CN101294811A - Strapdown inertial navigation system adopting strange perturbation method for taper cone error and rowing error compensation - Google Patents

Abstract

The invention discloses a strap-down inertial navigation system which compensates the coning error and the sculling error by adopting a method of singular perturbation. The strap-down inertial navigation system is characterized in that a singular perturbation model for compensating the coning error is embedded between an inertial measurement unit and an attitude calculation unit; and a singular perturbation model for compensating the sculling error is embedded between the inertial measurement unit and the navigation calculation unit. The compensation is a perturbation process in which the movement of a carrier changes in a sampling period T and utilizes the actual output value of an inertial unit at a starting sampling point to establish a forcing singular perturbation model. According to the forcing singular perturbation model, the coning error and the sculling error are compensated, and the clock diagram of attitude update and the amount of speed update in the sampling period are obtained. Through adjustment of the amounts of the attitude update and the speed update with close-to-precision variable parameters, the requirement for increasing the algorithmic precision of the calculation units of the strap-down inertial navigation system is met.

Description

Adopt singular perturbation method to carry out coning error and the strapdown inertial navitation system (SINS) of the error compensation of rowing the boat

Technical field

The present invention relates to that a kind of (the compensation deals method of the strap-down inertial measuring accuracy under 6～2000Hz) is more particularly said, is meant a kind ofly to adopt singular perturbation method to carry out coning error and row the boat the strapdown inertial navitation system (SINS) of error compensation to high dynamic environment.

Background technology

Strapdown inertial navitation system (SINS) has generally comprised (1) inertia assembly; (2) inertia component signals processing unit; (3) attitude calculation unit; (4) navigation calculating unit.The inertia assembly is made up of three gyros and three accelerometers.Inertia assembly and inertia component signals processing unit are installed in the stage body of six shapes together, form Inertial Measurement Unit.The purpose that is installed in the stage body is to guarantee that three measurement axis of inertia assembly are mutually orthogonal.Inertial Measurement Unit is installed on the carrier by vibroshock, is used for part and eliminates the influence of carrier vibration to Inertial Measurement Unit.Inertia component signals processing unit is mainly finished mould/number conversion and to the Filtering Processing of signal; Attitude calculation unit is used to calculate the attitude of carrier; The navigation calculating unit is used to calculate the speed and the position of carrier.

Singular perturbation theory originates from the research of earlier 1900s prandtl convection cell mechanics circumferential motion problem.Singular perturbation theory is the singular perturbation problem that high-order is contained fast realization elephant, and the problem that changes into the change slowly (ignoring fast change part) of low order is found the solution, and obtains having the analytic solution of arbitrary accuracy by introduce the boundary layer correction in the different time yardstick then.Singular perturbation theory be applicable to the ubiquitous linearity that comprises the speed phenomenon in the actual life, Kind of Nonlinear Singular Perturbation Problems and normal, partial differential equation is described decides the analysis of the problem of separating etc. and find the solution.

Savage, P.G.Strapdown Inertial Navigation Integration AlgorithmDesign Part 1:Attitude Algorithms[J] .Journal of Guidance, Control, andDynamics, 1998,21 (1): disclose a kind of equivalent rotating vector posture renewal algorithm among the 19-28.Below of the present invention, abbreviate document one as in the explanation.

Savage, P.G.Strapdown Inertial Navigation Integration AlgorithmDesign Part 2:Velocity and Position Algorithms[J] .Journal of Guidance, Control, and Dynamics, 1998,21 (2): disclose a kind of Velocity Updating algorithm among the 208-220.Below of the present invention, abbreviate document two as in the explanation.

" the strapdown inertial navitation system (SINS) principle " that Chen Zhe showed published for the first time in 1986 12.In the P148 page or leaf formula that a kind of parsing obtains the strapdown matrix is disclosed referring to the P145 page or leaf.Below of the present invention, abbreviate document three as in the explanation.

At present, research dynamic at height to strapdown inertial navitation system (SINS), the high precision navigation can be divided into both direction substantially, emphasizes to improve hardware performance for one, adopts high-precision optics inertance element and high performance signal processor, design high speed acquisition device etc.; Another studies new navigation algorithm emphatically, improves the precision of navigation algorithm in complex environment.Both respectively have its characteristics, and the problem of its existence is also respectively arranged.Improve the response speed that hardware performance can improve inertia system, but be limited, and cost is than higher the influence of inertia system precision; And new navigation algorithm precondition is too much, makes to be difficult to estimate the performance of this class algorithm in engineering reality.

Summary of the invention

In order to improve the precision of the strap inertial navigation algorithm under 6～2000Hz high dynamic environment, the present invention proposes and a kind ofly adopt singular perturbation method to carry out coning error and row the boat the strapdown inertial navitation system (SINS) of error compensation, should think that the variation (angular velocity and acceleration) of carrier movement was a kind of perturbation process in a sampling period T based on the strapdown inertial navitation system (SINS) of singular perturbation method compensation, and utilize inertance element (gyro and accelerometer) to set up and force Singular Perturbation Model in the real output value of the sampled point that rises, begins.According to forcing Singular Perturbation Model that coning error, the error of rowing the boat are compensated, obtain posture renewal rotating vector and Velocity Updating amount in the sampling period, approach posture renewal amount and Velocity Updating amount accurately by regulating variable element, improve the requirement of arithmetic accuracy in the navigation calculating unit in the strap down inertial navigation system thereby reach.

The present invention a kind ofly adopts singular perturbation method to carry out coning error and rows the boat the strapdown inertial navitation system (SINS) of error compensation, and this strapdown inertial navitation system (SINS) is to embed coning error compensation Singular Perturbation Model between Inertial Measurement Unit and attitude calculation unit; Between Inertial Measurement Unit and navigation calculating unit, embed the error compensation Singular Perturbation Model of rowing the boat.The inertia assembly is used to export the angular velocity of carrier

The acceleration of carrier

Described angular velocity

Acceleration

Angular velocity after the output filtering after signal processing unit carries out Filtering Processing

The filtering post-acceleration

Angular velocity after the filtering

Angular velocity after output compensation after the compensation of coning error compensation Singular Perturbation Model

Give attitude calculation unit; The angular velocity of attitude calculation unit after to the compensation that receives

Resolve and obtain this angular velocity

Under posture information and export to the navigation calculating unit; The filtering post-acceleration

Acceleration after output compensation after the error compensation Singular Perturbation Model compensation of rowing the boat

Give the navigation calculating unit; The navigation calculating unit is to the posture information that receives, the acceleration after the compensation

The parsing of navigating, thus navigation information output obtained.

Described employing singular perturbation method carries out coning error and the strapdown inertial navitation system (SINS) of the error compensation of rowing the boat, its coning error compensation Singular Perturbation Model $A=\left\{\begin{array}{c}{\mathrm{\ϵ}}_1\stackrel{\·\·}{\stackrel{\→}{w}}+\stackrel{\·}{\stackrel{\→}{w}}+{\stackrel{\→}{\mathrm{\β}}}_1=0\\ {\stackrel{\→}{w}}_n=w_1,{\stackrel{\→}{w}}_{n+1}=w_2\end{array}\right..$

Described employing singular perturbation method carries out coning error and the strapdown inertial navitation system (SINS) of the error compensation of rowing the boat, its error compensation Singular Perturbation Model of rowing the boat $B=\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_2\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{f}}+\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{f}}+{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_2=0\\ {\stackrel{\&RightArrow;}{f}}_n=f_1,{\stackrel{\&RightArrow;}{f}}_{n+1}={\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\end{array}\right..$

Description of drawings

Fig. 1 is the structured flowchart that the present invention is based on the singular perturbation compensation model.

Fig. 2 is the coning error graph of a relation before and after singular perturbation compensation of the present invention.

Fig. 3 is the error graph of a relation of rowing the boat before and after singular perturbation compensation of the present invention.

Embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

Referring to shown in Figure 1, the present invention be a kind of be applicable to high dynamic environment (6～2000Hz) times, adopt singular perturbation method to carry out the strapdown inertial navitation system (SINS) of coning error and the error compensation of rowing the boat, this strapdown inertial navitation system (SINS) is to embed coning error compensation Singular Perturbation Model between Inertial Measurement Unit and attitude calculation unit; Between Inertial Measurement Unit and navigation calculating unit, embed the error compensation Singular Perturbation Model of rowing the boat.The present invention compensates the strapdown inertial navitation system (SINS) of being made up of inertia assembly, inertia component signals processing unit, attitude calculation unit and navigation calculating unit.

In the present invention, the inertia assembly is used to export the angular velocity of carrier

The acceleration of carrier

Described angular velocity

Acceleration

Angular velocity after the output filtering after signal processing unit carries out Filtering Processing

The filtering post-acceleration

Angular velocity after the filtering

Angular velocity after output compensation after the compensation of coning error compensation Singular Perturbation Model

Give attitude calculation unit; The angular velocity of attitude calculation unit after to the compensation that receives

Resolve and obtain this angular velocity

Under posture information and export to the navigation calculating unit; The filtering post-acceleration

Acceleration after output compensation after the error compensation Singular Perturbation Model compensation of rowing the boat

Give the navigation calculating unit; The navigation calculating unit is to the posture information that receives, the acceleration after the compensation

The parsing of navigating, thus navigation information output obtained.About the inertia assembly is to be made of three gyros and three accelerometers, and signal processing unit is the part in the existing strapdown inertial navitation system (SINS), and inertia assembly and signal processing unit constitute the Inertial Measurement Unit of existing strapdown inertial navitation system (SINS).The present invention just utilizes angular velocity after the filtering of Inertial Measurement Unit output

The filtering post-acceleration

Information input as compensation model of the present invention.

Coning error compensation Singular Perturbation Model A of the present invention is:

$A=\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_1\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{w}}+\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{w}}+{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_1=0\\ {\stackrel{\&RightArrow;}{w}}_n=w_1,{\stackrel{\&RightArrow;}{w}}_{n+1}=w_2\end{array}\right.---\left(1\right)$

ε in the formula (1) ₁Represent the first singular perturbation small parameter, its value is [0,1];

Be illustrated in the angle acceleration vector of fast state under 6～2000Hz high dynamic environment;

Be illustrated in the angular acceleration vector of slow state under 6～2000Hz high dynamic environment;

Be illustrated in the angular oscillation frequency f of carrier in the sampling period T _wRelevant parameter vector;

Promptly ${\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_1=\frac{N}{T}({\stackrel{\&RightArrow;}{w}}_n-{\stackrel{\&RightArrow;}{w}}_{n+1}),$ N represents and the angular oscillation frequency f _wA relevant constant, this constant is a floating number;

T represents a sampling period;

The expression gyro is at the angular speed w of the actual output of current sampling point n ₁

The expression gyro is at the angular speed w of the actual output of next moment sampled point n+1 ₂

Under complicated angular oscillation condition, the carrier angular velocity vector

For:

$\stackrel{\&RightArrow;}{w}=(w_1-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}T-w_2)e^{-\left(\frac{t}{{\mathrm{\&epsiv;}}_1}\right)}-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}t+{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}T+w_2---(1-1)$

In the formula (1-1),

The carrier angular velocity vector of expression from the n sampled point to the n+1 sampled point, t represents the time from the n sampled point to the n+1 sampled point, value [0, T], e represents index.

The error compensation Singular Perturbation Model B that rows the boat of the present invention is:

$B=\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_2\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{f}}+\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{f}}+{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_2=0\\ {\stackrel{\&RightArrow;}{f}}_n=f_1,{\stackrel{\&RightArrow;}{f}}_{n+1}=f_2\end{array}\right.---\left(2\right)$

ε in the formula (2) ₂Represent the second singular perturbation small parameter, its value is [0,1];

Be illustrated in the carrier acceleration vector of fast state under 6～2000Hz high dynamic environment;

Be illustrated in the carrier acceleration of slow state under 6～2000Hz high dynamic environment;

Be illustrated in the line vibration frequency f of carrier in the sampling period T _aRelevant parameter vector;

Promptly ${\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_2=\frac{M}{T}({\stackrel{\&RightArrow;}{f}}_n-{\stackrel{\&RightArrow;}{f}}_{n+1}),$ M represents and line vibration frequency f _aA relevant constant, this constant is a floating number; T represents a sampling period;

The expression accelerometer is at the acceleration f of the actual output of current sampling point n ₁

The expression accelerometer is at the acceleration f of the actual output of next moment sampled point n+1 ₂

Under complicated angular oscillation and line vibration condition, the carrier acceleration For:

$\stackrel{\&RightArrow;}{f}=(f_1-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{2}T-f_2)e^{-\left(\frac{t}{{\mathrm{\&epsiv;}}_2}\right)}-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{2}t+{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{2}T+f_2---(2-1)$

In the formula (2-1),

The carrier acceleration of expression from the n sampled point to the n+1 sampled point, t represents the time from the n sampled point to the n+1 sampled point, value [0, T], e represents index.

One, the compensation of coning error

The present invention is compensated for as coning error: with the carrier angular velocity vector

Thereby the equivalent rotating vector φ that the formula in the substitution document one 34 obtains based on singular perturbation theory.

$\mathrm{\&phi;}={\mathrm{\&epsiv;}}_{1}a-\frac{1}{2}\mathrm{<figure-callout\; id="2"\; label="b\; T"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">b</figure-callout>}{T}^{}{}^2+\mathrm{cT}+\frac{1}{2}a\&times;b(\frac{1}{2}{\mathrm{\&epsiv;}}_1{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+2{{\mathrm{\&epsiv;}}_1}^3)+\frac{1}{2}c\&times;a({{2\mathrm{\&epsiv;}}_1}^3-{\mathrm{\&epsiv;}}_{1}T)+\frac{1}{12}b\&times;{\mathrm{cT}}^3---(1-2)$

In the formula (1-2), $a_1=(w_1-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}T-w_2),$ $b_1={\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_1,$ $c_1={\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}T+{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">w</figure-callout>}}_2.$

Obtain the plain q of quaternary according to resolving based on the formula in the equivalent rotating vector φ substitution document one of singular perturbation theory 62 _{BI (m)} ^{BI (m-1)}Utilize the quaternary element after formula 57 in the document one and formula 58 obtain upgrading, resolve in the formula (6-3) in the plain substitution document three of quaternary after will upgrading then and obtain the strapdown matrix, be compensated attitude of carrier behind the coning error according to the element information in the strapdown matrix.

The present invention carries out under the situation of complicated angular oscillation environment and inertial measurement cluster (three gyroscopes and three accelerometers) sample frequency not high (100Hz) the coning error in the strapdown inertial navitation system (SINS) and the compensation of error method of rowing the boat.In complicated angular oscillation environment, the variation of considering the carrier angular acceleration in sampling period T of inertial measurement cluster is the fast variable quantity that becomes with respect to the variation of angular velocity, the singular perturbation small parameter ε that becomes when forcing to add before the variable quantity of the carrier angular acceleration in sampling period T ₁, obtained the Singular Perturbation Model A of the carrier angular velocity varies of inertial measurement cluster in sampling period T.

By regulating singular perturbation small parameter ε ₁With with a sampling period T in the angular oscillation frequency f of carrier _wRelevant parameter vector

Carrier angular velocity varies Singular Perturbation Model is approached the real change of carrier angular velocity in the sampling period.Singular perturbation small parameter ε wherein ₁Span be [0,1].Angular oscillation frequency f with carrier in the sampling period T _wRelevant parameter vector ${\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_1=\frac{N}{T}({\stackrel{\&RightArrow;}{w}}_n-{\stackrel{\&RightArrow;}{w}}_{n+1}).$ In the angular oscillation frequency f _wIn, the value of N is big more, and then the angular oscillation frequency is high more.As, when carrier angular oscillation frequency f _wDuring for 20Hz, the N value is 501.

Equivalent rotating vector posture renewal algorithm φ for citing document one _m=α _m+ β _m, wherein, ${\mathrm{\&alpha;}}_m={\&Integral;}_{t_{m-1}}^{t_m}{\mathrm{\&omega;}}_{\mathrm{IB}}^B\mathrm{dt},$ α _m＝α(t _m)， ${\mathrm{\&beta;}}_m=\frac{1}{2}{\&Integral;}_{t_{m-1}}^{t_m}(\mathrm{\&alpha;}\left(t\right)\&times;{\mathrm{\&omega;}}_{\mathrm{IB}}^B)\mathrm{dt}.$ And in the present invention, the carrier angular velocity vector Be equivalent to ω _IB ^B, the n sampled point is equivalent to the m-1 sampled point, and the n+1 sampled point is equivalent to the m sampled point.β in equivalent rotating vector posture renewal algorithm _mBe coning error. ${\mathrm{\&beta;}}_m=\frac{1}{2}{\&Integral;}_{t_{m-1}}^{t_m}(\mathrm{\&alpha;}\left(t\right)\&times;{\mathrm{\&omega;}}_{\mathrm{IB}}^B)\mathrm{dt}$ Be the expression formula of coning error.

Two, the compensation of error of rowing the boat

The present invention to the compensation of error of rowing the boat is: with the carrier acceleration

With the carrier angular velocity vector

The error model of rowing the boat in the substitution document two, thus acquisition is based on the error estimate of rowing the boat of singular perturbation theory.The described error estimate of rowing the boat includes the carrier angular velocity vector

Integration α (t), carrier acceleration (promptly $\stackrel{\&RightArrow;}{f}=a_{\mathrm{SF}}^B$ ), the carrier acceleration

Integration v (t), carrier angular velocity vector

(promptly $\stackrel{\&RightArrow;}{w}={\mathrm{\&omega;}}_{\mathrm{IB}}^B$ )。The compensation of error value of rowing the boat in the present invention C is:

$C=\frac{1}{2}{\&Integral;}_{t_{m-1}}^{t_m}(\mathrm{\&alpha;}\left(t\right)\&times;\stackrel{\&RightArrow;}{f}+v\left(t\right)\&times;\stackrel{\&RightArrow;}{w})\mathrm{dt}---(2-2)$

In the formula (2-2), $\mathrm{\&alpha;}\left(t\right)=-{\mathrm{\&epsiv;}}_1{a}_1(e^{-\frac{t}{{\mathrm{\&epsiv;}}_1}}-1)-\frac{1}{2}{b}_1{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+c_{1}t,$

$v\left(t\right)=-{\mathrm{\&epsiv;}}_2{a}_2(e^{-\frac{t}{{\mathrm{\&epsiv;}}_2}}-1)-\frac{1}{2}{b}_2{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+c_{2}t,$

$\stackrel{\&RightArrow;}{f}=a_2{e}^{-\left(\frac{t}{{\mathrm{\&epsiv;}}_2}\right)}-b_{2}t+{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">c</figure-callout>}}_2,$

$\stackrel{\&RightArrow;}{w}=a_1{e}^{-\left(\frac{t}{{\mathrm{\&epsiv;}}_1}\right)}-b_{1}t+c_1,$

$a_1=(w_1-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}T-w_2),$

$b_1={\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_1,$

$c_1={\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}T+{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">w</figure-callout>}}_2,$

$a_2=(f_1-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{2}T-f_2),$

${\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">b</figure-callout>}}_2={\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_2,$

$c_2={\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{2}T+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">f</figure-callout>}}_2.$

Formula in the error estimate substitution document two of rowing the boat 36 is obtained row the boat speed increment after the error of carriers system compensation down, and this compensation is rowed the boat in the formula 4 in the speed increment substitution document two after the error, obtains the speed of carrier renewal.The carrier renewal speed is carried out the position that integration obtains carrier.

In the environment of complicated angular oscillation and line vibration, consider the variation of the carrier acceleration of inertial measurement cluster in a sampling period T

Variation with respect to acceleration

Be the fast variable quantity that becomes, the singular perturbation small parameter ε that becomes when forcing to add before the variable quantity of the carrier acceleration in the sampling period ₂(t), obtained the Singular Perturbation Model B of the carrier acceleration change in the inertial measurement cluster sampling period.

By regulating singular perturbation small parameter ε ₂(t) and with sampling period T in the line vibration frequency f of carrier _aRelevant parameter vector Carrier acceleration change Singular Perturbation Model is approached the real change of carrier acceleration in the sampling period.Singular perturbation small parameter ε wherein ₂(t) span is [0,1].Line vibration frequency f with carrier in the sampling period _aRelevant parameter vector ${\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_2=\frac{M}{T}({\stackrel{\&RightArrow;}{f}}_n-{\stackrel{\&RightArrow;}{f}}_{n+1}).$ As sampling period T=10ms, constant M is for to have related parameter with carrier line vibration frequency, and vibration frequency is high more, and the value of M is big more, as carrier line vibration frequency f _aDuring=20Hz, constant M=5.118.

For in the formula 36 of citing document two $\frac{1}{2}{\&Integral;}_{t_{m-1}}^{t_m}(\mathrm{\&alpha;}\left(t\right)\&times;f_{\mathrm{SF}}^B+v\left(t\right)\&times;{\mathrm{\&omega;}}_{\mathrm{IB}}^B)\mathrm{dt}$ Be the error of rowing the boat.

The advantage that the present invention is based on the compensation method of singular perturbation theory strap-down inertial is: because the sample frequency (100Hz) in the engineering is not high, therefore dynamically (the true carrier angular speed in 6～2000Hz) the environment down-samplings interval is unknowable at height, according to rising, 2 inertance element sampled value begins, in sampling interval, set up Singular Perturbation Model and regulate adjustable parameter, can the actual output of analog carrier in sampling interval, bring the basic posture renewal and the Velocity Updating equation of inertial navigation into according to the inertance element output of simulation then, thereby reach the requirement that improves the inertial navigation arithmetic accuracy.This method has dirigibility and robustness, by regulating any flare maneuver that parameter can analog carrier, makes strap inertial navigation algorithm not be subjected to the influence of actual vector motion.

For compensation process of the present invention be:

(A) according to playing, begin two point sampling value w ₁, w ₂, be updated to posture renewal rotating vector equation

Obtain the rotating vector behind the posture renewal;

(B) by regulating parameter vector

The first singular perturbation small parameter ε ₁, the true angular speed of the carrier of simulation in sampling period T, thus make the posture renewal rotating vector of calculating approach posture renewal rotating vector accurately;

(C) according to playing, begin two point sampling value f ₁, f ₂, be updated to the Velocity Updating equation

Carry out Velocity Updating;

(D) by regulating parameter vector

The second singular perturbation small parameter ε ₂, the real specific force output of the carrier of simulation in sampling period T, thus Velocity Updating accurately approached in the update cycle.

Embodiment

One, the conical motion of given classics supposes that as check aircraft exists same angular oscillation frequently to establish along the pairwise orthogonal axle:

$\mathrm{\&alpha;}\left(t\right)=\left[\begin{array}{c}0\\ {\mathrm{\&theta;}}_y\sin \left(2\mathrm{\&pi;}{f}_{w}t\right)\\ -{\mathrm{\&theta;}}_z\cos \left(2\mathrm{\&pi;}{f}_{w}t\right)\end{array}\right],$ $\stackrel{\&RightArrow;}{w}\left(t\right)=\left[\begin{array}{c}0\\ 2\mathrm{\&pi;}{f}_w{\mathrm{\&theta;}}_y\cos \left(2\mathrm{\&pi;}{f}_{w}t\right)\\ 2\mathrm{\&pi;}{f}_w{\mathrm{\&theta;}}_z\sin \left(2\mathrm{\&pi;}{f}_{w}t\right)\end{array}\right]$

θ _y, θ _zBe respectively carrier and be lower edge y direction of principal axis and along the axial attitude angle of z, α (t) is the attitude angle vector under the carrier coordinate,

Be the angular velocity vector under the carrier coordinate, α (t) and

Be vector true value ideally, the coning error actual value that then can get in this condition down-sampling cycle is:

$\frac{1}{2}\underset{t_n}{\overset{t_{n+1}}{\&Integral;}}\mathrm{\&alpha;}\&times;\stackrel{\&RightArrow;}{w}\mathrm{dt}=\left[\begin{array}{c}\mathrm{\&pi;}{f}_w{\mathrm{\&theta;}}_y{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="A20081011336800142.png"\; state="\{\{state\}\}">z</figure-callout>}}\\ 0\\ 0\end{array}\right]$

Given sampling period T=10ms, attitude of carrier motion frequency f _w=20Hz, under this condition, the actual coning error item that produces is 0.0057rad in the sampling period.

For the gyro angular velocity vector of reality, if will do following adjustment based on the parameter in the singular perturbation coning error compensation scheme:

${\mathrm{\&beta;}}_1=\frac{w_1-w_2}{T}+500\frac{w_1-w_2}{T},\mathrm{\&epsiv;}=0.00002$

The dynamic coning error that can calculate in the update cycle is 0.0056617rad.As seen, the dynamic coning error (0.0056617rad) of compensation this moment and actual coning error (0.0057rad) basically identical.When simulation time t=30s, in the emulation with the compensation of the coning error in above-mentioned sampling period conclusion substitution Attitude Calculation.Simulation result as shown in Figure 2.

Coning error as shown in Figure 2 before and after adopting singular perturbation compensation of the present invention.Wherein, phantom line segments is a uncompensated coning error in the carrier movement process, and real segment can find out obviously that for through the coning error based on the Singular Perturbation Model compensation the more uncompensated coning error of coning error of process singular perturbation algorithm compensation obviously reduces.

Two, the boating of given classics supposes that as check aircraft exists the angular oscillation and the line vibration of frequency together to establish along the pairwise orthogonal axle:

$\mathrm{\&alpha;}\left(t\right)=\left[\begin{array}{c}{A}_{\mathrm{\&alpha;}}\cos \left(\mathrm{\&Omega;t}\right)\\ 0\\ 0\end{array}\right],$ $\stackrel{\&RightArrow;}{w}\left(t\right)=\left[\begin{array}{c}-A_{\mathrm{\&alpha;}}\mathrm{\&Omega;}\sin \left(\mathrm{\&Omega;t}\right)\\ 0\\ 0\end{array}\right];$

$p\left(t\right)=\left[\begin{array}{c}0\\ A_p\cos \left(\mathrm{\&Omega;t}\right)\\ 0\end{array}\right],$ $v\left(t\right)=\left[\begin{array}{c}0\\ -A_p\mathrm{\&Omega;}\sin \left(\mathrm{\&Omega;t}\right)\\ 0\end{array}\right],$ $\stackrel{\&RightArrow;}{f}\left(t\right)=\left[\begin{array}{c}0\\ -A_p{\mathrm{\&Omega;}}^2\cos \left(\mathrm{\&Omega;t}\right)\\ 0\end{array}\right]$

A in the following formula _αBe the angular oscillation amplitude; A _pBe the line vibration amplitude; Ω is angular oscillation and line vibration frequency, and α (t) is the attitude angle vector under the carrier coordinate,

Be the angular velocity vector under the carrier coordinate, p (t) is the position vector under the carrier coordinate, and v (t) is the velocity under the carrier coordinate,

Be the acceleration under the carrier coordinate.

α (t),

P (t), v (t),

Be vector true value ideally, the error term of dynamically rowing the boat that then can get in this following update cycle of condition is:

$\frac{1}{2}\underset{t_n}{\overset{t_{n+1}}{\&Integral;}}(v\&times;\stackrel{\&RightArrow;}{w}+\mathrm{\&alpha;}\&times;{\stackrel{\&RightArrow;}{f}}^b)\mathrm{dt}=\left[\begin{array}{c}\\ 0\\ 0\\ -\frac{A_{\mathrm{\&alpha;}}{A}_p{\mathrm{\&Omega;}}^2\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A20081011336800141.png,A20081011336800142.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}\end{array}\right],$ Wherein, T=t _N+1-t _nBe the update cycle.

If simulated conditions A _α=1 °, A _p=0.0001m, Ω=2 π f _a, f _a=20Hz, the speed sampling cycle is T=10ms, under this condition, the actual error term of dynamically rowing the boat that produces is-0.00013781m/s.

If will do following adjustment based on the parameter that singular perturbation is rowed the boat in the error compensation scheme:

${\mathrm{\&beta;}}_1=\frac{w_1-w_2}{T}+4.118\frac{w_1-w_2}{T},$

${\mathrm{\&beta;}}_2=\frac{f_1-f_2}{T}+4.118\frac{f_1-f_2}{T},$

ε＝0.00004。

The error of dynamically rowing the boat that can calculate in the sampling period is-0.00013779m/s, the error of dynamically rowing the boat of compensation this moment is (0.00013779m/s) with the actual error of rowing the boat (0.00013781m/s) basically identical, when simulation time t=30s, in the emulation with the error compensation conclusion substitution speed calculation of rowing the boat in the above-mentioned sampling period, referring to shown in Figure 3.In Fig. 3, phantom line segments is the uncompensated error of rowing the boat in the carrier movement process, real segment can find out obviously that for through the error of rowing the boat based on the Singular Perturbation Model compensation the more uncompensated error of rowing the boat of the error of rowing the boat of process singular perturbation algorithm compensation obviously reduces.

Claims (5)

1, a kind ofly adopt singular perturbation method to carry out coning error and row the boat the strapdown inertial navitation system (SINS) of error compensation, it is characterized in that: this strapdown inertial navitation system (SINS) is to embed coning error compensation Singular Perturbation Model between Inertial Measurement Unit and attitude calculation unit; Between Inertial Measurement Unit and navigation calculating unit, embed the error compensation Singular Perturbation Model of rowing the boat;

The inertia assembly is used to export the angular velocity of carrier

The acceleration of carrier

Described angular velocity

Acceleration

Angular velocity after the output filtering after signal processing unit carries out Filtering Processing

The filtering post-acceleration

Angular velocity after the filtering

Angular velocity after output compensation after the compensation of coning error compensation Singular Perturbation Model

Give attitude calculation unit; The angular velocity of attitude calculation unit after to the compensation that receives

Resolve and obtain this angular velocity

Under posture information and export to the navigation calculating unit; The filtering post-acceleration

Acceleration after output compensation after the error compensation Singular Perturbation Model compensation of rowing the boat

Give the navigation calculating unit; The navigation calculating unit is to the posture information that receives, the acceleration after the compensation The parsing of navigating, thus navigation information output obtained.

2, employing singular perturbation method according to claim 1 carries out coning error and the strapdown inertial navitation system (SINS) of the error compensation of rowing the boat, and it is characterized in that: coning error compensation Singular Perturbation Model A is:

$A=\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_1\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{w}}+\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{w}}+{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_1=0\\ {\stackrel{\&RightArrow;}{w}}_n=w_1,{\stackrel{\&RightArrow;}{w}}_{n+1}=w_2\end{array}\right.$

ε in the formula ₁Represent the first singular perturbation small parameter, its value is [0,1];

Be illustrated in the angle acceleration vector of fast state under 6～2000Hz high dynamic environment;

Be illustrated in the angular acceleration vector of slow state under 6～2000Hz high dynamic environment;

Be illustrated in the angular oscillation frequency f of carrier in the sampling period T _wRelevant parameter vector;

Promptly ${\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_1=\frac{N}{T}({\stackrel{\&RightArrow;}{w}}_n-{\stackrel{\&RightArrow;}{w}}_{n+1}),$ N represents and the angular oscillation frequency f _wA relevant constant, this constant is a floating number;

T represents a sampling period;

The expression gyro is at the angular speed w of the actual output of current sampling point n ₁

The expression gyro is at the angular speed w of the actual output of next moment sampled point n+1 ₂

3, employing singular perturbation method according to claim 2 carries out coning error and the strapdown inertial navitation system (SINS) of the error compensation of rowing the boat, and it is characterized in that: under complicated angular oscillation condition, and the carrier angular velocity vector

For:

$\stackrel{\&RightArrow;}{w}=(w_1-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}T-w_2)e^{-\left(\frac{t}{{\mathrm{\&epsiv;}}_1}\right)}-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}t+{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{1}T+w_2$

In the formula,

The carrier angular velocity vector of expression from the n sampled point to the n+1 sampled point, t represents the time from the n sampled point to the n+1 sampled point, value [0, T], e represents index.

4, employing singular perturbation method according to claim 1 carries out coning error and the strapdown inertial navitation system (SINS) of the error compensation of rowing the boat, and it is characterized in that: the error compensation of rowing the boat Singular Perturbation Model B is:

$B=\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_2\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{f}}+\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{f}}+{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_2=0\\ {\stackrel{\&RightArrow;}{f}}_n=f_1,{\stackrel{\&RightArrow;}{f}}_{n+1}=f_2\end{array}\right.$

ε in the formula ₂Represent the second singular perturbation small parameter, its value is [0,1];

Be illustrated in the carrier acceleration vector of fast state under 6～2000Hz high dynamic environment;

Be illustrated in the carrier acceleration of slow state under 6～2000Hz high dynamic environment;

Be illustrated in the line vibration frequency f of carrier in the sampling period T _aRelevant parameter vector;

Promptly ${\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_2=\frac{M}{T}({\stackrel{\&RightArrow;}{f}}_n-{\stackrel{\&RightArrow;}{f}}_{n+1}),$ M represents and line vibration frequency f _aA relevant constant, this constant is a floating number;

T represents a sampling period;

The expression accelerometer is at the acceleration f of the actual output of current sampling point n ₁

The expression accelerometer is at the acceleration f of the actual output of next moment sampled point n+1 ₂

5, employing singular perturbation method according to claim 4 carries out coning error and the strapdown inertial navitation system (SINS) of the error compensation of rowing the boat, and it is characterized in that: under complicated angular oscillation and line vibration condition, and the carrier acceleration

For:

$\stackrel{\&RightArrow;}{f}=(f_1-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{2}T-f_2)e^{-\left(\frac{t}{{\mathrm{\&epsiv;}}_2}\right)}-{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{2}t+{\stackrel{\&RightArrow;}{\mathrm{\&beta;}}}_{2}T+f_2$

In the formula,

The carrier acceleration of expression from the n sampled point to the n+1 sampled point, t represents the time from the n sampled point to the n+1 sampled point, value [0, T], e represents index.

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