CN103424127A - Method for transfer alignment of speed and specific force matching - Google Patents

Abstract

The invention provides a method for transfer alignment of speed and specific force matching. According to the method, precise estimation is conducted on the misalignment angle of a platform in a short time under the dynamic environment. The method comprises the steps that according to the work principle and characteristics of a platform inertial navigation system, a speed error model and an attitude error model between main inertial navigation and sub inertial navigation are established; according to the obtained system error models, a state equation of system filtering is established and an observing equation of the filtering is established, wherein speed and specific force serve as the observed quantity; the system state is estimated through the Kalman filtering, so that the platform misalignment angle relative to the sub platform inertial navigation is finally obtained. The method is suitable for transfer alignment of the platform inertial navigation system under the dynamic condition.

Description

A kind of speed adds specific force coupling Transfer Alignment

Technical field

The present invention relates to boats and ships Platform Inertial Navigation System Transfer Alignment, specifically a kind of speed adds specific force coupling Transfer Alignment.

Background technology

Transfer Alignment is the technology for resolved vector Initial Alignment under moving pedestal condition.In the Transfer Alignment process, need to introduce the navigation information of carrier with high accuracy master inertial navigation system, and take this information as benchmark, by certain navigation, eliminate the alignment error factor between two cover systems, determine sub-inertial navigation course, attitude and speed accurately.Be directed to Platform Inertial Navigation System, because the attitude of platform-type inertial navigation is by the platform microsyn output, it,, because of factors such as synchronizer error, inertial navigation alignment error and carrier flexible deformations, is greatly affected alignment precision, the use of Chang Zuowei coarse alignment.Therefore for Platform Inertial Navigation System, traditional Transfer Alignment only has speeds match.And the high precision of Transfer Alignment and rapidity are the key factors of evaluation algorithms, because the speed and motor-driven of boats and ships is restricted, adopt traditional speeds match scheme that the Transfer Alignment time is greatly affected.

In the patent of invention file that application number is 200910031769.9, a kind of " the specific force difference-product of surely taking aim at gondola divides coupling Transfer Alignment and Combinated navigation method thereof " disclosed.The method has only adopted specific force difference-product minute coupling Transfer alignment algorithm.

Summary of the invention

The object of the present invention is to provide a kind of speed that can shorten the boats and ships Platform INS Transfer Alignment time to add specific force coupling Transfer Alignment.

The object of the present invention is achieved like this:

(1) sub-inertial navigation is before entering the navigation duty, and the bearer rate that main inertial navigation is provided, position and attitude information are as initial velocity and position and the attitude of sub-inertial navigation;

(2) in order to obtain the state error information of sub-inertial navigation system, set up the state equation of Kalman filter, obtain sub-inertial navigation state equation;

(3) speed of utilizing main inertial navigation to provide and than force information, obtain the observational error information of sub-inertial navigation speed and specific force, obtains observation equation;

(4) state equation and the observation equation according to (2), (3), set up, utilize Kalman filtering to carry out Transfer Alignment, completes the estimation of error of antithetical phrase inertial navigation.

Technical scheme in the patent document that the present invention is 200910031769.9 with application number is compared, and its application, the Transfer Alignment that uses are all different.

The beneficial effect of the inventive method is mainly manifested in: 1. the speed that the inertial device of usining resolves adds specific force as observed quantity, the accelerometer precision is greatly improved, and versus speed has been lacked integration one time, more direct on the impact of Kalman filtering than force information, for shortening, Transfer Alignment filtering chronergy is obvious; 2. meet Transfer Alignment high precision and rapidity under maneuvering condition; 3. be measurement information than force information, directly obtain in accelerometer, it is carried out, the researchs such as time delay and deflection deformation are relative simple.The present invention can estimate the platform error angle of sub-inertial navigation with respect to navigational system fast and accurately, and it is compensated to improve navigation accuracy, has the remarkable advantages such as speed is fast, precision is high, calculated amount is little.

The accompanying drawing explanation

Fig. 1 is overall flow figure of the present invention;

Fig. 2 is Kalman filtering recursion flow process;

Fig. 3 is the platform error angle estimation curve of utilizing two kinds of Transfer alignment algorithms to draw under hull linear uniform motion state;

Fig. 4 is the platform error angle estimation curve of utilizing two kinds of Transfer alignment algorithms to draw under the hull maneuvering condition.

Embodiment

In conjunction with Fig. 1, speed of the present invention adds specific force coupling Transfer alignment algorithm and comprises the following steps:

(1) sub-inertial navigation is before entering the navigation duty, and the bearer rate that main inertial navigation is provided, position and attitude information are as initial velocity and position and the attitude of sub-inertial navigation.If it is that n is geographic coordinate system that the platform of Platform INS Inertial requires the navigation coordinate of simulation, the actual platform coordinate of setting up is n '.Because the error of calculation, error source affect and execute the square error, n ' is that relative n has deviation angle φ ⁿ.

(2) in order to obtain the state error information of Platform Inertial Navigation System, set up the state equation of Kalman filter:

Choosing quantity of state is: $X={\left[\begin{array}{cccccccccc}{\mathrm{\δv}}_e& {\mathrm{\δv}}_n& {\mathrm{\φ}}_e& {\mathrm{\φ}}_n& {\mathrm{\φ}}_u& {\▿}_x& {\▿}_y& {\mathrm{\ϵ}}_x& {\mathrm{\ϵ}}_y& {\mathrm{\ϵ}}_z\end{array}\right]}^T,$ According to Platform Inertial Navigation System mechanization equation, can obtain:

$\left\{\begin{array}{c}\mathrm{\δ}{\stackrel{.}{v}}^n=f^n\×{\mathrm{\φ}}^n-(2{\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n)\×\mathrm{\δv}+{\▿}^n\\ \mathrm{\δ}{\stackrel{.}{\mathrm{\φ}}}^n=-{\mathrm{\ω}}_{\mathrm{in}}^n\×{\mathrm{\φ}}^n+\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{ie}}^n+\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{en}}^n+{\mathrm{\ϵ}}^n\\ \mathrm{\δ}{\stackrel{.}{\▿}}^n=0\\ \mathrm{\δ}{\stackrel{.}{\mathrm{\ϵ}}}^n=0\end{array}\right.$

Wherein

For boss's inertial navigation velocity error δ v ⁿProjection about the derivative of time t in n system; φ ⁿIt is the platform error angle between main inertial navigation and sub-inertial navigation; f ⁿBe the projection of main inertial navigation specific force output in n system; For the earth rotation angular speed, in navigation, be the projection of n,

For navigation is the projection of the turning rate of relative earth system in n system;

For the inclined to one side projection in n system of sub-inertial navigation accelerometer zero.

For the differential at attitude error angle between boss's inertial navigation,

For partially opening ideal value

Deviation, and ε ^sFor sub-inertial navigation gyroscopic drift.

State equation is: $\stackrel{.}{X}=\mathrm{AX}+\mathrm{BW}$

Wherein

$A=\left[\begin{array}{cccc}{A}_{11}& A_{12}& I_{2\×3}& 0_{2\×3}\\ A_{21}& A_{22}& 0_{3\×3}& I_{3\×3}\\ 0_{2\×3}& 0_{2\×3}& 0_{2\×3}& 0_{2\×3}\\ 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}\end{array}\right]$

$B=\left[\begin{array}{ccc}{I}_{2\×2}& 0_{2\×3}& 0_{2\×5}\\ 0_{3\×2}& I_{3\×3}& 0_{3\×5}\\ 0_{5\×2}& 0_{5\×3}& 0_{5\×5}\end{array}\right]$

In formula

$A_{12}=\left[\begin{array}{ccc}0& -f_u& f_n\\ f_u& 0& -f_e\end{array}\right]$

$A_{22}=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{inu}}^n& -{\mathrm{\&omega;}}_{\mathrm{inn}}^n\\ -{\mathrm{\&omega;}}_{\mathrm{inu}}^{\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="2013103949413100003DEST\_PATH\_IMAGE001.png,2013103949413100003DEST\_PATH\_IMAGE002.png"\; state="\{\{state\}\}">n</figure-callout>}}& 0& {\mathrm{\&omega;}}_{\mathrm{ine}}^n\\ {\mathrm{\&omega;}}_{\mathrm{inn}}^n& -{\mathrm{\&omega;}}_{\mathrm{ine}}^{\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="2013103949413100003DEST\_PATH\_IMAGE001.png,2013103949413100003DEST\_PATH\_IMAGE002.png"\; state="\{\{state\}\}">n</figure-callout>}}& 0\end{array}\right].$

The noise battle array is: W=[w _Axw _Ayw _{ε x}w _{ε y}w _Az0000 0] ^T

W wherein _Ax, w _AyFor accelerometer bias random white noise, w _{ε x}, w _{ε y}, w _{ε z}For the gyroscopic drift random white noise.

(3) speed of utilizing main inertial navigation to provide and than force information, the observational error information of acquisition speed and specific force, observation equation is as follows:

Z=HX+V

Take boss's inertial navigation as reference information, poor as observed quantity with speed and the specific force of the speed of sub-inertial navigation and specific force and main inertial navigation

Z=[δv _x δv _y δf _x δf _y] ^T

The pass of their every errors is:

$\left[\begin{array}{c}{Z}_1\\ Z_2\\ Z_3\\ Z_4\end{array}\right]=\left[\begin{array}{c}\mathrm{\&delta;}{v}_e\\ \mathrm{\&delta;}{v}_n\\ \mathrm{\&delta;}{f}_e\\ \mathrm{\&delta;}{f}_n\end{array}\right]+\left[\begin{array}{c}\mathrm{\&delta;}{v}_{\mathrm{eMINS}}\\ \mathrm{\&delta;}{v}_{\mathrm{nMINS}}\\ \mathrm{\&delta;}{f}_{\mathrm{eMINS}}\\ \mathrm{\&delta;}{f}_{\mathrm{nMINS}}\end{array}\right]$

δ v wherein _EMINS, δ v _NMINS, δ f _EMINS, δ f _NMINSIt is main inertial navigation measuring error.

Observing matrix $H=\left[\begin{array}{cccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -f_u& {\mathrm{<figure-callout\; id="1"\; label="f\; n"\; filenames="HDA0000376623030000012.png"\; state="\{\{state\}\}">f</figure-callout>}}_n& 1& 0& 0& 0& 0\\ 0& 0& f_u& 0& -{\mathrm{<figure-callout\; id="0"\; label="f\; e"\; filenames="2013103949413100003DEST\_PATH\_IMAGE001.png,2013103949413100003DEST\_PATH\_IMAGE002.png"\; state="\{\{state\}\}">f</figure-callout>}}_e& 0& 1& 0& 0& 0\end{array}\right]$

Measurement noise V=[w _Vxw _Vyw _Fxw _Fy].

(4) state equation and the observation equation that utilize step 3 and step 4 to set up, utilize Kalman filtering to carry out Transfer Alignment, completes the estimation of error of antithetical phrase inertial navigation, and the Kalman filtering formula of using is as follows:

${\hat{X}}_{k,k-1}={\mathrm{\&Phi;}}_{k,k-1}{\hat{X}}_{k-1}$

${\hat{X}}_k={\hat{X}}_{k,k-1}+K_k[Z_k-H_k{\hat{X}}_{k,k-1}]$

$K_k=P_{k,k-1}{H}_k^T[H_k{P}_{k,k-1}{H}_k^T+R_k{]}^{-1}$

$P_{k,k-1}={\mathrm{\&Phi;}}_{k,k-1}{P}_{k-1}{\mathrm{\&Phi;}}_{k,k-1}^T+{\mathrm{\&Gamma;}}_{k,k-1}{Q}_{k-1}{\mathrm{\&Gamma;}}_{k,k-1}^T$

$P_k=[I-K_k{H}_k]P_{k,k-1}[I-K_k{H}_k{]}^T+K_k{R}_k{K}_k^T$

P _k=[I-K _kH _k]P _k，k-1

$P_k^{-1}=P_{k,k-1}^{-1}+H_k^T{P}_k{H}_k$

Filtering recursion flow process is shown in Fig. 2.For Kalman filter, as gain matrix K _kWhile being reduced to a very low value, wave filter upgrades dependence less and less the measured value of one step, and this just means, the state variable of all not modelings can make filter divergence, in order to prevent the appearance of this phenomenon, gives Q _kDiagonal entry with little on the occasion of, this is called imaginary process noise, like this after repeatedly measuring, K _kReach the steady-state level of a non-zero, and the observation information of measurement after this is utilized.In addition, stable in order to make wave filter, can make the priori covariance designed a model accomplish than normal value is large.

Below in conjunction with accompanying drawing, the present invention is done further and describes.The embodiment of the present invention is used for the present invention that explains, rather than limits the invention, and in the protection domain of spirit of the present invention and claim, any modification and change that the present invention is made, all fall into protection scope of the present invention.

Embodiment

As shown in Figure 3, Figure 4, estimation and evaluated error to Transfer Alignment under following starting condition have been carried out emulation, and simulation result has been carried out analyzing relatively.

Starting condition:

1) suppose that main inertial navigation is error free, the lever arm effect error is fully compensated;

2) carrier initial position: 117 ° of longitudes, 39 °, latitude.Carrier initial attitude angle (pitching, rolling, course) is respectively: 0 °, and 0 °, 45 °; Sub-Inertial navigation platform initial error angle is ψ _x=5 ', ψ _y=5 ', ψ _z=5 ';

3) sub-inertial navigation gyro drift be 0.01 (°)/h, the random drift noise be 0.001 (°)/h; The normal value zero of accelerometer is 1 * 10 partially ^-4G, random zero inclined to one side noise is 1 * 10 ^-5G;

4) the state estimation initial value is 0; Initial variance battle array P ₀The above-mentioned inertial device error of parameter foundation is arranged, and guarantees that the Kalman filters the optimality of estimation,

P ₀=diag{(0.1m／s) ²(0.1m／s) ²(5′) ²(5′) ²(5′) ²(1×10 ^-4g) ²(1×10 ^-4g) ²(1°×10 ^-3) ²(1°×10 ^-3) ²(1°×10 ^-3) ²)；

5) to be that carrier is done at the uniform velocity motor-driven for Fig. 3, at first with the speed linear uniform motion of 10m/s.It is motor-driven that Fig. 4 is that carrier is done serpentine, at first with the speed linear uniform motion of 10m/s, the motor-driven turning rate of serpentine be 1 (°)/s.

Analyze relatively:

Fig. 3 provides boats and ships under state at the uniform velocity, the platform error angle estimation curve of utilizing two kinds of Transfer alignment algorithms to draw, and wherein solid line is the evaluated error value of speeds match to the platform error angle, dotted line is that speed adds the evaluated error value of specific force coupling to the platform error angle.By Fig. 3, found out under boats and ships are done at the uniform velocity maneuvering condition, speed add the specific force matching way for estimated time at lateral error angle in 10s, and precision is high, the estimated time at azimuthal error angle is in 80s, but precision is not high.As seen from Figure 4, do serpentine at carrier motor-driven, have had the estimated accuracy at azimuthal error angle and estimated time and significantly improved, so speed adds certain motor-driven of specific force coupling needs and reaches satisfied effect.Simultaneously comparison diagram 3 and Fig. 4 medium velocity add the estimation curve of specific force coupling and speeds match, can find out do motor-driven after, speed adds ratio and mates and obtained estimated time for the azimuthal error angle obvious lifting.

Claims (5)

1. a speed adds specific force coupling Transfer alignment algorithm, it is characterized in that comprising the steps:

(1) sub-inertial navigation is before entering the navigation duty, and the bearer rate that main inertial navigation is provided, position and attitude information are as initial velocity and position and the attitude of sub-inertial navigation;

(2) set up the state equation of Kalman filter, obtain the state equation of sub-inertial navigation;

(3) speed of utilizing main inertial navigation to provide and than force information, obtain the observational error information of sub-inertial navigation speed and specific force, obtains observation equation;

(4) state equation and the observation equation according to (2), (3), set up, utilize Kalman filtering to carry out Transfer Alignment, completes the estimation of error of antithetical phrase inertial navigation, obtains the estimated value at sub-ins error angle.

2. speed according to claim 1 adds specific force coupling Transfer alignment algorithm, it is characterized in that the described state equation of setting up Kalman filter further comprises:

Choosing quantity of state is: $X={\left[\begin{array}{cccccccccc}{\mathrm{\&delta;v}}_e& {\mathrm{\&delta;v}}_n& {\mathrm{\&phi;}}_e& {\mathrm{\&phi;}}_n& {\mathrm{\&phi;}}_u& {\&dtri;}_x& {\&dtri;}_y& {\mathrm{\&epsiv;}}_x& {\mathrm{\&epsiv;}}_y& {\mathrm{\&epsiv;}}_z\end{array}\right]}^T,$ According to Platform Inertial Navigation System mechanization equation, obtain:

$\left\{\begin{array}{c}\mathrm{\&delta;}{\stackrel{.}{v}}^n=f^n\&times;{\mathrm{\&phi;}}^n-({2\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)\&times;\mathrm{\&delta;v}+{\&dtri;}^n\\ \mathrm{\&delta;}{\stackrel{.}{\mathrm{\&phi;}}}^n={-\mathrm{\&omega;}}_{\mathrm{in}}^n\&times;{\mathrm{\&phi;}}^n+{\mathrm{\&delta;\&omega;}}_{\mathrm{ie}}^n+\mathrm{\&delta;}{\mathrm{\&omega;}}_{\mathrm{en}}^n+{\mathrm{\&epsiv;}}^n\\ \mathrm{\&delta;}{\stackrel{.}{\&dtri;}}^n=0\\ \mathrm{\&delta;}{\stackrel{.}{\mathrm{\&epsiv;}}}^n=0\end{array}\right.$

Wherein For boss's inertial navigation velocity error δ v ⁿProjection about the derivative of time t in n system; φ ⁿIt is the platform error angle between main inertial navigation and sub-inertial navigation; f ⁿBe the projection of main inertial navigation specific force output in n system;

For the earth rotation angular speed, in navigation, be the projection of n,

For navigation is the projection of the turning rate of relative earth system in n system;

For the inclined to one side projection in n system of sub-inertial navigation accelerometer zero;

For the differential at attitude error angle between boss's inertial navigation,

For partially opening ideal value

Deviation, and ε ^sFor sub-inertial navigation gyroscopic drift;

State equation is: $\stackrel{.}{X}=\mathrm{AX}+\mathrm{BW}$

Wherein

$A=\left[\begin{array}{cccc}{A}_{11}& A_{12}& I_{2\&times;3}& 0_{2\&times;3}\\ A_{21}& A_{22}& 0_{3\&times;3}& I_{3\&times;3}\\ 0_{2\&times;3}& 0_{2\&times;3}& 0_{2\&times;3}& 0_{2\&times;3}\\ 0_{3\&times;3}& 0_{3\&times;3}& 0_{3\&times;3}& 0_{3\&times;3}\end{array}\right]$

$B=\left[\begin{array}{ccc}{I}_{2\&times;2}& 0_{2\&times;3}& 0_{2\&times;5}\\ 0_{3\&times;2}& I_{3\&times;3}& 0_{3\&times;5}\\ 0_{5\&times;2}& 0_{5\&times;3}& 0_{5\&times;5}\end{array}\right]$

In formula

$A_{12}=\left[\begin{array}{ccc}0& {-f}_u& f_n\\ f_u& 0& -f_e\end{array}\right]$

$A_{22}=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{inu}}^n& -{\mathrm{\&omega;}}_{\mathrm{inn}}^n\\ {-\mathrm{\&omega;}}_{\mathrm{inu}}^n& 0& {\mathrm{\&omega;}}_{\mathrm{ine}}^n\\ {\mathrm{\&omega;}}_{\mathrm{inn}}^n& {-\mathrm{\&omega;}}_{\mathrm{ine}}^n& 0\end{array}\right].$

The system noise acoustic matrix is: W=[w _Axw _Ayw _{ε x}w _{ε y}w _Az0000 0] ^T

W wherein _Ax, w _AyFor accelerometer bias random white noise, w _{ε x}, w _{ε y}, w _{ε z}For the gyroscopic drift random white noise.

3. speed according to claim 1 and 2 adds specific force coupling Transfer alignment algorithm, it is characterized in that described observation equation is:

Z=HX+V

Take boss's inertial navigation as reference information, and the speed of use sub-platform inertial navigation and speed and the specific force of specific force and main Platform INS are poor as observed quantity

Z=[δv _x δv _y δf _x δf _y] ^T

The pass of their every errors is:

$\left[\begin{array}{c}{Z}_1\\ Z_2\\ Z_3\\ Z_4\end{array}\right]=\left[\begin{array}{c}{\mathrm{\&delta;v}}_e\\ {\mathrm{\&delta;v}}_n\\ {\mathrm{\&delta;f}}_e\\ {\mathrm{\&delta;f}}_n\end{array}\right]+\left[\begin{array}{c}{\mathrm{\&delta;v}}_{\mathrm{eMINS}}\\ {\mathrm{\&delta;v}}_{\mathrm{nMINS}}\\ {\mathrm{\&delta;f}}_{\mathrm{eMINS}}\\ {\mathrm{\&delta;f}}_{\mathrm{nMINS}}\end{array}\right]$

δ v wherein _EMINS, δ v _NMINS, δ f _EMINS, δ f _NMINSIt is main inertial navigation measuring error;

Observing matrix $H=\left[\begin{array}{cccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& {-f}_u& f_n& 1& 0& 0& 0& 0\\ 0& 0& f_u& 0& {-f}_e& 0& 1& 0& 0& 0\end{array}\right]$

Measurement noise V=[w _Vxw _Vyw _Fxw _Fy].

4. speed according to claim 1 and 2 adds specific force coupling Transfer alignment algorithm, it is characterized in that the formula of Kalman filtering is:

${\hat{X}}_{k,k-1}={\mathrm{\&Phi;}}_{k,k-1}{\hat{X}}_{k-1}$

${\hat{X}}_k={\hat{X}}_{k,k-1}+K_k[Z_k-H_k{\hat{X}}_{k,k-1}]$

$K_k=P_{k,k-1}{H}_k^T{[H_k{P}_{k,k-1}{H}_k^T+R_k]}^{-1}$

$P_{k,k-1}={\mathrm{\&Phi;}}_{k,k-1}{P}_{k-1}{\mathrm{\&Phi;}}_{k,k-1}^T+{\mathrm{\&Gamma;}}_{k,k-1}{Q}_{k-1}{\mathrm{\&Gamma;}}_{k,k-1}^T$

$P_k=[I-K_k{H}_k]P_{k,k-1}{[I-K_k{H}_k]}^T+K_k{R}_k{K}_k^T$

P _k＝[I-K _kH _k]P _k，k-1

$P_k^{-1}=P_{k,k-1}^{-1}+H_k^T{R}_k{H}_k.$

5. speed according to claim 3 adds specific force coupling Transfer alignment algorithm, it is characterized in that the formula of Kalman filtering is:

${\hat{X}}_{k,k-1}={\mathrm{\&Phi;}}_{k,k-1}{\hat{X}}_{k-1}$

${\hat{X}}_k={\hat{X}}_{k,k-1}+K_k[Z_k-H_k{\hat{X}}_{k,k-1}]$

$K_k=P_{k,k-1}{H}_k^T{[H_k{P}_{k,k-1}{H}_k^T+R_k]}^{-1}$

$P_{k,k-1}={\mathrm{\&Phi;}}_{k,k-1}{P}_{k-1}{\mathrm{\&Phi;}}_{k,k-1}^T+{\mathrm{\&Gamma;}}_{k,k-1}{Q}_{k-1}{\mathrm{\&Gamma;}}_{k,k-1}^T$

$P_k=[I-K_k{H}_k]P_{k,k-1}{[I-K_k{H}_k]}^T+K_k{R}_k{K}_k^T$

P _k=[I-K _kH _k]P _k，k-1

$P_k^{-1}=P_{k,k-1}^{-1}+H_k^T{R}_k{H}_k.$

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