CN103363989B - Estimation and error compensation method for inner lever arm of strapdown inertial navigation system - Google Patents

Abstract

The invention belongs to the technical field of inertial navigation, and relates to an estimation and error compensation method for an inner lever arm of a strapdown inertial navigation system. The method comprises the steps of initially aligning, estimating parameters of the inner lever arm, and compensating the error of the inner lever arm. According to the estimation and error compensation method for the inner lever arm of the strapdown inertial navigation system, the inner lever arm of the strapdown inertial navigation system can be estimated, further, the error compensation can be performed on the inner lever arm according to the estimated inner lever arm, and thus the navigation precision of the strapdown inertial navigation system in a dynamic environment can be improved.

Description

A kind of estimation of inner lever arm of strapdown inertial navigation system and error compensating method

Technical field

The invention belongs to technical field of inertial, it is related to a kind of estimation of inner lever arm of strapdown inertial navigation system and mends with error Compensation method.

Background technology

In strap-down inertial technical field, prior art often regards inertial measurement cluster as " point measurement assembly ", Thus only considering to be somebody's turn to do the lever arm effect error between navigational reference point, i.e. outer lever arm error on " point measurement assembly " and carrier.

In fact, when the barycenter of SINS and the barycenter of three accelerometers are misaligned, then inertial navigation system Lever arm in system presence, if SINS has angular movement, will cause in accelerometer output and produce one and interior lever arm Length and the proportional centripetal disturbing acceleration of SINS angular speed square product, and one with interior lever arm length and victory The proportional tangential disturbing acceleration of connection inertial navigation system angular acceleration product, the two is equivalent to interior lever arm error, and it can reduce victory The navigation accuracy of connection inertial navigation.

In SINS, three accelerometers are arranged on the orthogonal bracket of three axles, and this necessarily brings inertial navigation system System barycenter and three accelerometer barycenter are misaligned, thus lever arm error in existing, for raising system leading under dynamic environment Boat precision, needs lever arm estimation error and compensation method in research badly.

Content of the invention

The technical problem to be solved in the invention is: proposes a kind of estimation of inner lever arm of strapdown inertial navigation system and error compensation Method, the method can estimate the interior lever arm of SINS, and then carries out interior lever arm by mistake using the interior lever arm estimating Difference compensates, and improves navigation accuracy under dynamic environment for the SINS.

Technical scheme is as described below:

A kind of estimation of inner lever arm of strapdown inertial navigation system and error compensating method, comprise the following steps: step one: initially right Accurate；Step 2: lever arm parameter in estimation；Step 3: lever arm error in compensation.

In step one, SINS is arranged on the axle three-axle table mutually orthogonal with axle, SINS Three orthogonal direction of principal axis of body coordinate system and turntable are consistent.

In step 2, turntable is controlled to make SINS simultaneously around three axial period rotations of turntable, using with speed Degree error is that the kalman filtering of observed quantity estimates, correlation formula is as follows to the interior lever arm of SINS:

Quantity of state: $x={\left[\begin{array}{cc}{x}_1^t& x_2^t\end{array}\right]}^t,$ Wherein

$x_1={\left[\begin{array}{cccccccccccc}\mathrm{\δ}{v}_n& \mathrm{\δ}{v}_u& \mathrm{\δ}{v}_e& {\mathrm{\φ}}_n& {\mathrm{\φ}}_u& {\mathrm{\φ}}_e& {\mathrm{\ϵ}}_x& {\mathrm{\ϵ}}_y& {\mathrm{\ϵ}}_z& {\▿}_x& {\▿}_y& {\▿}_z\end{array}\right]}^t,$

x₂=[r_1xr_1yr_1zr_2xr_2yr_2zr_3xr_3yr_3z]^t,

Error state equation is:Wherein

$a=\left[\begin{array}{cc}{a}_1& a_2\\ 0_{9\×14}& 0_{9\×9}\end{array}\right],$

a₁It is and x₁Corresponding sytem matrix；

$a_2={\left[\begin{array}{cccc}-c_{11}({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)& -c_{21}({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)& -c_{31}({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)& \\ c_{11}(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{21}(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{31}(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& \\ c_{11}({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{21}({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{31}({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& \\ c_{12}({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{22}({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{32}({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& \\ -c_{12}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)& -c_{22}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)& -c_{32}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)& 0_{9\×11}\\ c_{12}(-{\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{22}(-{\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{33}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& \\ c_{13}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{23}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{33}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& \\ c_{13}({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{23}({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{33}({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& \\ -c_{12}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)& -c_{22}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)& -c_{32}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)& \end{array}\right]}^t,$

Observed quantity is: z=[δ v_nδv_uδv_e]^t,

In above-mentioned formula:

δv_n、δv_u、δv_eVelocity error for SINS；

φ_n、φ_u、φ_eMisalignment for SINS；

ε_x、ε_y、ε_zInclined for the gyro zero of SINS；

Accelerometer bias for SINS；

r_1xInterior lever arm component for the body coordinate system x-axis in SINS for the x-axis accelerometer barycenter；

r_1yInterior lever arm component for the body coordinate system y-axis in SINS for the x-axis accelerometer barycenter；

r_1zInterior lever arm component for the body coordinate system z-axis in SINS for the x-axis accelerometer barycenter；

r_2xInterior lever arm component for the body coordinate system x-axis in SINS for the y-axis accelerometer barycenter；

r_2yInterior lever arm component for the body coordinate system y-axis in SINS for the y-axis accelerometer barycenter；

r_2zInterior lever arm component for the body coordinate system z-axis in SINS for the y-axis accelerometer barycenter；

r_3xInterior lever arm component for the body coordinate system x-axis in SINS for the z-axis accelerometer barycenter；

r_3yInterior lever arm component for the body coordinate system y-axis in SINS for the z-axis accelerometer barycenter；

r_3zInterior lever arm component for the body coordinate system z-axis in SINS for the z-axis accelerometer barycenter；

$c_b^n=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right]$ For SINS attitude matrix；

${\mathrm{\ω}}_{\mathrm{ib}}^b=\left[\begin{array}{ccc}{\mathrm{\ω}}_x& {\mathrm{\ω}}_y& {\mathrm{\ω}}_z\end{array}\right]$ The carrier angular speed recording for gyro；

ω_xAngular speed for the measurement of x-axis gyroscope；

ω_yAngular speed for the measurement of y-axis gyroscope；

ω_zAngular speed for the measurement of z-axis gyroscope；

For angular velocity omega_xDifferential, represent x-axis angular acceleration；

For angular velocity omega_yDifferential, represent y-axis angular acceleration；

For angular velocity omega_zDifferential, represent z-axis angular acceleration.

In step 3, carry out interior lever arm error compensation using following formula:

$f_{\mathrm{ib}}^b={\tilde{f}}_{\mathrm{ib}}^b-\mathrm{\δ}{f}_r$

Wherein,Carrier acceleration for the accelerometer measures before compensating；

Carrier acceleration for the accelerometer measures after compensating；

$\mathrm{\δ}{f}_r=\left[\begin{array}{c}-({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)r_{1x}+(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)r_{1y}+({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)r_{1z}\\ ({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)r_{2x}-({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)r_{2y}+(-{\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)r_{2z}\\ (-{\stackrel{\·}{\mathrm{\ω}}}_y{\mathrm{\ω}}_x{\mathrm{\ω}}_z)r_{3x}+({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)r_{3y}-({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)r_{3z}\end{array}\right]$ For interior lever arm error.

Preferably, in Periodic Rotating described in step 2, each axle rotational steps controls in 60 °～180 ° scopes Interior, such as 90 °；Rotating speed controls in the range of 5 °/s～50 °/s, such as 10 °/s；TRH controls between 5min～10min, As 8min.

Beneficial effects of the present invention are；

The method of the present invention passes through to estimate inner lever arm of strapdown inertial navigation system, lever arm error in calculating, and then internal lever arm is by mistake Difference compensates, and improves navigation accuracy under dynamic environment for the SINS.

Specific embodiment

By analysis in lever arm error produce mechanism it is proposed that a kind of estimation of the interior lever arm based on kalman filtering with Error compensating method, the method can be in SINS simultaneously after its three sensitive axes rotations, using kalman filtering Entirely estimate the interior lever arm of SINS, and then carry out interior lever arm error compensation using the interior lever arm estimating, improve prompt Connection navigation accuracy under dynamic environment for the inertial navigation system.

The method of the present invention comprises the steps:

Step one: SINS is arranged on the axle three-axle table mutually orthogonal with axle, SINS body Three orthogonal direction of principal axis of coordinate system and turntable are consistent, complete initially to be aligned.Described initial be aligned is known to the skilled person General knowledge.

Step 2: after the completion of initial be aligned, control turntable to make SINS simultaneously around three axial periods of turntable Rotation, each axle rotational steps controls in the range of 60 °～180 °, and rotating speed controls in the range of 5 °/s～50 °/s, when always rotating Between control between 5min～10min, filtered in SINS using the kalman with velocity error as observed quantity Lever arm is estimated, correlation formula is as follows:

Quantity of state: $x={\left[\begin{array}{cc}{x}_1^t& x_2^t\end{array}\right]}^t,$ Wherein

$x_1={\left[\begin{array}{cccccccccccc}\mathrm{\δ}{v}_n& \mathrm{\δ}{v}_u& \mathrm{\δ}{v}_e& {\mathrm{\φ}}_n& {\mathrm{\φ}}_u& {\mathrm{\φ}}_e& {\mathrm{\ϵ}}_x& {\mathrm{\ϵ}}_y& {\mathrm{\ϵ}}_z& {\▿}_x& {\▿}_y& {\▿}_z\end{array}\right]}^t$

x₂=[r_1xr_1yr_1zr_2xr_2yr_2zr_3xr_3yr_3z]^t

Error state equation is:Wherein

$a=\left[\begin{array}{cc}{a}_1& a_2\\ 0_{9\×14}& 0_{9\×9}\end{array}\right],$

a₁It is and x₁Corresponding sytem matrix；

$a_2={\left[\begin{array}{cccc}-c_{11}({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)& -c_{21}({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)& -c_{31}({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)& \\ c_{11}(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{21}(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{31}(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& \\ c_{11}({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{21}({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{31}({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& \\ c_{12}({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{22}({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{32}({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& \\ -c_{12}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)& -c_{22}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)& -c_{32}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)& 0_{9\×11}\\ c_{12}(-{\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{22}(-{\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{33}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& \\ c_{13}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{23}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{33}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& \\ c_{13}({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{23}({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{33}({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& \\ -c_{12}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)& -c_{22}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)& -c_{32}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)& \end{array}\right]}^t$

Observed quantity is: z=[δ v_nδv_uδv_e]^t.

In above-mentioned formula:

δv_n、δv_u、δv_eVelocity error for SINS；

φ_n、φ_u、φ_eMisalignment for SINS；

ε_x、ε_y、ε_zInclined for the gyro zero of SINS；

Accelerometer bias for SINS；

r_1xInterior lever arm component for the body coordinate system x-axis in SINS for the x-axis accelerometer barycenter；

r_1yInterior lever arm component for the body coordinate system y-axis in SINS for the x-axis accelerometer barycenter；

r_1zInterior lever arm component for the body coordinate system z-axis in SINS for the x-axis accelerometer barycenter；

r_2xInterior lever arm component for the body coordinate system x-axis in SINS for the y-axis accelerometer barycenter；

r_2yInterior lever arm component for the body coordinate system y-axis in SINS for the y-axis accelerometer barycenter；

r_2zInterior lever arm component for the body coordinate system z-axis in SINS for the y-axis accelerometer barycenter；

r_3xInterior lever arm component for the body coordinate system x-axis in SINS for the z-axis accelerometer barycenter；

r_3yInterior lever arm component for the body coordinate system y-axis in SINS for the z-axis accelerometer barycenter；

r_3zInterior lever arm component for the body coordinate system z-axis in SINS for the z-axis accelerometer barycenter；

$c_b^n=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right]$ For SINS attitude matrix；

${\mathrm{\ω}}_{\mathrm{ib}}^b=\left[\begin{array}{ccc}{\mathrm{\ω}}_x& {\mathrm{\ω}}_y& {\mathrm{\ω}}_z\end{array}\right]$ The carrier angular speed recording for gyro；

ω_xAngular speed for the measurement of x-axis gyroscope；

ω_yAngular speed for the measurement of y-axis gyroscope；

ω_zAngular speed for the measurement of z-axis gyroscope；

For angular velocity omega_xDifferential, represent x-axis angular acceleration；

For angular velocity omega_yDifferential, represent y-axis angular acceleration；

For angular velocity omega_zDifferential, represent z-axis angular acceleration.

Step 3: interior lever arm error compensation

Need accelerometer output is compensated after estimating interior lever arm, compensation method is as follows:

$f_{\mathrm{ib}}^b={\tilde{f}}_{\mathrm{ib}}^b-\mathrm{\δ}{f}_r$

Wherein,Carrier acceleration for the accelerometer measures before compensating；

Carrier acceleration for the accelerometer measures after compensating；

$\mathrm{\δ}{f}_r=\left[\begin{array}{c}-({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)r_{1x}+(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)r_{1y}+({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)r_{1z}\\ ({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)r_{2x}-({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)r_{2y}+(-{\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)r_{2z}\\ (-{\stackrel{\·}{\mathrm{\ω}}}_y{\mathrm{\ω}}_x{\mathrm{\ω}}_z)r_{3x}+({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)r_{3y}-({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)r_{3z}\end{array}\right]$ For interior lever arm error.

Carry out estimation and the error compensation of interior lever arm using certain type Ring Laser Gyroscope SINS in laboratory, be embodied as walking Suddenly as follows:

The first step: first Ring Laser Gyroscope SINS is arranged on the axle three-axle table mutually orthogonal with axle, strapdown is used to Three orthogonal direction of principal axis of guiding systems body coordinate system and turntable are consistent, complete initially to be aligned.

Second step: after the completion of initial be aligned, make turntable simultaneously around interior, neutralization outer shroud Periodic Rotating, each axle rotation amplitude For 90 °, rotating speed is 10 °/s, and TRH is 8min, using the kalman filtering with velocity error as observed quantity, strapdown is used to The interior lever arm of guiding systems is estimated, the interior lever arm value estimating this SINS is

r_1x=-0.064m, r_1y=-0.016m, r_1z=0.094m；

r_2x=-0.061m, r_2y=-0.094m, r_2z=0.094m；

r_3x=-0.060m, r_3y=-0.054m, r_3z=0.097m.

3rd step: after estimating interior lever arm, lever arm error delta f in calculating_r, and then realize to lever arm in accelerometer by mistake Difference compensates.

The validity of the interior lever arm error estimated to verify and compensate, is carried out using above-mentioned SINS data Off-line simulation checking test.Carry out after error compensation with the above-mentioned interior lever arm estimating, inertial navigation system horizontal velocity before and after rotation Error change is less than 0.2m/s, and in uncompensation during lever arm error, before and after rotation, inertial navigation system horizontal velocity error change exceedes In 0.5m/s, and rotation process, horizontal velocity error rises appreciably.This comparing result illustrate the method estimate and compensate Validity.

Claims (4)

1. a kind of estimation of inner lever arm of strapdown inertial navigation system and error compensating method it is characterised in that: comprise the following steps:

Step one: initial be aligned；

Step 2: lever arm parameter in estimation；

Step 3: lever arm error in compensation.

In step one, SINS is arranged on the axle three-axle table mutually orthogonal with axle, SINS body is sat Mark system is consistent with three orthogonal direction of principal axis of turntable；

In step 2, turntable is controlled to make SINS simultaneously around three axial period rotations of turntable, using with speed by mistake Difference estimates, correlation formula is as follows for the kalman filtering of observed quantity to the interior lever arm of SINS:

Quantity of state: $x={\left[\begin{array}{cc}{x}_1^t& x_2^t\end{array}\right]}^t,$ Wherein

$x_1={\left[\begin{array}{cccccccccccc}{\mathrm{\δv}}_n& {\mathrm{\δv}}_u& {\mathrm{\δv}}_e& {\mathrm{\φ}}_n& {\mathrm{\φ}}_u& {\mathrm{\φ}}_e& {\mathrm{\ϵ}}_x& {\mathrm{\ϵ}}_y& {\mathrm{\ϵ}}_z& {\▿}_x& {\▿}_y& {\▿}_z\end{array}\right]}^t,$

x₂=[r_1xr_1yr_1zr_2xr_2yr_2zr_3xr_3yr_3z]^t,

Error state equation is:Wherein

$a=\left[\begin{array}{cc}{a}_1& a_2\\ 0_{9\×14}& 0_{9\×9}\end{array}\right],$

a₁It is and x₁Corresponding sytem matrix；

$a_2={\left[\begin{array}{cccc}-c_{11}({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)& -c_{21}({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)& -c_{31}({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)& \\ c_{11}(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{21}(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{31}(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& \\ c_{11}({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{21}({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{31}({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& \\ c_{12}({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{22}({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& c_{32}({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)& \\ -c_{12}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)& -c_{22}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)& -c_{32}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)& 0_{9\×11}\\ c_{12}(-{\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{22}(-{\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{33}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& \\ c_{13}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{23}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& c_{33}(-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)& \\ c_{13}({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{23}({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& c_{33}({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)& \\ -c_{12}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)& -c_{22}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)& -c_{32}({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)& \end{array}\right]}^t,$

Observed quantity is: z=[δ v_nδv_uδv_e]^t,

In above-mentioned formula:

δv_n、δv_u、δv_eVelocity error for SINS；

φ_n、φ_u、φ_eMisalignment for SINS；

e_x、e_y、e_zInclined for the gyro zero of SINS；

Accelerometer bias for SINS；

r_1xInterior lever arm component for the body coordinate system x-axis in SINS for the x-axis accelerometer barycenter；

r_1yInterior lever arm component for the body coordinate system y-axis in SINS for the x-axis accelerometer barycenter；

r_1zInterior lever arm component for the body coordinate system z-axis in SINS for the x-axis accelerometer barycenter；

r_2xInterior lever arm component for the body coordinate system x-axis in SINS for the y-axis accelerometer barycenter；

r_2yInterior lever arm component for the body coordinate system y-axis in SINS for the y-axis accelerometer barycenter；

r_2zInterior lever arm component for the body coordinate system z-axis in SINS for the y-axis accelerometer barycenter；

r_3xInterior lever arm component for the body coordinate system x-axis in SINS for the z-axis accelerometer barycenter；

r_3yInterior lever arm component for the body coordinate system y-axis in SINS for the z-axis accelerometer barycenter；

r_3zInterior lever arm component for the body coordinate system z-axis in SINS for the z-axis accelerometer barycenter；

$c_b^n=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right]$ For SINS attitude matrix；

${\mathrm{\ω}}_{ib}^b=\left[\begin{array}{ccc}{\mathrm{\ω}}_x& {\mathrm{\ω}}_y& {\mathrm{\ω}}_z\end{array}\right]$ The carrier angular speed recording for gyro；

ω_xAngular speed for the measurement of x-axis gyroscope；

ω_yAngular speed for the measurement of y-axis gyroscope；

ω_zAngular speed for the measurement of z-axis gyroscope；

For angular velocity omega_xDifferential, represent x-axis angular acceleration；

For angular velocity omega_yDifferential, represent y-axis angular acceleration；

For angular velocity omega_zDifferential, represent z-axis angular acceleration.

2. the estimation of inner lever arm of strapdown inertial navigation system according to claim 1 and error compensating method it is characterised in that:

In Periodic Rotating described in step 2, each axle rotational steps controls in the range of 60 °～180 °, and rotating speed controls in 5 °/s In the range of～50 °/s, TRH controls between 5min～10min.

3. the estimation of inner lever arm of strapdown inertial navigation system according to claim 2 and error compensating method it is characterised in that:

In Periodic Rotating described in step 2, each axle rotation amplitude is 90 °, and rotating speed is 10 °/s, and TRH is 8min.

4. the estimation of inner lever arm of strapdown inertial navigation system according to claim 1 and error compensating method it is characterised in that:

In step 3, carry out interior lever arm error compensation using following formula:

$f_{ib}^b={\tilde{f}}_{ib}^b-{\mathrm{\δf}}_r$

Wherein,Carrier acceleration for the accelerometer measures before compensating；

Carrier acceleration for the accelerometer measures after compensating；

${\mathrm{\δf}}_r=\left[\begin{array}{c}-({\mathrm{\ω}}_y^2+{\mathrm{\ω}}_z^2)r_{1x}+(-{\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)r_{1y}+({\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)r_{1z}\\ ({\stackrel{\·}{\mathrm{\ω}}}_z+{\mathrm{\ω}}_x{\mathrm{\ω}}_y)r_{2x}-({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_z^2)r_{2y}+(-{\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)r_{2z}\\ (-{\stackrel{\·}{\mathrm{\ω}}}_y+{\mathrm{\ω}}_x{\mathrm{\ω}}_z)r_{3x}+({\stackrel{\·}{\mathrm{\ω}}}_x+{\mathrm{\ω}}_y{\mathrm{\ω}}_z)r_{3y}-({\mathrm{\ω}}_x^2+{\mathrm{\ω}}_y^2)r_{3z}\end{array}\right]$ For interior lever arm error.