CN104296780A - SINS self-alignment and latitude calculation method based on apparent motion of gravity - Google Patents

Abstract

The invention discloses an SINS self-alignment and latitude calculation method based on apparent motion of gravity. The method comprises the following steps: (1) constructing vectors of the apparent motion of gravity according to measured values of a gyroscope and an accelerometer; (2) eliminating influences caused by random noises of instruments via a parameter identification and reconstruction method; (3) calculating the coordinate of a central point of a base circle of a cone of the apparent motion of gravity and the radius of the base circle according to the vectors of the apparent motion of gravity at three moments; (4) constructing the vector of a center axis of the cone and finishing initial alignment according to a vector calculation method; and (5) finishing the calculation of a latitude L according to geometrical relationships of all vectors in the cone.

Description

A kind of SINS autoregistration based on gravity apparent motion and latitude computing method

Technical field

The present invention relates to a kind of SINS initial alignment based on gravity apparent motion and latitude computing method, the initial alignment be applicable under carrier aircraft radio motion, swinging condition is aimed at, without any need for external reference information in alignment procedures, and in the aligning process, the calculating of latitude can be completed, belong to the technical field of navigation algorithm.

Background technology

For the inertial navigation system based on integration working method, initial alignment is prerequisite and the basis of its work, is also one of the key and Technology Difficulties of INS.Specifically for SINS, initial alignment refers to that acquisition carrier system b and navigation are the attitude matrix between n.In many SINS Initial Alignment Methods, self-aligned technology is widely studied and concern because not needing to utilize external reference navigation information.Conventional Alignment Method includes: aim at the analytical method of rotational-angular velocity of the earth based on acceleration of gravity, aim at based on the compass method of compass effect, retrain aim at the zero-speed of Kalman filter technology based on zero-speed.

But said method when carrying out initial alignment on swaying base, all there is the shortcoming of antijamming capability deficiency.As on swaying base, because rotational-angular velocity of the earth is submerged in gyro noise completely, aligning cannot be completed.

In addition, said method all needs to utilize external location information in initial alignment process.Need to utilize latitude information to decompose rotational-angular velocity of the earth as resolved aligning; During compass method is aimed at zero-speed, need positional information to form SINS and resolve loop.

Summary of the invention

Goal of the invention: the object of the invention is to, under the condition of unknown latitude information, utilize the measurement data of inertia type instrument self completely, complete the initial alignment of SINS, and obtain latitude information and resolve for subsequent navigation.

Technical scheme: the SINS autoregistration based on gravity apparent motion of the present invention and latitude computing method,

Compared with prior art, its beneficial effect is in the present invention: 1) in initial alignment process, do not need external reference supplementary guiding information; 2) accelerometer measures noise does not need Negotiation speed integration method smoothing, but is removed by parameter identification and reconstructing method; 3) for the actual information containing all measuring values in alignment procedures of three vectors of initial alignment, but not only three time points; 4), after aligning terminal procedure and aligning terminate, can externally export with reference to dimensional information, for navigation calculation or other equipment use of SINS.

Accompanying drawing explanation

Fig. 1 is the gravity apparent motion schematic diagram that the present invention uses;

Fig. 2 is that the gravity apparent motion circular cone central shaft that the present invention uses solves schematic diagram;

Fig. 3 is misalignment estimation of error Error Graph of the present invention;

Fig. 4 is latitude error of calculation figure of the present invention.

Embodiment

Below technical solution of the present invention is described in detail, but protection scope of the present invention is not limited to described embodiment.

Embodiment:

The present invention is directed to the cone that in inertial system, gravity apparent motion is formed, gyroscope and acceleration measuring value is utilized to build gravity apparent motion vector, parameter identification and reconstructing method is utilized to eliminate the impact of instrument random noise, the gravity apparent motion in three moment vector is utilized to ask for center point coordinate and the end radius of circle of circle at the bottom of gravity apparent motion cone, and build cone center axial vector, complete initial alignment by vector operation method, complete latitude according to vector geometry relation each in cone and calculate.

Below in conjunction with accompanying drawing, the invention process method is described in more detail:

Fig. 1 is the gravity apparent motion schematic diagram that the present invention uses, and the acceleration of gravity observed in inertial system with certain point of earth rotation points to the change with size, forms this circular cone.

Utilize gyroscope and accelerometer specifically to obtain each gravity apparent motion vector of circular cone in Fig. 1, specifically comprise the steps:

Solidify initial time t ₀carrier coordinate system b be inertial coordinates system obtain initial time b system with between system, attitude matrix is i is the unit matrix of 3 × 3;

Utilize gyrostatic measured value follow the tracks of b system and the change of system:

${\stackrel{\stackrel{\·}{^}}{C}}_b^{i_{b0}}\left(t\right)={\hat{C}}_b^{i_{b0}}\left(t\right)({\widetilde{\mathrm{\ω}}}_{i_{b0}b}^b\×)---\left(1\right)$

In formula, subscript " ^ " represents calculated value; " ~ " represents measured value.

Utilize attitude matrix the measured value of degree of will speed up meter projects to in system, thus complete the calculating of gravity apparent motion vector in inertial system:

${\hat{f}}^{i_{b0}}\left(t\right)={\hat{C}}_b^{i_{b0}}\left(t\right){\tilde{f}}^b\left(t\right)---\left(2\right)$

Utilize parameter identification and reconstructing method to eliminate the impact of instrument random noise, specifically comprise:

Gravity apparent motion cone geometric parameter in Fig. 1 and the selection of inertial system have nothing to do, but embody need launch in the coordinate system of feature.According to projection relation, the ideal expression can asking for gravity apparent motion is as follows:

$\begin{array}{c}{f}^{i_{b0}}\left(t\right)=C_{e_0}^{i_{b0}}{C}_e^{e_0}\left(t\right)C_n^e{f}^n\\ =\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)& -\sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)& 0\\ \sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)& \cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}{b}_{11}& b_{12}& b_{13}\\ b_{21}& b_{22}& b_{23}\\ b_{31}& b_{32}& b_{33}\end{array}\right]\left[\begin{array}{c}0\\ 0\\ -g\end{array}\right]\\ =\begin{array}{c}\left[\begin{array}{ccc}{A}_{11}& A_{12}& A_{13}\\ A_{21}& A_{22}& A_{23}\\ A_{31}& A_{32}& A_{33}\end{array}\right]\left[\begin{array}{c}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)\\ \sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)\\ 1\end{array}\right]=\begin{array}{c}\left[\begin{array}{c}{A}_{11}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{12}\sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{13}\\ A_{21}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{22}\sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{23}\\ A_{31}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{32}\sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{23}\end{array}\right]\end{array}\end{array}\begin{array}{}\end{array}\end{array}---\left(3\right)$

In formula, f ⁿfor navigation is gravitational acceleration vector in n; G is acceleration of gravity; e ₀for initial time earth system; e ₀for earth system; ω _iefor rotational-angular velocity of the earth; a _ijwith b _ij(i, j=1 ~ 3) are respectively matrix with in relevant unknown element; A _ijfor a _ij, b _ijcombination.

Utilize the actual computation value of gravity apparent motion in formula (2) by the parameter A in recursive least-squares identification method distinguishing type (3) _ij, and according to the parameter that identification obtains, the apparent motion of reconstruct gravity specifically comprise the following steps:

21) right in system axle parameter carries out identification, and selection mode vector is X=[A ₁₁a ₁₂a ₁₃] ^t, measuring vector is wherein k is iteration update times, and system equation, range matrix and range equation are as follows respectively:

X _k+1＝X _k (4)

H _k＝[cos(ω _iet) sin(ω _iet) 1] (5)

Z _k＝H _kX _k+V _k (6)

In formula, V _kfor range noise.Recursive Least-square is specific as follows:

$\left\{\begin{array}{c}{K}_k=P_{k-1}{H}_k^T{(H_k{P}_{k-1}{H}_k^T+R_k)}^{-1}\\ X_k=X_{k+1}+K_k(Z_k-H_k{X}_{k-1})\\ P_k=(I-K_k{H}_k)P_{k-1}\end{array}\right.---\left(7\right)$

In formula, K _kfor gain matrix; P _kfor state covariance matrix; R _kfor V _kcovariance matrix.

22) right in system axle parameter carries out identification, and selection mode vector is X=[A ₂₁a ₂₂a ₂₃] ^t, measuring vector is all the other various cotypes (4-7).

23) right in system axle parameter carries out identification, and selection mode vector is X=[A ₃₁a ₃₂a ₃₃] ^t, measuring vector is all the other various cotypes (4-7).

According to 2) in identification obtain parameter A _ij, build matrix and according to ω _iet, the apparent motion of reconstruct gravity concrete select time point is respectively T _a=-t, T _b=0 and T _c=t, wherein T _cfor current time,

$\hat{A}=\left[\begin{array}{ccc}{\hat{A}}_{11}& {\hat{A}}_{12}& {\hat{A}}_{13}\\ {\hat{A}}_{21}& {\hat{A}}_{22}& {\hat{A}}_{23}\\ {\hat{A}}_{31}& {\hat{A}}_{32}& {\hat{A}}_{33}\end{array}\right]---\left(8\right)$

As shown in Figure 2, t is utilized _a, t _bwith t _cthe gravity apparent motion vector in three moment asks for center point coordinate and the end radius of circle of circle at the bottom of gravity apparent motion cone, specifically comprises:

At the bottom of cone, circle central point is:

$\left[\begin{array}{c}{x}_0\\ y_0\\ z_0\end{array}\right]={\left[\begin{array}{ccc}{A}_1& B_1& C_1\\ A_2& B_2& C_2\\ A_3& B_3& C_3\end{array}\right]}^{-1}\left[\begin{array}{c}{D}_1\\ D_2\\ D_3\end{array}\right]---\left(10\right)$

In formula,

$\left\{\begin{array}{c}{A}_1={\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}-{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}-{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}+{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}+{\hat{f}}_{t_C}^{z_{i_{b_0}}}-{\hat{f}}_{t_C}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}\\ B_1=-{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}+{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}+{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_B}^{x_{i_{b_0}}}-{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_C}^{x_{i_{b_0}}}-{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}+{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}\\ C_1={\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}-{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}-{\hat{f}}_{t_A}^{y_{i_{b_0}}}-{\hat{f}}_{t_B}^{x_{i_{b_0}}}+{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{x_{i_{b_0}}}+{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}-{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}\\ D_1=-{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}+{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}+{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}-{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}-{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}{\hat{f}}_{t_A}^{z_{i_{b_0}}}+{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}{\hat{f}}_{t_A}^{z_{i_{b_0}}}\\ A_2=2({\hat{f}}_{t_B}^{x_{i_{b_0}}}-{\hat{f}}_{t_A}^{x_{i_{b_0}}}),B_2=2({\hat{f}}_{t_B}^{y_{i_{b_0}}}-{\hat{f}}_{t_A}^{y_{i_{b_0}}}),C_2=2({\hat{f}}_{t_B}^{z_{i_{b_0}}}-{\hat{f}}_{t_A}^{z_{i_{b_0}}})\\ D_2={\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_A}^{x_{i_{b_0}}}+{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_A}^{y_{i_{b_0}}}+{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_A}^{z_{i_{b_0}}}-{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{x_{i_{b_0}}}-{\hat{f}}_{t_B}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}-{\hat{f}}_{t_B}^{z_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}\\ A_3=2({\hat{f}}_{t_C}^{x_{i_{b_0}}}-{\hat{f}}_{t_A}^{x_{i_{b_0}}}),B_3=2({\hat{f}}_{t_C}^{y_{i_{b_0}}}-{\hat{f}}_{t_A}^{y_{i_{b_0}}}),C_3=2({\hat{f}}_{t_C}^{z_{i_{b_0}}}-{\hat{f}}_{t_A}^{z_{i_{b_0}}})\\ D_3={\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_A}^{x_{i_{b_0}}}+{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_A}^{y_{i_{b_0}}}+{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_A}^{z_{i_{b_0}}}-{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{x_{i_{b_0}}}-{\hat{f}}_{t_C}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}-{\hat{f}}_{t_C}^{z_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}\end{array}\right.---\left(11\right)$

End radius of circle is:

$R=\sqrt{{({\hat{f}}_{t_C}^{x_{i_{b_0}}}-x_0)}^2+{({\hat{f}}_{t_C}^{y_{i_{b_0}}}-y_0)}^2+{({\hat{f}}_{t_C}^{z_{i_{b_0}}}-z_0)}^2}---\left(12\right)$

Build cone center axial vector, complete initial alignment by vector operation method, specifically comprise:

Structure central shaft vector:

As shown in Figure 2, in inertial system sky to axial vector with overlap, thus build sky to vector:

Utilize vector operation, build east orientation vector:

Utilize vector operation, build north orientation vector:

$\hat{N}=\frac{\hat{U}\×\hat{E}}{\left|\right|\hat{U}\×\hat{E}\left|\right|}---\left(16\right)$

Build n system relative to the attitude matrix of system:

${\hat{C}}_{i_{b_0}}^n\left(t\right)=\left[\begin{array}{ccc}{\hat{E}}^T& {\hat{N}}^T& {\hat{U}}^T\end{array}\right]---\left(17\right)$

Build n system relative to the attitude matrix of system:

${\hat{C}}_b^n\left(t\right)={\hat{C}}_{i_{b_0}}^n\left(t\right){\hat{C}}_b^{i_{b_0}}\left(t\right)---\left(18\right)$

Complete latitude according to vector geometry relation each in cone to calculate, specifically comprise:

$L=\arccos \frac{\left|\right|\left[\begin{array}{ccc}{x}_0& y_0& z_0\end{array}\right]\left|\right|}{\left|\right|{\hat{f}}^{i_{b0}}\left(t_C\right)\left|\right|}---\left(19\right)$

Beneficial effect of the present invention is verified by following emulation:

Matlab simulates inertia type instrument data

Carrier is in zero-speed swinging condition, does oscillating motion with sinusoidal rule around three axles, and its pitching, transverse direction and course are waved mathematical model and be:

In formula, θ, γ and ψ are respectively the angle variables in pitching, rolling and course; A _p, A _r, A _ybe respectively pitching, rolling and course wave amplitude; ω _p, ω _pwith ω _yrepresent the angle of oscillation frequency in pitching, rolling and course respectively; with pitching respectively, rolling and course initial phase; ψ ₀represent initial heading; ω _i=2 π/T _i, i=P, R, Y, T _irepresent corresponding rolling period.

Obtain sub-inertial navigation instrument gross data by above-mentioned emulated data simulation, and superpose corresponding site error thereon as instrument actual acquired data, sub-inertial navigation is sampled to described instrument actual acquired data, and for navigation calculation, the sampling period is 10ms.

The correlation parameter of emulation:

Naval vessel initial position: east longitude 118 °, north latitude 32 °;

Ship speed: 0m/s;

Ship sway amplitude: pitching 7 °, rolling 15 °, boat shake 5 °;

The ship sway cycle: pitching 8s, rolling 7.5s, boat shake 6s;

Ship sway initial phase: be 0;

Initial heading, naval vessel: 0 °;

Equatorial radius: 6378165m;

Earth ellipsoid degree: 1/298.3;

Earth surface acceleration of gravity: 9.8m/s2;

Rotational-angular velocity of the earth: 15.04088 °/h;

Gyroscope constant value error: 0.05 °/h;

Gyro white noise error: 0.05 °/h;

Accelerometer bias: 500ug;

Accelerometer white noise error: 500ug;

Aim at the checking calculated with latitude

Proof of algorithm is carried out in ordinary PC.1200s is carried out in emulation, and in simulation process process, (1) produces instrumented data; (2) gravity apparent motion is built according to instrumented data; (3) gravity apparent motion calculated value is utilized to carry out parameter identification and reconstruct; (4) the gravity apparent motion of reconstruct is utilized to carry out aligning computing; (5) the gravity apparent motion of reconstruct is utilized to carry out latitude calculating; (6) above-mentioned steps is repeated.Fig. 3 and 4 is respectively alignment result and the latitude error of calculation.

In Fig. 3, each curve shows, under swaying base, the method for the present invention's design effectively completes initial alignment.

In Fig. 4, curve shows, under swaying base, the method for the present invention's design effectively completes the calculating of latitude.

As mentioned above, although represented with reference to specific preferred embodiment and described the present invention, it shall not be construed as the restriction to the present invention self.Under the spirit and scope of the present invention prerequisite not departing from claims definition, various change can be made in the form and details to it.

Claims (6)

1., based on SINS autoregistration and the latitude computing method of gravity apparent motion, it is characterized in that, comprise the following steps:

1) gravity apparent motion vector is built by gyroscope and acceleration measuring value;

2) parameter identification and reconstructing method is adopted to eliminate the impact of instrument random noise;

3) center point coordinate and the end radius of circle of circle at the bottom of gravity apparent motion cone is asked for by the gravity apparent motion vector in three moment;

4) build cone center axial vector, complete initial alignment by vector operation method;

5) complete latitude L according to vector geometry relation each in cone to calculate.

2. a kind of SINS autoregistration based on gravity apparent motion according to claim 1 and latitude computing method, its step 1 described in feature) build gravity apparent motion vector by gyroscope and acceleration measuring value and specifically comprise the steps:

Solidify initial time t ₀carrier coordinate system b be inertial coordinates system obtain initial time b system with between system, attitude matrix is i is the unit matrix of 3 × 3;

Utilize gyrostatic measured value follow the tracks of b system relative to the change of system:

${\stackrel{\stackrel{\·}{^}}{C}}_b^{i_{b0}}\left(t\right)={\hat{C}}_b^{i_{b0}}\left(t\right)({\widetilde{\mathrm{\ω}}}_{i_{b0}b}^b\×)---\left(1\right)$

In formula, subscript " ^ " represents calculated value; " ~ " represents measured value;

The attitude matrix that through type (1) calculates the measured value of degree of will speed up meter project to in system, obtain gravity apparent motion vector in inertial system for:

${\hat{f}}^{i_{b0}}\left(t\right)={\hat{C}}_b^{i_{b0}}\left(t\right){\tilde{f}}^b\left(t\right)---\left(2\right).$

3. a kind of SINS autoregistration based on gravity apparent motion according to claim 1 and latitude computing method, is characterized in that, described step 2) adopt parameter identification and reconstructing method to eliminate the impact of instrument random noise, specifically comprise:

The ideal expression asking for gravity apparent motion is as follows:

$\begin{array}{c}{f}^{i_{b0}}\left(t\right)=C_{e_0}^{i_{b0}}{C}_e^{e_0}\left(t\right)C_n^e{f}^n\\ =\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)& -\sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)& 0\\ \sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)& \cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}{b}_{11}& b_{12}& b_{13}\\ b_{21}& b_{22}& b_{23}\\ b_{31}& b_{32}& b_{33}\end{array}\right]\left[\begin{array}{c}0\\ 0\\ -g\end{array}\right]\\ =\left[\begin{array}{ccc}{A}_{11}& A_{12}& A_{13}\\ A_{21}& A_{22}& A_{23}\\ A_{31}& A_{32}& A_{33}\end{array}\right]\left[\begin{array}{c}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)\\ \sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)\\ 1\end{array}\right]=\begin{array}{c}\left[\begin{array}{c}{A}_{11}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{12}\sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{13}\\ A_{21}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{22}\sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{23}\\ A_{31}\cos \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{32}\sin \left({\mathrm{\ω}}_{\mathrm{ie}}t\right)+A_{33}\end{array}\right]\end{array}\end{array}---\left(3\right)$

In formula, f ⁿfor navigation is gravitational acceleration vector in n; G is acceleration of gravity; e ₀for initial time earth system; E is earth system; ω _iefor rotational-angular velocity of the earth; a _ijwith b _ij(i, j=1 ~ 3) are respectively matrix with in each element; A _ijfor computing obtain about a _ij, b _ijfunction;

Utilize the actual computation value of gravity apparent motion in formula (2) by the parameter A in recursive least-squares identification method distinguishing type (3) _ij, and according to the parameter that identification obtains, the apparent motion of reconstruct gravity specifically comprise the following steps:

21) right in system axle parameter carries out identification, and selection mode vector is X=[A ₁₁a ₁₂a ₁₃] ^t, measuring vector is wherein k is iteration update times, system equation, range matrix H _kand measurement equation is as follows successively respectively:

X _k+1＝X _k (4)

H _k＝[cos(ω _iet) sin(ω _iet) 1] (5)

Z _k＝H _kX _k+V _k (6)

In formula, V _kfor range noise.Recursive Least-square is specific as follows:

$\left\{\begin{array}{c}{K}_k=P_{k-1}{H}_k^T{(H_k{P}_{k-1}{H}_k^T+R_k)}^{-1}\\ X_k=X_{k-1}+K_k(Z_k-H_k{X}_{k-1})\\ P_k=(I-K_k{H}_k)P_{k-1}\end{array}\right.---\left(7\right)$

In formula, K _kfor gain matrix; P _kfor state covariance matrix; R _kfor V _kcovariance matrix;

22) right in system axle parameter carries out identification, and selection mode vector is X=[A ₂₁a ₂₂a ₂₃] ^t, measuring vector is all the other various cotype (4)-(7);

23) right in system axle parameter carries out identification, and selection mode vector is X=[A ₃₁a ₃₂a ₃₃] ^t, measuring vector is all the other various cotype (4)-(7);

According to step 2) in identification obtain parameter A _ij, build matrix and according to ω _iet, the apparent motion of reconstruct gravity concrete select time point is respectively T _a=-t, T _b=0 and T _c=t, wherein T _cfor current time,

$\hat{A}=\left[\begin{array}{ccc}{\hat{A}}_{11}& {\hat{A}}_{12}& {\hat{A}}_{13}\\ {\hat{A}}_{21}& {\hat{A}}_{22}& {\hat{A}}_{23}\\ {\hat{A}}_{31}& {\hat{A}}_{32}& {\hat{A}}_{33}\end{array}\right]---\left(8\right)$

4. a kind of SINS autoregistration based on gravity apparent motion according to claim 1 and latitude computing method, its step 3 described in feature) center point coordinate and the end radius of circle of circle at the bottom of gravity apparent motion cone is asked for by the gravity apparent motion vector in three moment, specifically comprise:

At the bottom of cone, circle central point is:

$\left[\begin{array}{c}{x}_0\\ y_0\\ z_0\end{array}\right]={\left[\begin{array}{ccc}{A}_1& B_1& C_1\\ A_2& B_2& C_2\\ A_3& B_3& C_3\end{array}\right]}^{-1}\left[\begin{array}{c}{D}_1\\ D_2\\ D_3\end{array}\right]---\left(10\right)$

In formula,

$\left\{\begin{array}{c}{A}_1={\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}-{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}-{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}+{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}+{\hat{f}}_{t_B}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}-{\hat{f}}_{t_C}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}\\ B_1=-{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}+{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}+{\hat{f}}_{t_A}^{x_{i_{b_0}}}-{\hat{f}}_{t_B}^{x_{i_{b_0}}}-{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_C}^{x_{i_{b_0}}}-{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}+{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}\\ C_1={\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}-{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}-{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{x_{i_{b_0}}}+{\hat{f}}_{t_A}^{y_{i{b}_0}}{\hat{f}}_{t_C}^{x_{i_{b_0}}}+{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}-{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}\\ D_1=-{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}+{\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}+{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}-{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}-{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}{\hat{f}}_{t_A}^{z_{i_{b_0}}}+{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}{\hat{f}}_{t_A}^{z_{i_{b_0}}}\\ A_2=2({\hat{f}}_{t_B}^{x_{i_{b_0}}}-{\hat{f}}_{t_A}^{x_{i_{b_0}}}),B_2=2({\hat{f}}_{t_B}^{y_{i_{b_0}}}-{\hat{f}}_{t_A}^{y_{i_{b_0}}}),C_2=2({\hat{f}}_{t_B}^{z_{i_{b_0}}}-{\hat{f}}_{t_A}^{z_{i_{b_0}}})\\ D_2={\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_A}^{x_{i_{b_0}}}+{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_A}^{y_{i_{b_0}}}+{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_A}^{z_{i_{b_0}}}-{\hat{f}}_{t_B}^{x_{i_{b_0}}}{\hat{f}}_{t_B}^{x_{i_{b_0}}}-{\hat{f}}_{t_B}^{y_{i_{b_0}}}{\hat{f}}_{t_B}^{y_{i_{b_0}}}-{\hat{f}}_{t_B}^{z_{i_{b_0}}}{\hat{f}}_{t_B}^{z_{i_{b_0}}}\\ A_3=2({\hat{f}}_{t_C}^{x_{i_{b_0}}}-{\hat{f}}_{t_A}^{x_{i_{b_0}}}),B_3=2({\hat{f}}_{t_C}^{y_{i_{b_0}}}-{\hat{f}}_{t_A}^{y_{i_{b_0}}}),C_3=2({\hat{f}}_{t_C}^{z_{i_{b_0}}}-{\hat{f}}_{t_A}^{z_{i_{b_0}}})\\ D_3={\hat{f}}_{t_A}^{x_{i_{b_0}}}{\hat{f}}_{t_A}^{x_{i_{b_0}}}+{\hat{f}}_{t_A}^{y_{i_{b_0}}}{\hat{f}}_{t_A}^{y_{i_{b_0}}}+{\hat{f}}_{t_A}^{z_{i_{b_0}}}{\hat{f}}_{t_A}^{z_{i_{b_0}}}-{\hat{f}}_{t_C}^{x_{i_{b_0}}}{\hat{f}}_{t_C}^{x_{i_{b_0}}}-{\hat{f}}_{t_C}^{y_{i_{b_0}}}{\hat{f}}_{t_C}^{y_{i_{b_0}}}-{\hat{f}}_{t_C}^{z_{i_{b_0}}}{\hat{f}}_{t_C}^{z_{i_{b_0}}}\end{array}\right.---\left(11\right)$

End radius of circle is:

$R=\sqrt{{({\hat{f}}_{t_C}^{x_{i_{b_0}}}-x_0)}^2+{({\hat{y}}_{t_C}^{y_{i_{b_0}}}-y_0)}^2+{({\hat{f}}_{t_C}^{z_{i_{b_0}}}-z_0)}^2}---\left(12\right).$

5. a kind of SINS autoregistration based on gravity apparent motion according to claim 1 and latitude computing method, it is characterized in that, described step 3) to ask at the bottom of gravity apparent motion cone the center point coordinate of circle by the gravity apparent motion vector in three moment and end radius of circle is specially:

Structure central shaft vector:

Build sky to vector:

Structure east orientation vector:

Structure north orientation vector:

$\hat{N}=\frac{\hat{U}\×\hat{E}}{\left|\right|\hat{U}\×\hat{E}\left|\right|}---\left(16\right)$

Build n system relative to the attitude matrix of system:

${\hat{C}}_{i_{b_0}}^n\left(t\right)=\left[\begin{array}{ccc}{\hat{E}}^T& {\hat{N}}^T& {\hat{U}}^T\end{array}\right]---\left(17\right)$

Build n system relative to the attitude matrix of system:

${\hat{C}}_b^n\left(t\right)={\hat{C}}_{i_{b_0}}^n\left(t\right){\hat{C}}_b^{i_{b_0}}\left(t\right).$

6. a kind of SINS autoregistration based on gravity apparent motion according to claim 1 and latitude computing method, is characterized in that, described step 5) complete latitude L according to vector geometry relation each in cone and calculate, be specially:

$L=\arccos \frac{\left|\right|\left[\begin{array}{ccc}{x}_0& y_0& z_0\end{array}\right]\left|\right|}{\left|\right|{\hat{f}}^{i_{b0}}\left(t_C\right)\left|\right|}.$