CN103917850B - A kind of motion alignment methods of inertial navigation system - Google Patents

Abstract

The present invention relates to inertial navigation system technical field, particularly relate to a kind of motion alignment methods of inertial navigation system, this inertial navigation system is installed on motion carrier, comprising: the rotation information of inertial navigation system measurement self and linear acceleration information; Its reference velocity in reference frame that inertial navigation system synchronously receives that external auxiliary information source provides and positional information; And inertial navigation system carries out data processing to rotation information and linear acceleration information and reference velocity and positional information, obtain from the body coordinate system in current time relative to the attitude of reference frame.Utilize the present invention, efficiently solve reference frame speed/positional assist under inertial navigation system motion alignment issues, when without any achieve when attitude priori initial value rapid posture aim at.

Description

A kind of motion alignment methods of inertial navigation system

Technical field

The present invention relates to inertial navigation system technical field, particularly relate to a kind of motion alignment methods of inertial navigation system, namely how under motion conditions by the attitude tracking of speed/positional information realization inertial navigation system.

Background technology

Before formally starting navigation work, inertial navigation system (InertialNavigationSystem, INS) needs to know some starting condition, such as initial attitude, initial velocity and initial position.Determine the process of starting condition so-called " aligning ".Initial velocity and initial position are easy to obtain, and therefore aim at generally to refer in particular to and determine the process of the body coordinate system of INS relative to the attitude relation of reference frame.

Conventional reference frame comprises local horizontal coordinates, terrestrial coordinate system etc.The effect of attitude tracking is most important, and the quality of aligning directly determines the precision level of INS in the subsequent navigation stage.In the application such as carrier-borne aircraft, guided munition, under water autonomous underwater vehicle and ground maneuver vehicle, require that INS can aim in motion process.

INS motion is aimed to be needed to complete under the assistance of oracle.Global Positioning System (GPS) (GlobalPositioningSystem, GPS) is common oracle, and it can provide the speed of carrier under local horizontal coordinates or terrestrial coordinate system and positional information.

The main stream approach that current motion is aimed at has used for reference the realization approach under static or quasi-static situation, namely generally includes coarse alignment and two stages of fine alignment.Coarse alignment for obtaining rough initial attitude, for fine alignment provides initial value.Fine alignment adopts the non-linear filtering method based on Taylor (Taylor) series expansion usually, EKF (ExtendedKalmanFilter, EKF) etc. as approximate in first-order linear.The non-linear filtering methods such as EKF are adopted to carry out fine alignment, need to know inertia device more accurately, such as gyro and accelerometer, and the noisiness of external speed/positional information, and the initial attitude error requiring coarse alignment to provide can not be excessive, otherwise wave filter can not converge to desirable fine alignment result in official hour, sometimes even disperse.It's a pity, in various carrier movement situation, the error of the initial attitude that coarse alignment obtains is usually very large, particularly azimuth angle error.

Therefore, the research emphasis that current kinetic is aimed at mainly concentrates on and how to design non-linear large misalignment angle error model or select more complicated wave filter, and to tackle inevitably large initial orientation angle error, but effect is desirable all not to the utmost.

Summary of the invention

In view of this, fundamental purpose of the present invention is the motion alignment methods providing a kind of inertial navigation system, to solve the motion alignment issues that reference frame speed/positional assists lower inertial navigation system, when without any realize when attitude priori initial value inertial navigation system rapid posture aim at.

For achieving the above object, the invention provides a kind of motion alignment methods of inertial navigation system, this inertial navigation system is installed on motion carrier, and the method comprises: the rotation information of inertial navigation system measurement self and linear acceleration information; Inertial navigation system synchronously receives (after the compensating via the lever arm of necessity) that provided by external auxiliary information source from reference velocity in reference frame and positional information; And inertial navigation system carries out data processing to rotation information and linear acceleration information and reference velocity and positional information, obtain from the body coordinate system in current time relative to the attitude of reference frame.

As can be seen from technique scheme, the present invention has following beneficial effect:

1, the motion alignment methods of inertial navigation system provided by the invention, based on special speed and position integral formula, design achieves rate integrating motion alignment algorithm and the position integrated motion alignment algorithm of iteration form respectively, can according to auxiliary speed/positional information, calculate the current pose of inertial navigation system in real time, efficiently solve the motion alignment issues that reference frame speed/positional assists lower inertial navigation system, when without any achieve when attitude priori initial value inertial navigation system rapid posture aim at.

2, the motion alignment methods of inertial navigation system provided by the invention, without the need to knowing the noisiness of inertia device and external speed/positional information, without the need to any attitude initial value, there is absolute computational stability, there is not the situation of dispersing, as long as speed/positional supplementary is effective, attitude tracking can be realized under any motion conditions, significantly shorten the setup time before carrier navigation.

3, the motion alignment methods of inertial navigation system provided by the invention, in the application scenario that the embodiment of the present invention is considered, INS is arranged on motion carrier, and the speed of INS in reference frame and positional information are provided by GPS or other oracles (after compensating via the lever arm of necessity).

4, the motion alignment methods of inertial navigation system provided by the invention, according to the requirement of inertial device error whether online compensation, the Output rusults of rate integrating motion alignment algorithm and position integrated motion alignment algorithm both can be directly used in inertial navigation and resolve (fine alignment), also can carry out Combined estimator and calibration as the attitude initial value (coarse alignment) of non-linear filtering method to navigational parameter and inertial device error.

Accompanying drawing explanation

Fig. 1 is the input/output relation schematic diagram of rate integrating motion alignment algorithm according to the embodiment of the present invention and position integrated motion alignment algorithm;

Fig. 2 is the method flow diagram of the rate integrating motion alignment algorithm according to the embodiment of the present invention;

Fig. 3 utilizes rate integrating motion alignment algorithm and position integrated motion alignment algorithm to calculate attitude matrix according to the embodiment of the present invention with method flow diagram;

Fig. 4 calculates α in the rate integrating motion alignment algorithm according to the embodiment of the present invention _v(t _m) method flow diagram;

Fig. 5 calculates β in the rate integrating motion alignment algorithm according to the embodiment of the present invention _v(t _m) method flow diagram;

Fig. 6 is according to calculating K (t in the rate integrating motion alignment algorithm of the embodiment of the present invention and position integrated motion alignment algorithm _m) method flow diagram;

Fig. 7 calculates according in the rate integrating motion alignment algorithm of the embodiment of the present invention and position integrated motion alignment algorithm method flow diagram.

Fig. 8 is the method flow diagram of the position integrated motion alignment algorithm according to the embodiment of the present invention;

Fig. 9 calculates α in the position integrated motion alignment algorithm according to the embodiment of the present invention _p(t _m) method flow diagram;

Figure 10 calculates β in the position integrated motion alignment algorithm according to the embodiment of the present invention _p(t _m) method flow diagram.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly understand, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.

The motion alignment methods of inertial navigation system provided by the invention, reference velocity in reference frame of the INS that provides and positional information after compensating via the lever arm of necessity according to oracle (as GPS), and based on special speed and position integral formula, design achieves rate integrating motion aligning and the position integrated motion aligning of iteration form respectively, can according to auxiliary speed/positional information, calculate the body coordinate system of INS at current time in real time relative to the attitude of reference frame.

The coordinate system that the embodiment of the present invention is used has at least following: inertial coordinates system (I), reference frame (N), terrestrial coordinate system (E) and body coordinate system (B).

Without loss of generality, the reference frame in the embodiment of the present invention is the local horizontal coordinates selecting east, northern sky (North-Up-East) to point to.For other reference frames (as terrestrial coordinate system), description below will slightly change, but this does not affect the understanding to main thought of the present invention.

Assuming that INS aims in the time period at [0, t].Motion alignment methods of the present invention realizes based on following integral formula design

Rate integrating formula:

$\begin{array}{c}{C}_b^n\left(0\right){\mathrm{\α}}_v={\mathrm{\β}}_v\\ {\mathrm{\α}}_v\stackrel{\mathrm{\Δ}}{=}{\∫}_0^t{C}_{b\left(t\right)}^{b\left(0\right)}{f}^b\mathrm{dt}\\ {\mathrm{\β}}_v\stackrel{\mathrm{\Δ}}{=}{C}_{n\left(t\right)}^{n\left(0\right)}{v}^n-v^n\left(0\right)+{\∫}_0^t{C}_{n\left(t\right)}^{n\left(0\right)}{\mathrm{\ω}}_{\mathrm{ie}}^n\×v^n\mathrm{dt}-{\∫}_0^t{C}_{n\left(t\right)}^{n\left(0\right)}{g}^n\mathrm{dt}\end{array}$ Formula 1

Position integral formula:

$\begin{array}{c}{C}_b^n\left(0\right){\mathrm{\α}}_p={\mathrm{\β}}_p\\ {\mathrm{\α}}_p\stackrel{\mathrm{\Δ}}{=}{\∫}_0^t{\∫}_0^{\mathrm{\τ}}{C}_{b\left(\mathrm{\σ}\right)}^{b\left(0\right)}{f}^b\mathrm{d\σd\τ}\\ {\mathrm{\β}}_p\stackrel{\mathrm{\Δ}}{=}{C}_{n\left(t\right)}^{n\left(0\right)}{r}^n-t{v}^n\left(0\right)-{\∫}_0^t{C}_{n\left(\mathrm{\τ}\right)}^{n\left(0\right)}{\mathrm{\ω}}_{\mathrm{in}}^n\×r^n\mathrm{d\τ}\\ +{\∫}_0^t{\∫}_0^{\mathrm{\τ}}{C}_{n\left(\mathrm{\σ}\right)}^{n\left(0\right)}{\mathrm{\ω}}_{\mathrm{ie}}^n\×v^n\mathrm{d\σd\τ}-{\∫}_0^t{\∫}_0^{\mathrm{\τ}}{C}_{n\left(\mathrm{\σ}\right)}^{n\left(0\right)}{g}^n\mathrm{d\σd\τ}\end{array}$ Formula 2

Wherein for being tied to the attitude matrix (orthogonal and determinant is 1) of reference frame from body coordinate, for attitude matrix is in the value of initial time, f ^bfor the specific force that accelerometer measures arrives, $v^n={\left[\begin{array}{ccc}{v}_n& v_U& v_E\end{array}\right]}^T$ For the ground speed that INS represents in reference frame, v ⁿ(0) for ground speed is in the value of initial time, the earth rate represented in reference frame, g ⁿthe local gravitational acceleration represented in reference frame, r ⁿbe defined as the integration of ground speed, namely $r^n\left(t\right)={\∫}_0^t{v}^n\mathrm{dt}={\∫}_0^t{R}_{\mathrm{ic}}\stackrel{.}{p}\mathrm{dt},$ Wherein $R_{\mathrm{ic}}=\left[\begin{array}{ccc}0& R_N+h& 0\\ 0& 0& 1\\ (R_E+h)\cos L& 0& 0\end{array}\right],$ The INS position represented with local geographic coordinate $p\stackrel{\mathrm{\Δ}}{=}{\left[\begin{array}{ccc}\mathrm{\λ}& L& h\end{array}\right]}^T$ (longitude, latitude, highly).R _eand R _nlocal radius of curvature in prime vertical and radius of curvature of meridian respectively.If not special instruction, above variable is all the function of time t, and for simplicity, time t omits.

Rate integrating formula 1 or position integral formula 2 all can be used for determining initial attitude matrix be called " rate integrating motion alignment algorithm " and " position integrated motion alignment algorithm ".We need the continuous integration in design value algorithm approximate formula 1-formula 2, and the error that integral approach calculates is less, estimated result better.Attention: it is a normal matrix.The attitude matrix of initial attitude matrix and current time is associated by chain type product rule, namely

$C_b^n\left(t\right)=C_{n\left(0\right)}^{n\left(t\right)}{C}_b^n\left(0\right)C_{b\left(t\right)}^{b\left(0\right)}$ Formula 3

Wherein, the function of position and speed, it is the function of the rotational angular velocity of gyro to measure.According to formula 3, if three, the right can obtain respectively, naturally just obtain the attitude matrix of any time.

To set forth the design details of rate integrating motion alignment algorithm and position integrated motion alignment algorithm successively below, both common steps will be unified in rate integrating motion alignment algorithm and set forth.

Fig. 1 gives the input/output relation schematic diagram of rate integrating motion alignment algorithm according to the embodiment of the present invention and position integrated motion alignment algorithm.The input of the method comprises the angle increment that gyro to measure in INS arrives, the speed increment that accelerometer measures arrives, and the speed of the INS that provides of oracle in reference frame and positional information.What suppose in the present embodiment that INS exports is increment information, and be the INS of angular velocity and specific force for output information, calculating below can be slightly different.Angle increment and the usual of speed increment input (as 200Hz) with higher frequency, and external speed and position are usually with lower frequency input (as 1Hz).In order to reduce the error that integral approach calculates, external speed and position are preferably with the input of as far as possible high frequency.The method processes in real time to input information, exports as current time INS body coordinate system is relative to the direction cosine matrix of reference frame, also can be converted to other attitude parameters according to actual requirement, as hypercomplex number or Eulerian angle.

Fig. 2 gives the method flow diagram of the rate integrating motion alignment algorithm according to the embodiment of the present invention.Consider that actual discrete system realizes, assuming that current time t is the integral multiple upgrading interval T, i.e. t=M × T, wherein T is for upgrading interval (as 0.01s), and M is integer.Upgrade time interval be [ _tkt _k+1], k=0,1,2 ..., M 1, wherein t _k=kT.The method flow process comprises successively: initialization, and the time upgrades M=M+1, attitude matrix with upgrade, vectorial α _v(t _m) calculate, vectorial β _v(t _m) calculate, matrix K (t _m) calculate, initial attitude matrix determine, finally obtain the current pose of INS according to chain type product rule (i.e. formula 3).The method initialization comprise arrange current time t=0 and in the method associated vector reset, i.e. M=0, α _v(0)=β ' _v(0)=0 _{3 × 1}, and K (0)=0 _{4 × 4}.

Fig. 3 gives and calculates attitude matrix according to the rate integrating motion alignment algorithm of the embodiment of the present invention and position integrated motion alignment algorithm with method flow diagram. with calculating be coordination, not free sequencing.Note as M=0, with be unit matrix. that reference frame is relative to inertial coordinates system angular velocity function.Be reference frame owing to have selected (Bei Tiandong) local horizontal coordinate, as follows with the relation of speed and position

${\mathrm{\ω}}_{\mathrm{in}}^n={\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n=\mathrm{\Ω}\left[\begin{array}{c}\cos L\\ \sin L\\ 0\end{array}\right]+\left[\begin{array}{c}{v}_E/(R_E+h)\\ v_E\tan L/(R_E+h)\\ -v_N/(R_N+h)\end{array}\right]$ Formula 4

Wherein earth rotation angular speed Ω ≈ 7.292115 × 10 ^-5rad/s.Consider for in a small amount, in a update time interval, the rotating vector of reference frame relative inertness coordinate system according to the transforming relationship between direction cosine matrix and rotating vector,

formula 5

Again by the chain type product rule of attitude matrix, i.e. formula 3, Wo Menyou

$C_{n\left(t_M\right)}^{n\left(0\right)}=C_{n\left(t_{M-1}\right)}^{n\left(0\right)}{C}_{n\left(t_M\right)}^{n\left(t_{M-1}\right)}.$

Because INS body coordinate system is very fast relative to the change of inertial coordinates system, corresponding rotating vector needs to carry out shallow conical shell usually.Assuming that in a update time interval, gyro is double sampling successively, is denoted as Δ θ ₁, Δ θ ₂, accelerometer is double sampling successively, is denoted as Δ v ₁, Δ v ₂.INS body coordinate system can be approximately relative to the rotating vector of inertial coordinates system according to the transforming relationship between direction cosine matrix and rotating vector,

formula 6

Equally by the chain type product rule of attitude matrix, i.e. formula 3, Wo Menyou

$C_{b\left(t_M\right)}^{b\left(0\right)}=C_{b\left(t_{M-1}\right)}^{b\left(0\right)}{C}_{b\left(t_M\right)}^{b\left(t_{M-1}\right)}.$

Can find out, calculating used speed and the positional information of external auxiliary. calculating then suppose to have in the update time of interval twice INS sampling, for the situation of other increment numbers, only need in calculating time do corresponding change.

Fig. 4 gives in the rate integrating motion alignment algorithm according to the embodiment of the present invention and calculates α _v(t _m) method flow diagram.According to the definition provided in rate integrating formula 1, α _v(t _m) relate to the integration of specific force after approximate treatment conversion utilize priority twice angle increment in interval T update time and speed increment sampling, and carry out corresponding drawing and shake compensation, α _v(t _m) can according to following formula iterative computation

$u={\mathrm{\Δv}}_1+{\mathrm{\Δv}}_2+\frac{1}{2}({\mathrm{\Δ\θ}}_1+{\mathrm{\Δ\θ}}_2)\×({\mathrm{\Δv}}_1+{\mathrm{\Δv}}_2)+\frac{2}{3}({\mathrm{\Δ\θ}}_1\×{\mathrm{\Δ\θ}}_2+{\mathrm{\Δv}}_1\×{\mathrm{\Δ\θ}}_2)$ Formula 7

${\mathrm{\α}}_v\left(t_M\right)={\mathrm{\α}}_v\left(t_{M-1}\right)+C_{b\left(t_{M-1}\right)}^{b\left(0\right)}u$

Note as M=0, α _v(0)=0 _{3 × 1}.For the situation of other increment numbers, draw to shake and compensate the calculating of u by different.

Fig. 5 gives in the rate integrating motion alignment algorithm according to the embodiment of the present invention and calculates β _v(t _m) method flow diagram.Local gravitational acceleration g ⁿbe the function of position, can calculate according to gravity field model, and β _v(t _m) calculating used external speed and positional information.According to the definition provided in rate integrating formula 1, β _v(t _m) relate to approximate treatment two integrations: with assuming that upgrade in interval approximately linear changes, g ⁿapproximate constant value, β _v(t _m) can according to formula 8 iterative computation below:

$u=(\frac{T}{2}I+\frac{T^2}{6}{\mathrm{\ω}}_{\mathrm{in}}^n\×){\mathrm{\ω}}_{\mathrm{ie}}^n\×v^n\left(t_{M-1}\right)+(\frac{T}{2}I+\frac{T^2}{3}{\mathrm{\ω}}_{\mathrm{in}}^n\×){\mathrm{\ω}}_{\mathrm{ie}}^n\×v^n\left(t_M\right)-(\mathrm{TI}+\frac{T^2}{2}{\mathrm{\ω}}_{\mathrm{in}}^n\×)g^n$

${\mathrm{\β}}_v^{\′}\left(t_M\right)={\mathrm{\β}}_v^{\′}\left(t_{M-1}\right)+C_{n\left(t_{M-1}\right)}^{n\left(0\right)}u$

${\mathrm{\β}}_v\left(t_M\right)=C_{n\left(t_M\right)}^{n\left(0\right)}{v}^n-v^n\left(0\right)+{\mathrm{\β}}_v^{\′}\left(t_M\right)$

Note as M=0, β ' _v(0)=0 _{3 × 1}.

Fig. 6 gives according to calculating K (t in the rate integrating motion alignment algorithm of the embodiment of the present invention and position integrated motion alignment algorithm _m) method flow diagram.First rate integrating algorithm, is defined as follows 4 × 4 matrixes

$K\left(t\right)={\∫}_0^t{(\stackrel{+}{\left[{\mathrm{\β}}_v\right]}-\stackrel{-}{\left[{\mathrm{\α}}_v\right]})}^T(\stackrel{+}{\left[{\mathrm{\β}}_v\right]}-\stackrel{-}{\left[{\mathrm{\α}}_v\right]})\mathrm{dt}$ Formula 9

Which use two special hypercomplex number multiplication matrix.For tri-vector r, hypercomplex number multiplication matrix is defined as follows

$\stackrel{+}{\left[r\right]}\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cc}0& {-r}^T\\ r& (r\×)\end{array}\right],$ $\stackrel{-}{\left[r\right]}\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cc}0& {-r}^T\\ r& -(r\×)\end{array}\right],$ Formula 10

Wherein r × be the antisymmetric matrix of r.Assuming that integrand approximate constant value in renewal is interval, K (t _m) can according to following formula iterative computation

$K\left(t_M\right)=K\left(t_{M-1}\right)+T{(\stackrel{+}{\left[{\mathrm{\β}}_v\left(t_M\right)\right]}-\stackrel{-}{\left[{\mathrm{\α}}_v\left(t_M\right)\right]})}^T(\stackrel{+}{\left[{\mathrm{\β}}_v\left(t_M\right)\right]}-\stackrel{-}{\left[{\mathrm{\α}}_v\left(t_M\right)\right]})$ Formula 11

Note as M=0, K (0)=0 _{4 × 4}.

For position integral algorithm, said process is substantially identical, and difference is to use β _psubstitute β _v, α _psubstitute α _v, specifically comprise: be defined as follows 4 × 4 matrixes which use two special hypercomplex number multiplication matrix; For tri-vector r, hypercomplex number multiplication matrix is defined as follows:

$\stackrel{+}{\left[r\right]}\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cc}0& {-r}^T\\ r& (r\×)\end{array}\right],$ $\stackrel{-}{\left[r\right]}\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cc}0& {-r}^T\\ r& -(r\×)\end{array}\right],$ Wherein r × be the antisymmetric matrix of r;

Assuming that integrand approximate constant value in renewal is interval, K (t _m) can according to following formula iterative computation

$K\left(t_M\right)=K\left(t_{M-1}\right)+T{(\stackrel{+}{\left[{\mathrm{\β}}_p\left(t_M\right)\right]}-\stackrel{-}{\left[{\mathrm{\α}}_p\left(t_M\right)\right]})}^T(\stackrel{+}{\left[{\mathrm{\β}}_p\left(t_M\right)\right]}-\stackrel{-}{\left[{\mathrm{\α}}_p\left(t_M\right)\right]})$

Wherein as M=0, K (0)=0 _{4 × 4}.

Fig. 7 gives and calculates according in the rate integrating motion alignment algorithm of the embodiment of the present invention and position integrated motion alignment algorithm method flow diagram.For rate integrating algorithm, can prove: meet initial attitude matrix corresponding attitude quaternion is the proper vector corresponding to minimal eigenvalue of matrix K, is denoted as q.Ripe algorithm can be found in canonical algorithm storehouse to be used for solving 4 × 4 matrix K (t _m) proper vector, computation burden is little.Q is write as [s η ^t] ^t, according to the transforming relationship between direction cosine matrix and hypercomplex number, Wo Menyou

$C_b^n\left(0\right)=(s^2-{\mathrm{\η}}^T\mathrm{\η})I+2{\mathrm{\η\η}}^T+2s(\mathrm{\η}\×)$ Formula 12

More than only give one to solve by hypercomplex number specific process, can certainly solve with additive method.The last current pose obtaining INS according to chain type product rule (i.e. formula 3)

$C_{n\left(0\right)}^{n\left(t_M\right)}{C}_b^n\left(0\right)C_{b\left(t_M\right)}^{b\left(0\right)}$ Formula 13

For position integral algorithm, said process is substantially identical, and difference is to use β _psubstitute β _v, α _psubstitute α _v, specifically comprise: meet initial attitude matrix corresponding attitude quaternion is the proper vector corresponding to minimal eigenvalue of matrix K, is denoted as q; Ripe algorithm can be found in canonical algorithm storehouse to be used for solving 4 × 4 matrix K (t _m) proper vector, q is write as [s η ^t] ^t, according to the transforming relationship between direction cosine matrix and hypercomplex number, obtain $C_b^n\left(0\right)=(s^2-{\mathrm{\η}}^T\mathrm{\η})I+2{\mathrm{\η\η}}^T+2s(\mathrm{\η}\×).$

Fig. 8 gives the method flow diagram of the position integrated motion alignment algorithm according to the embodiment of the present invention, and its basic structure is substantially identical with the internal information flow process figure of rate integrating motion alignment algorithm.Internal information flow process comprises successively: initialization, and the time upgrades M=M+1, attitude matrix with upgrade, vectorial α _p(t _m) calculate, vectorial β _p(t _m) calculate, matrix K (t _m) calculate, initial attitude matrix determine, finally obtain the current pose of INS according to chain type product rule (i.e. formula 3).Method initialization comprise arrange current time t=0 and in method associated vector reset, i.e. M=0, α _v(0)=β ' _v(0)=0 _{3 × 1}, u _p(0)=u _r(0)=u _v(0)=u _g(0)=0 _{3 × 1}and K (0)=0 _{4 × 4}.

Fig. 9 gives in the position integrated motion alignment algorithm according to the embodiment of the present invention and calculates α _p(t _m) method flow diagram.According to the definition provided in position integral formula 2, α _p(t _m) relate to the dual-integration of specific force after approximate treatment conversion utilize priority twice angle increment in a update time interval and speed increment sampling, and carry out corresponding spool compensation, α _p(t _m) can according to formula 14 iterative computation below:

$u=\frac{T}{30}(25{\mathrm{\Δv}}_1+5{\mathrm{\Δv}}_2+12{\mathrm{\Δ\θ}}_1\×{\mathrm{\Δv}}_1+8{\mathrm{\Δ\θ}}_1\×{\mathrm{\Δv}}_2+2{\mathrm{\Δv}}_1\×{\mathrm{\Δ\θ}}_2+2{\mathrm{\Δ\θ}}_2\×{\mathrm{\Δv}}_2)$

$u_p\left(M\right)=u_p(M-1)+C_{b\left(t_{M-1}\right)}^{b\left(0\right)}u$

${\mathrm{\α}}_p\left(t_M\right)=u_p\left(M\right)+T\underset{m=0}{\overset{M-2}{\mathrm{\Σ}}}{C}_{b\left(t_m\right)}^{b\left(0\right)}({\mathrm{\Δv}}_1+{\mathrm{\Δv}}_2+\frac{1}{2}({\mathrm{\Δ\θ}}_1+{\mathrm{\Δ\θ}}_2)\×({\mathrm{\Δv}}_1+{\mathrm{\Δv}}_2)+\frac{2}{3}({\mathrm{\Δ\θ}}_1\×{\mathrm{\Δv}}_2+{\mathrm{\Δv}}_1\×{\mathrm{\Δ\θ}}_2))$

Note as M=0, α _p(0)=0 _{3 × 1}.For the situation of other increment numbers, spool compensates the calculating of u by different.

Figure 10 gives in the position integrated motion alignment algorithm according to the embodiment of the present invention and calculates β _p(t _m) method flow diagram.According to the definition provided in position integral formula 2, β _p(t _m) relate to approximate treatment substance integration: and two dual-integrations: ${\∫}_0^t{\∫}_0^{\mathrm{\τ}}{C}_{n\left(\mathrm{\σ}\right)}^{n\left(0\right)}{\mathrm{\ω}}_{\mathrm{ie}}^n\×v^n\mathrm{d\σd\τ}$ With ${\∫}_0^t{\∫}_0^{\mathrm{\τ}}{C}_{n\left(\mathrm{\σ}\right)}^{n\left(0\right)}{g}^n\mathrm{d\σd\τ}.$ Assuming that upgrade in interval approximately linear changes, g ⁿapproximate constant value, β _p(t _m) can according to formula 15 iterative computation below:

$\begin{array}{c}{u}_r\left(M\right)=u_r(M-1)+C_{n\left(t_{M-1}\right)}^{n\left(0\right)}[(\frac{T^2}{3}{\mathrm{\ω}}_{\mathrm{in}}^n\×+\frac{{5T}^3}{24}{({\mathrm{\ω}}_{\mathrm{in}}^n\×)}^2)v^n\left(t_{M-1}\right)+(\frac{T^2}{6}{\mathrm{\ω}}_{\mathrm{in}}^n\×+\frac{T^3}{8}{({\mathrm{\ω}}_{\mathrm{in}}^n\×)}^2)v^n\left(t_M\right)\\ +({\mathrm{T\ω}}_{\mathrm{in}}^n\×+\frac{T^2}{2}{({\mathrm{\ω}}_{\mathrm{in}}^n\×)}^2)\underset{m=01}{\overset{M-2}{\mathrm{\Σ}}}{R}_{\mathrm{ic}}^{-1}\left(t_m\right)(p\left(t_{m+1}\right)-p\left(t_m\right))]\end{array}$

$\begin{array}{c}{u}_v\left(M\right)=u_v(M-1)+C_{n\left(t_{M-1}\right)}^{n\left(0\right)}[(\frac{T^2}{3}\mathrm{I\ω}+\frac{T^3}{12}{\mathrm{\ω}}_{\mathrm{in}}^n\×){\mathrm{\ω}}_{\mathrm{ie}}^n\×v^n\left(t_{M-1}\right)+(\frac{T^2}{6}I+\frac{T^3}{12}{\mathrm{\ω}}_{\mathrm{in}}^n\×){\mathrm{\ω}}_{\mathrm{ie}}^n\×v^n\left(t_M\right)]\\ +T\underset{m=01}{\overset{M-2}{\mathrm{\Σ}}}{C}_{n\left(t_m\right)}^{n\left(0\right)}[(\frac{T}{2}I+\frac{T^2}{6}{\mathrm{\ω}}_{\mathrm{in}}^n\×){\mathrm{\ω}}_{\mathrm{ie}}^n\×v^n\left(t_m\right)+(\frac{T}{2}I+\frac{T^2}{3}{\mathrm{\ω}}_{\mathrm{in}}^n\×){\mathrm{\ω}}_{\mathrm{ie}}^n\×v^n\left(t_{m+1}\right)]\end{array}$

$u_g\left(M\right)=u_g(M-1)+C_{n\left(t_{M-1}\right)}^{n\left(0\right)}(\frac{T^2}{2}I+\frac{T^3}{6}{\mathrm{\ω}}_{\mathrm{in}}^n\×)g^n+T\underset{m=0}{\overset{M-2}{\mathrm{\Σ}}}{C}_{n\left(t_m\right)}^{n\left(0\right)}(\mathrm{TI}+\frac{T^2}{2}{\mathrm{\ω}}_{\mathrm{in}}^n\×)g^n$ ${{\mathrm{\β}}^{\′}}_p\left(M\right)={{\mathrm{\β}}^{\′}}_p(M-1)+R_{\mathrm{ic}}^{-1}\left(t_{M-1}\right)(p\left(t_M\right)-p\left(t_{M-1}\right))$

${\mathrm{\β}}_p\left(M\right)=C_{n\left(t_M\right)}^{n\left(0\right)}{{\mathrm{\β}}^{\′}}_p\left(M\right)-t_M{v}^n\left(0\right)-u_r\left(M\right)+u_v\left(M\right)-u_g\left(M\right)$

Note as M=0, β ' _p(0)=0 _{3 × 1}.

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; be understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (19)

1. a motion alignment methods for inertial navigation system, this inertial navigation system is installed on motion carrier, it is characterized in that, the method comprises:

The rotation information of inertial navigation system measurement self and linear acceleration information;

Inertial navigation system synchronously receives its reference velocity in reference frame and positional information of being provided by external auxiliary information source; And

Inertial navigation system carries out data processing to rotation information and linear acceleration information and reference velocity and positional information, obtain from the body coordinate system in current time relative to the attitude of reference frame, comprise: described inertial navigation system utilizes rate integrating motion alignment algorithm or position integrated motion alignment algorithm to calculate rotation information and linear acceleration information and reference velocity and positional information, obtains attitude matrix with and initial attitude matrix then by chain type product rule obtain from the body coordinate system in current time t relative to the attitude of reference frame, wherein n represents reference frame, and b represents body coordinate system, and 0 represents initial time, t _m=M × T, T represents the time interval, and M is integer.

2. the motion alignment methods of inertial navigation system according to claim 1, it is characterized in that, described inertial navigation system comprises three axle gyro and three axis accelerometers, and wherein three axle gyros are for measuring angle of rotation increment or angular velocity, and three axis accelerometer is used for measuring speed increment or specific force.

3. the motion alignment methods of inertial navigation system according to claim 1, it is characterized in that, in the process that described inertial navigation system utilizes rate integrating motion alignment algorithm or position integrated motion alignment algorithm to calculate rotation information and linear acceleration information and reference velocity and positional information

The rate integrating formula adopted is:

$\begin{array}{c}{C}_b^n\left(0\right){\mathrm{\α}}_v={\mathrm{\β}}_v\\ {\mathrm{\α}}_v\stackrel{\mathrm{\Δ}}{=}{\∫}_0^t{C}_{b\left(t\right)}^{b\left(0\right)}{f}^{b}dt\\ {\mathrm{\β}}_v\stackrel{\mathrm{\Δ}}{=}{C}_{n\left(t\right)}^{n\left(0\right)}{v}^n-v^n\left(0\right)+{\∫}_0^t{C}_{n\left(t\right)}^{n\left(0\right)}{\mathrm{\ω}}_{ie}^n\×v^{n}dt-{\∫}_0^t{C}_{n\left(t\right)}^{n\left(0\right)}{g}^{n}dt\end{array}$ Formula 1

The position integral formula adopted is:

$\begin{array}{c}{C}_b^n\left(0\right){\mathrm{\α}}_p={\mathrm{\β}}_p\\ {\mathrm{\α}}_p\stackrel{\mathrm{\Δ}}{=}{\∫}_0^t{\∫}_0^{\mathrm{\τ}}{C}_{b\left(\mathrm{\σ}\right)}^{b\left(0\right)}{f}^{b}d\mathrm{\σ}d\mathrm{\τ}\\ {\mathrm{\β}}_p\stackrel{\mathrm{\Δ}}{=}{C}_{n\left(t\right)}^{n\left(0\right)}{r}^n-{\mathrm{tv}}^n\left(0\right)-{\∫}_0^t{C}_{n\left(\mathrm{\τ}\right)}^{n\left(0\right)}{\mathrm{\ω}}_{in}^n\×r^{n}d\mathrm{\τ}\\ +{\∫}_0^t{\∫}_0^{\mathrm{\τ}}{C}_{n\left(\mathrm{\σ}\right)}^{n\left(0\right)}{\mathrm{\ω}}_{ie}^n\×v^{n}d\mathrm{\σ}d\mathrm{\τ}-{\∫}_0^t{\∫}_0^{\mathrm{\τ}}{C}_{n\left(\mathrm{\σ}\right)}^{n\left(0\right)}{g}^{n}d\mathrm{\σ}d\mathrm{\τ}\end{array}$ Formula 2

Wherein, for being tied to the attitude matrix of reference frame from body coordinate, it is orthogonal and determinant is 1, for attitude matrix is in the value of initial time, f ^bfor the specific force that accelerometer measures arrives, v ⁿ=[v _nv _uv _e] ^tfor the ground speed that inertial navigation system represents in reference frame, v ⁿ(0) for ground speed is in the value of initial time, the earth rate represented in reference frame, g ⁿthe local gravitational acceleration represented in reference frame, r ⁿbe defined as the integration of ground speed $r^n\left(t\right)={\∫}_0^t{v}^{n}dt={\∫}_0^t{R}_{ic}\stackrel{\·}{p}dt,$ Wherein $R_{ic}=\left[\begin{array}{ccc}0& R_N+h& 0\\ 0& 0& 1\\ (R_E+h)\cos L& 0& 0\end{array}\right],$ The inertial navigation system position represented with local geographic coordinate $p\stackrel{\mathrm{\Δ}}{=}{\left[\begin{array}{ccc}\mathrm{\λ}& L& h\end{array}\right]}^T,$ λ, L, h represent longitude respectively, latitude, highly; R _eand R _nlocal radius of curvature in prime vertical and radius of curvature of meridian respectively.

4. the motion alignment methods of inertial navigation system according to claim 3, it is characterized in that, described inertial navigation system utilizes rate integrating motion alignment algorithm or position integrated motion alignment algorithm to calculate rotation information and linear acceleration information and reference velocity and positional information, obtains attitude matrix with comprise:

that reference frame is relative to inertial coordinates system angular velocity function, select northern sky east horizontal coordinate be reference frame, as follows with the relation of speed and position:

${\mathrm{\ω}}_{in}^n={\mathrm{\ω}}_{ie}^n+{\mathrm{\ω}}_{en}^n=\mathrm{\Ω}\left[\begin{array}{c}\cos L\\ \sin L\\ 0\end{array}\right]+\left[\begin{array}{c}{v}_E/(R_E+h)\\ v_E\tan L/(R_E+h)\\ -v_N/(R_N+h)\end{array}\right]$

Wherein earth rotation angular speed Ω ≈ 7.292115 × 10 ^-5rad/s, considers for in a small amount, in a update time interval, the rotating vector of reference frame relative inertness coordinate system according to the transforming relationship between direction cosine matrix and rotating vector

Again by the chain type product rule of attitude matrix, obtain

Because the body coordinate system of inertial navigation system is very fast relative to the change of inertial coordinates system, corresponding rotating vector needs to carry out shallow conical shell usually; Assuming that in a update time interval, gyro is double sampling successively, is denoted as Δ θ ₁, Δ θ ₂, accelerometer is double sampling successively, is denoted as Δ v ₁, Δ v ₂; Inertial navigation system body coordinate system can be approximately relative to the rotating vector of inertial coordinates system according to the transforming relationship between direction cosine matrix and rotating vector

Equally by the chain type product rule of attitude matrix, obtain

5. the motion alignment methods of inertial navigation system according to claim 4, is characterized in that, described in with calculating be coordination, not free sequencing, and as M=0 with be unit matrix.

6. the motion alignment methods of inertial navigation system according to claim 4, it is characterized in that, described inertial navigation system utilizes rate integrating motion alignment algorithm to calculate rotation information and linear acceleration information and reference velocity and positional information, obtains initial attitude matrix comprise:

Compute vector α _v(t _m);

Compute vector β _v(t _m);

Compute matrix K (t _m); And

Calculate

7. the motion alignment methods of inertial navigation system according to claim 6, is characterized in that, described compute vector α _v(t _m) comprising:

According in formula 1 i.e. α _v(t _m) relate to the integration of specific force after approximate treatment conversion utilize priority twice angle increment in interval T update time and speed increment sampling, and carry out corresponding drawing and shake compensation, α _v(t _m) can according to following formula iterative computation

$u={\mathrm{\Δv}}_1+{\mathrm{\Δv}}_2+\frac{1}{2}({\mathrm{\Δ\θ}}_1+{\mathrm{\Δ\θ}}_2)\×({\mathrm{\Δv}}_1+{\mathrm{\Δv}}_2)+\frac{2}{3}({\mathrm{\Δ\θ}}_1\×{\mathrm{\Δv}}_2+{\mathrm{\Δv}}_1\×{\mathrm{\Δ\θ}}_2)$

${\mathrm{\α}}_v\left(t_M\right)={\mathrm{\α}}_v\left(t_{M-1}\right)+C_{b\left(t_{M-1}\right)}^{b\left(0\right)}u$

Wherein as M=0, α _v(0)=0 _{3 × 1}.

8. the motion alignment methods of inertial navigation system according to claim 6, is characterized in that, described compute vector β _v(t _m) comprising:

Gravity acceleration g ⁿbe the function of position, can calculate according to gravity field model, and β _v(t _m) calculating used external speed and positional information, according to the definition provided in rate integrating formula 1, β _v(t _m) relate to approximate treatment two integrations: with assuming that upgrade in interval approximately linear changes, g ⁿapproximate constant value, β _v(t _m) can according to following formula iterative computation

$u=(\frac{T}{2}I+\frac{T^2}{6}{\mathrm{\ω}}_{in}^n\×){\mathrm{\ω}}_{ie}^n\×v^n\left(t_{M-1}\right)+(\frac{T}{2}I+\frac{T^2}{3}{\mathrm{\ω}}_{in}^n\×){\mathrm{\ω}}_{ie}^n\×v^n\left(t_M\right)-(TI+\frac{T^2}{2}{\mathrm{\ω}}_{in}^n\×)g^n$

${\mathrm{\β}}_v^{\′}\left(t_M\right)={\mathrm{\β}}_v^{\′}\left(t_{M-1}\right)+C_{n\left(t_{M-1}\right)}^{n\left(0\right)}u$

${\mathrm{\β}}_v\left(t_M\right)=C_{n\left(t_M\right)}^{n\left(0\right)}{v}^n-v^n\left(0\right)+{\mathrm{\β}}_v^{\′}\left(t_M\right)$

Wherein as M=0, β ' _v(0)=0 _{3 × 1}.

9. the motion alignment methods of inertial navigation system according to claim 6, is characterized in that, described compute matrix K (t _m) comprising:

Be defined as follows 4 × 4 matrixes which use two special hypercomplex number multiplication matrix; For tri-vector r, hypercomplex number multiplication matrix is defined as follows

$\stackrel{+}{\[r\]}\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cc}0& -r^T\\ r& (r\×)\end{array}\right],\stackrel{-}{\[r\]}\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cc}0& -r^T\\ r& -(r\×)\end{array}\right],$ Wherein r × be the antisymmetric matrix of r;

Assuming that integrand approximate constant value in renewal is interval, K (t _m) can according to following formula iterative computation

$K\left(t_M\right)=K\left(t_{M-1}\right)+T{(\stackrel{+}{\left[{\mathrm{\β}}_v\left(t_M\right)\right]}-\stackrel{-}{\left[{\mathrm{\α}}_v\left(t_M\right)\right]})}^T(\stackrel{+}{\left[{\mathrm{\β}}_v\left(t_M\right)\right]}-\stackrel{-}{\left[{\mathrm{\α}}_v\left(t_M\right)\right]})$

Wherein as M=0, K (0)=0 _{4 × 4}.

10. the motion alignment methods of inertial navigation system according to claim 6, is characterized in that, described calculating comprise:

Meet initial attitude matrix corresponding attitude quaternion is the proper vector corresponding to minimal eigenvalue of matrix K, is denoted as q; Ripe algorithm can be found in canonical algorithm storehouse to be used for solving 4 × 4 matrix K (t _m) proper vector, q is write as [s η ^t] ^t, s and η represents scalar component and the vector portion of hypercomplex number q respectively, according to the transforming relationship between direction cosine matrix and hypercomplex number, obtains $C_b^n\left(0\right)=(s^2-{\mathrm{\η}}^T\mathrm{\η})I+2{\mathrm{\η\η}}^T+2s(\mathrm{\η}\×).$

The motion alignment methods of 11. inertial navigation systems according to claim 4, it is characterized in that, described inertial navigation system utilizes position integrated motion alignment algorithm to calculate rotation information and linear acceleration information and reference velocity and positional information, obtains initial attitude matrix comprise:

Compute vector α _p(t _m);

Compute vector β _p(t _m);

Compute matrix K (t _m); And

Calculate

The motion alignment methods of 12. inertial navigation systems according to claim 11, is characterized in that, described compute vector α _p(t _m) comprising:

According to the definition provided in position integral formula 2, α _p(t _m) relate to the dual-integration of specific force after approximate treatment conversion utilize priority twice angle increment in a update time interval and speed increment sampling, and carry out corresponding spool compensation, α _p(t _m) can according to following formula iterative computation

$u=\frac{T}{30}(25{\mathrm{\Δv}}_1+5{\mathrm{\Δv}}_2+12{\mathrm{\Δ\θ}}_1\×{\mathrm{\Δv}}_1+8{\mathrm{\Δ\θ}}_1\×{\mathrm{\Δv}}_2+2{\mathrm{\Δv}}_1\×{\mathrm{\Δ\θ}}_2+2{\mathrm{\Δ\θ}}_2\×{\mathrm{\Δv}}_2)$

$u_p\left(M\right)=u_p(M-1)+C_{b\left(t_{M-1}\right)}^{b\left(0\right)}u$

${\mathrm{\α}}_p\left(t_M\right)=u_p\left(M\right)+T\underset{m=0}{\overset{M-2}{\Σ}}{C}_{b\left(t_m\right)}^{b\left(0\right)}({\mathrm{\Δv}}_1+{\mathrm{\Δv}}_2+\frac{1}{2}({\mathrm{\Δ\θ}}_1+{\mathrm{\Δ\θ}}_2)\×({\mathrm{\Δv}}_1+{\mathrm{\Δv}}_2)+\frac{2}{3}({\mathrm{\Δ\θ}}_1\×{\mathrm{\Δv}}_2+{\mathrm{\Δv}}_1\×{\mathrm{\Δ\θ}}_2\left)\right)$

Wherein as M=0, α _p(0)=0 _{3 × 1}; For the situation of other increment numbers, spool compensates the calculating of u by different.

The motion alignment methods of 13. inertial navigation systems according to claim 11, is characterized in that, described compute vector β _p(t _m) comprising:

According to the definition provided in position integral formula 2, β _p(t _m) relate to approximate treatment substance integration: and two dual-integrations: with assuming that upgrade in interval approximately linear changes, g ⁿapproximate constant value, β _p(t _m) can according to following formula iterative computation

$\begin{array}{c}{u}_r\left(M\right)=u_r\left(M-1\right)+C_{n\left(t_{M-1}\right)}^{n\left(0\right)}\[\left(\frac{T^2}{3}{\mathrm{\ω}}_{in}^n\×+\frac{5T^3}{24}{\left({\mathrm{\ω}}_{in}^n\×\right)}^2\right)v^n\left(t_{M-1}\right)+\left(\frac{T^2}{6}{\mathrm{\ω}}_{in}^n\×+\frac{T^3}{8}{\left({\mathrm{\ω}}_{in}^n\×\right)}^2\right)v^n\left(t_M\right)\\ +\left({\mathrm{T\ω}}_{in}^n\×+\frac{T^2}{2}{\left({\mathrm{\ω}}_{in}^n\×\right)}^2\right)\underset{m=0}{\overset{M-2}{\Σ}}{R}_{ic}^{-1}\left(t_m\right)\left(p\left(t_{m+1}\right)-p\left(t_m\right)\right)\]\end{array}$

$\begin{array}{c}{u}_v\left(M\right)=u_v\left(M-1\right)+C_{n\left(t_{M-1}\right)}^{n\left(0\right)}\[\left(\frac{T^2}{3}I+\frac{T^3}{12}{\mathrm{\ω}}_{in}^n\×\right){\mathrm{\ω}}_{ie}^n\×v^n\left(t_{M-1}\right)+\left(\frac{T^2}{6}I+\frac{T^3}{12}{\mathrm{\ω}}_{in}^n\×\right){\mathrm{\ω}}_{ie}^n\×v^n\left(t_M\right)\]\\ +T\underset{m=0}{\overset{M-2}{\Σ}}{C}_{n\left(t_m\right)}^{n\left(0\right)}\[\left(\frac{T}{2}I+\frac{T^2}{6}{\mathrm{\ω}}_{in}^n\×\right){\mathrm{\ω}}_{ie}^n\×v^n\left(t_m\right)+\left(\frac{T}{2}I+\frac{T^2}{3}{\mathrm{\ω}}_{in}^n\×\right){\mathrm{\ω}}_{ie}^n\×v^n\left(t_{m+1}\right)\]\end{array}$

$u_g\left(M\right)=u_g(M-1)+C_{n\left(t_{M-1}\right)}^{n\left(0\right)}(\frac{T^2}{2}I+\frac{T^3}{6}{\mathrm{\ω}}_{in}^n\×)g^n+T\underset{m=0}{\overset{M-2}{\Σ}}{C}_{n\left(t_m\right)}^{n\left(0\right)}(TI+\frac{T^2}{2}{\mathrm{\ω}}_{in}^n\×)g^n$

${\mathrm{\β}}_p^{\′}\left(M\right)={\mathrm{\β}}_p^{\′}(M-1)+R_{ic}^{-1}\left(t_{M-1}\right)\left(p\right(t_M)-p(t_{M-1}\left)\right)$

${\mathrm{\β}}_p\left(M\right)=C_{n\left(t_M\right)}^{n\left(0\right)}{\mathrm{\β}}_p^{\′}\left(M\right)-t_M{v}^n\left(0\right)-u_r\left(M\right)+u_v\left(M\right)-u_g\left(M\right)$

Wherein as M=0, β ' _p(0)=0 _{3 × 1}.

The motion alignment methods of 14. inertial navigation systems according to claim 11, is characterized in that, described compute matrix K (t _m), its computation process and employing rate integrating motion alignment algorithm compute matrix K (t _m) process substantially identical, difference is to use β _psubstitute β _v, α _psubstitute α _v, specifically comprise:

Be defined as follows 4 × 4 matrixes $K\left(t\right)={\∫}_0^t{\left(\stackrel{+}{\[{\mathrm{\β}}_p\]}-\stackrel{-}{\[{\mathrm{\α}}_p\]}\right)}^T\left(\stackrel{+}{\[{\mathrm{\β}}_p\]}-\stackrel{-}{\[{\mathrm{\α}}_p\]}\right)dt,$ Which use two special hypercomplex number multiplication matrix; For tri-vector r, hypercomplex number multiplication matrix is defined as follows:

$\stackrel{+}{\[r\]}\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cc}0& -r^T\\ r& (r\×)\end{array}\right],\stackrel{-}{\[r\]}\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cc}0& -r^T\\ r& -(r\×)\end{array}\right],$ Wherein r × be the antisymmetric matrix of r;

Assuming that integrand approximate constant value in renewal is interval, K (t _m) can according to following formula iterative computation

$K\left(t_M\right)=K\left(t_{M-1}\right)+T{(\stackrel{+}{\left[{\mathrm{\β}}_p\left(t_M\right)\right]}-\stackrel{-}{\left[{\mathrm{\α}}_p\left(t_M\right)\right]})}^T(\stackrel{+}{\left[{\mathrm{\β}}_p\left(t_M\right)\right]}-\stackrel{-}{\left[{\mathrm{\α}}_p\left(t_M\right)\right]})$

Wherein as M=0, K (0)=0 _{4 × 4}.

The motion alignment methods of 15. inertial navigation systems according to claim 11, is characterized in that, described calculating its computation process calculates with adopting rate integrating motion alignment algorithm process substantially identical, difference is to use β _psubstitute β _v, α _psubstitute α _v, specifically comprise:

Meet initial attitude matrix corresponding attitude quaternion is the proper vector corresponding to minimal eigenvalue of matrix K, is denoted as q; Ripe algorithm can be found in canonical algorithm storehouse to be used for solving 4 × 4 matrix K (t _m) proper vector, q is write as [s η ^t] ^t, s and η represents scalar component and the vector portion of hypercomplex number q respectively, according to the transforming relationship between direction cosine matrix and hypercomplex number, obtains $C_b^n\left(0\right)=(s^2-{\mathrm{\η}}^T\mathrm{\η})I+2{\mathrm{\η\η}}^T+2s(\mathrm{\η}\×).$

The motion alignment methods of 16. inertial navigation systems according to claim 1, is characterized in that, described external auxiliary information source is equipment or the mode that can provide required speed and positional information.

The motion alignment methods of 17. inertial navigation systems according to claim 16, is characterized in that, described external auxiliary information source is Global Positioning System (GPS) GPS.

The motion alignment methods of 18. inertial navigation systems according to claim 16, it is characterized in that, according to the different accuracy requirement that motion is aimed at, described external auxiliary information source is the mode accurately measured or provides required speed and positional information in the mode of approximate estimation.

The motion alignment methods of 19. inertial navigation systems according to claim 16, is characterized in that, described external auxiliary information source compensates backward inertial navigation system via lever arm and provides speed in reference frame and positional information.