstimateSo that | | Tk (Ff)||<γ, and meet
Wherein, P0It is the evaluated error of zero moment state vector, WkAnd VkThe respectively system noise sequence and amount at k moment Survey noise sequence.
Step 2.5:Calculate this kalman filtering gain K(2)And estimation error variance P (k+1)(2)(k+1):
P(2)(k+1)=A (k) ((P(2)(k))-1+CT(k)C(k))-1AT(k)+B(k)BT(k) 17
K(2)(k+1)=P(2)(k+1)CT(k+1)(I+C(k+1)P(2)(k+1)CT(k+1))-1 18
Step 2.6:Step 2.1 is returned to, continues to iterate to calculate.
Self adaptation fast transfer alignment method of the invention has used the H based on adaptive weighted algorithm2/HFiltering is calculated Method, can automatically adjust H according to the size of the flexural deformations between master/sub- inertial navigation2Filtering gain and HThe weighting of filtering gain is calculated Son;Increase H when deflection deformation is bigThe weighted operator of filtering gain battle array, reduces H2The weighted operator of filtering gain battle array;Deflection deformation Hour increases H2The weighted operator of filtering gain battle array, reduces HThe weighted operator of filtering gain battle array.The method can be scratched unknown In the case of song deformation, H is automatically adjusted according to deformation quantity size2Filtering and HThe weighted operator of filtering gain battle array, effectively improves Filtering accuracy, realizes boss's inertial navigation fast transfer alignment of unknown deflection deformation.
It is as shown in Figure 1 the relative installation of boss's inertial navigation, when Fig. 1 a are without deflection deformation, the relative peace of boss's inertial navigation Holding position;Fig. 1 b are the relative installations of boss's inertial navigation when having deflection deformation.It is respectively as shown in figs. 2 to 4 in the absence of flexure H during deformationFiltering, adaptive HFiltering and H of the invention2/HThe pitching of filtering, rolling and course attitude error;Specific number According to as shown in table 1.It is respectively H when there is deflection deformation as shown in Fig. 5~7Filtering, adaptive HFiltering and H of the invention2/ HThe pitching of filtering, rolling and course attitude error;Specific data are as shown in table 2.
Table 1
Table 2
The performance indications of sensor are set in simulated environment:The constant value drift of gyroscope is 0.01/h, and random drift isPlus table zero is 100 μ g (g=9.8m partially2/ s), random deviation is 50 μ g;Local geographic latitude is 32.37 °, warp Spend is 118.22 °;Simulation time is 1500s;Naval vessel pitching, rolling, the amplitude of waving in course are respectively 6 °, 10 °, 5 °;Wave Cycle is respectively 8s, 10s, 6s;At the uniform velocity navigated by water with 10m/s direct norths on naval vessel.Fix error angle between master/sub- inertial navigation is 0.5 °, 0.6 °, 0.2 °, deck deflection deformation is respectively 30 ', 5 ', 8 around the variance of x, y, z direction of principal axis, correlation time is respectively 2s、3s、5s.The deflection deformation on deck is by second order Makov process simulations.

Claims (3)

1. a kind of self adaptation fast transfer alignment method, it is characterised in that:Comprise the following steps:
(1) " speed+attitude " Matching Model of main inertial navigation and sub- inertial navigation system is set up, by the flexure between main inertial navigation and sub- inertial navigation Deform as the measurement noise of finite energy;
(2) H of the design based on adaptive weighted algorithm2/HFiltering algorithm, completes the Transfer Alignment of main inertial navigation and sub- inertial navigation.
2. self adaptation fast transfer alignment method according to claim 1, it is characterised in that:The step (1) is specifically wrapped Include:
Step 1.1:Set up SYSTEM ERROR MODEL:
X k = F k , k - 1 X k - 1 + &Gamma; k , k - 1 W k Y k = H k X k + V k , k = 0 , 1 , 2... - - - 1
Wherein, Xk∈Rn×1For the n of system ties up state vector;Fk,k-1∈Rn×nFor n × n ties up step status predication battle array;Wk∈Rn×1It is The process noise of system;Γk,k-1It is systematic procedure noise inputs matrix;Yk∈Rm×1It is the observed quantity of m dimensions;Hk∈Rm×nIt is observation Matrix;Vk∈Rm×1It is system measurements noise;
Step 1.2:The state vector X of 15 dimensions is set:
X = &phi; E &phi; N &phi; U &delta;V E &delta;V N &delta;V U &delta; L &delta; &lambda; &delta; h &epsiv; E &epsiv; N &epsiv; U &dtri; E &dtri; N &dtri; U - - - 2 Wherein, δ VE、δVN、δVUThe east of respectively sub- inertial navigation, north, day to velocity error;φE、φN、φURespectively sub- inertial navigation it is vertical Shake, rolling, course attitude error;δ λ, δ L, δ h are respectively longitude, latitude, the height error of sub- inertial navigation;εE、εN、εUIt is respectively sub The three axis accelerometer drift of inertial navigation;Three axles of respectively sub- inertial navigation add table zero inclined;
Step 1.3:Set up velocity error equation:
&delta; V &CenterDot; n = - &phi; n &times; f n + &delta;V n &times; ( 2 &omega; i e n + &omega; e n n ) + V n &times; ( 2 &delta;&omega; i e n + &delta;&omega; e n n ) + &dtri; n - - - 3
Wherein, φ is the attitude error of sub- inertial navigation, and f represents specific force, and δ V are the velocity errors of sub- inertial navigation, and V is the speed of sub- inertial navigation,It is that sub- inertial navigation plus table zero are inclined;N, i, e are respectively navigation system, inertial system and terrestrial coordinate system, Respectively the earth from Turn the projection in n systems and its error,Represent rotational angular velocity and its error of the n systems with respect to e systems;Subscript n is represented Projection in n systems;"×" represents backslash battle array;
Step 1.4:Set up systematic error equation:
Attitude error equations:
&phi; &CenterDot; = &phi; &times; &omega; i n n + &delta;&omega; i n n - &epsiv; n - - - 4
Site error equation:
&delta; L &CenterDot; = &delta;V N / R &delta; &lambda; &CenterDot; = sec L ( &delta;V E / R ) + &delta; L ( V E / R ) tan L sec L &delta; h &CenterDot; = &delta;V U - - - 5
Wherein, ε is the gyroscopic drift of sub- inertial navigation,Rotational angular velocity and its error of the n systems with respect to i systems are represented, R is ground The radius of a ball, L is the latitude of sub- inertial navigation, VEThe speed of sub- inertial navigation east orientation;
The gyroscopic drift single order Markov equation inclined with table zero is added:
&epsiv; &CenterDot; = 0 &dtri; &CenterDot; = 0 - - - 6
Step 1.5:Set up system measurements equation;
Calculate measuring value Y:
Y=[VE-VME VN-VMN VU-VMU φEME φNMN φUMU] 7
Wherein, VME、VMN、VMURepresent east orientation, north orientation, the sky orientation speed of main inertial navigation, φME、φMN、φMURepresent the attitude of main inertial navigation Angle;
Calculate and measure matrix H:
H=[I6×6 06×9] 8
Wherein, I6×6It is the unit matrix of 6 × 6 dimensions, 06×9It is 0 matrix of 6 × 9 dimensions.
3. self adaptation fast transfer alignment method according to claim 1, it is characterised in that:The step (2) is specifically wrapped Include:
Step 2.1:Calculate weight coefficient d:
d = t r ( P ( &infin; ) ( k ) ) t r ( P ( 2 ) ( k ) + P ( &infin; ) ( k ) ) - - - 9
Wherein, the mark of tr () representing matrix;P(2)(k)、P(∞)K () represents previous kalman filtering and H respectivelyWhat is filtered estimates Meter error variance;D is real constant, 0≤d≤1;
Step 2.2:Calculate previous H2/HFilter gain K (k):
K (k)=dK(2)(k)+(1-d)K(∞)(k) 10
Wherein, K(2)K () is previous kalman filtering gains, K(∞)K () is previous HFiltering gain;
Step 2.3:Calculate this state estimation
X ^ ( k + 1 ) = F k + 1 , k X ^ ( k ) + K ( k + 1 ) ( y ( k + 1 ) - H k + 1 F k + 1 , k X ^ ( k ) ) - - - 11
Wherein,It is previous state estimation, y (k+1) is Current observation value, Fk+1,kIt is a state transfer matrix, Hk+1 It is current state observing matrix;
Step 2.4:Calculate this HFiltering gain K(∞)And estimation error variance P (k+1)(∞)(k+1):
P ( &infin; ) ( k + 1 ) = F k + 1 , k ( ( P ( &infin; ) ( k ) ) - 1 + H k T H k - &gamma; - 2 L T ( k ) L ( k ) ) - 1 F k + 1 , k T + &Gamma; k &Gamma; k T - - - 12
K ( &infin; ) ( k + 1 ) = P ( &infin; ) ( k + 1 ) H k + 1 T ( I + H k + 1 P ( &infin; ) ( k + 1 ) H k + 1 T ) - 1 - - - 13
&gamma; = &delta; { ( ( P ( &infin; ) ( k ) ) - 1 + H k T H k ) - 1 } 1 / 2 - - - 14
Wherein, L (k) ∈ R are the matrix that dimension gives, and I is unit matrix, and δ is real coefficient;
Calculate filtering error:
e k = Y ^ k - L k X k - - - 15
Wherein,Measure across subjects { Y is being given in expression0,Y1,…YkUnder the conditions of to YkEstimation;
Tk(Ff) represent uncertain interferenceMap to filtering error { ekTransmission function, give γ >0, find suboptimum HEstimateSo that | | Tk(Ff)||<γ, and
s u p X 0 , W , V &Element; h 2 | | e k | | 2 2 ( X 0 - X ^ 0 ) P 0 - 1 ( X 0 - X ^ 0 ) T + | | W k | | 2 2 + | | V k | | 2 2 < &gamma; - - - 16
Wherein, P0It is the evaluated error of zero moment state vector, WkAnd VkThe respectively system noise sequence at k moment and measurement is made an uproar Sound sequence;
Step 2.5:Calculate this kalman filtering gain K(2)And estimation error variance P (k+1)(2)(k+1):
P(2)(k+1)=A (k) ((P(2)(k))-1+CT(k)C(k))-1AT(k)+B(k)BT(k) 17
K(2)(k+1)=P(2)(k+1)CT(k+1)(I+C(k+1)P(2)(k+1)CT(k+1))-1 18
Step 2.6:Step 2.1 is returned to, continues to iterate to calculate.
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