CN102538821B - Fast and parameter sectional type self-alignment method for strapdown inertial navigation system - Google Patents

Abstract

The invention relates to a fast and parameter sectional type self-alignment method for a strapdown inertial navigation system. A coarse alignment process is finished through an analysis method, and then horizontal precise alignment and directional precise alignment are conducted. The directional precise alignment is divided into three stages, and each stage selects different adjustment time and attenuation coefficient to determine alignment parameters according to characteristics of the stage. Acceleration correction and angular velocity correction are calculated based on the alignment parameters, input acceleration information and angular velocity information are corrected, an initial attitude angle is obtained through hypercomplex number calculating by using corrected information, and a precise alignment process is finished. The fast and parameter sectional type self-alignment method finishes initial alignment through an analysis method and a compass method by collecting data of a gyroscope and an accelerometer, other sensor information is not required, and safety and security of the initial alignment are guaranteed. The fast and parameter sectional type self-alignment method selects the optimum adjusting time and attenuation coefficient according to alignment characteristics of different stages to calculate other alignment parameters, fast convergence performance and anti-interference performance of an alignment curve are improved.

Description

A kind of quick, parameter sectional type self-alignment method for strapdown inertial navigation system

Technical field

The invention belongs to strap-down inertial technical field, relate to initial alignment, is a kind of quick, parameter sectional type self-alignment method for strapdown inertial navigation system.

Background technology

Strap-down inertial, is called for short inertial navigation, and an important problem of strapdown inertial navitation system (SINS) is initial alignment.Within the short as far as possible time, reaching the highest alignment precision, is the target that inertial navigation Initial Alignment Technique is pursued.The initial alignment of inertial navigation is exactly to determine the attitude matrix of initial time.

Initial alignment has the requirement of precision and two aspects of rapidity.In order to meet high-precision requirement, wish that inertial sensor has high as far as possible precision and stability, and disturbance is insensitive to external world to wish system.For improving the precision of system, while also wishing initial alignment, can gyroscopic drift, accelerometer bias and their scaling ratio be demarcated and be compensated.Obviously, the requirement of this two aspect of precision and rapidity is conflicting, therefore need to reasonably carry out system, takes into account as far as possible the requirement of this two aspect, to trying to achieve satisfied effect.

The process of utilizing compass effect to carry out self alignment is generally divided into coarse alignment and fine alignment two steps are carried out.Coarse alignment requires as early as possible mathematical platform to be adjusted in some accuracy ratings, and leading indicator is the shorter aligning time; Fine alignment carries out on the basis of coarse alignment, general first level-off, and then carry out azimuthal alignment, leading indicator is alignment precision.Precision when fine alignment finishes is exactly that inertial navigation system enters the initial precision while navigating mode of operation.

The present invention is directed in the alignment procedures occurring in traditional Alignment Method the problems such as long and antijamming capability of shake, aligning time is not high, the present invention divides fine alignment process for three phases, and each stage selects different adjustment time and attenuation coefficient to have reached quick, jamproof object according to the parameter of aiming at characteristics design the best of different phase.

Summary of the invention

Technology of the present invention is dealt with problems and is: the problem such as long and poor anti jamming capability for the alignment procedures shake occurring in traditional Alignment Method, aligning time, a kind of quick, parameter sectional type self-alignment method for strapdown inertial navigation system is provided, is specially adapted to strapdown inertial navigation system and completes passive autonomous rapid alignment process.

Technical solution of the present invention is: a kind of quick, parameter sectional type self-alignment method for strapdown inertial navigation system, be divided into coarse alignment and fine alignment two steps, first utilize analytical method to complete coarse alignment process, then carry out horizontal alignment and azimuthal alignment, based on fine alignment calculation of parameter acceleration correction amount and rate correction amount, acceleration information and angular velocity information to input strapdown inertial navigation system are revised, utilizing revised information to carry out hypercomplex number resolves and obtains initial attitude angle, complete fine alignment process, comprise the following steps:

1) before aligning, first determine self aligned fine alignment parameter, comprise that each stage damping is than ξ, attenuation coefficient σ, adjustment time t _s, aim at time T _iand other damping parameters of each stage that gone out by described calculation of parameter;

Fine alignment segmentation is carried out, and according to the different designs horizontal alignment of selecting alignment parameter, is a stage, and azimuthal alignment is three phases, specific as follows:

The horizontal alignment stage: the aligning time is T ₁=100s

$\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.045， $t_s=\frac{3}{\mathrm{\σ}}=66.7$

The azimuthal alignment first stage: aim at time T ₂=300s

$\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.02， $t_s=\frac{3}{\mathrm{\σ}}=150$

Azimuthal alignment subordinate phase: aim at time T ₃=300s

$\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.015， $t_s=\frac{3}{\mathrm{\σ}}=200$

The azimuthal alignment phase III: aim at time T ₄=300s

$\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.01， $t_s=\frac{3}{\mathrm{\σ}}=300$

According to damping ratio ξ and attenuation coefficient σ, be calculated as follows other damping parameters of each stage:

Strapdown inertial navitation system (SINS) adopts sky, northeast coordinate system, according to the horizontal compass alignment principles of strapdown inertial navitation system (SINS), obtains the damping parameter on each rank of horizontal alignment stage system:

K ₁＝3σ

$K_2=\frac{{\mathrm{\σ}}^2}{{\mathrm{\ω}}_s^2}(2+\frac{1}{{\mathrm{\ξ}}^2})-1$

$K_3=\frac{{\mathrm{\σ}}^3}{{\mathrm{g\ξ}}^2}$

According to strapdown inertial navitation system (SINS) azimuth compass alignment principles, obtain the damping parameter on each rank of azimuthal alignment stage system:

K′ ₁＝K′ ₄＝2σ

${K^{\′}}_2=\frac{{4\mathrm{\σ}}^2}{{\mathrm{\ω}}_s^2}-1$

${K^{\′}}_3=\frac{{4\mathrm{\σ}}^4}{g}$

Wherein, g is acceleration of gravity, and R is earth radius;

2) utilize analytical method to carry out coarse alignment, determine initial attitude matrix and angle, initial heading initial pitch angle θ ₀with initial horizontal cradle angle γ ₀;

3) in step 2) start fine alignment process on the basis of coarse alignment, according to fine alignment institute stage by stage, each stage is by quasi loop being calculated to the lower acceleration correction information of navigation coordinate system with rate correction information described navigation coordinate is sky, northeast coordinate system;

4) by step 3) the middle acceleration correction information of calculating gained with rate correction information be transformed in carrier coordinate system, for the transition matrix of navigation coordinate to carrier coordinate, thus the specific force to the accelerometer in strapdown inertial navigation system with gyrostatic angular velocity revise,

5) utilize step 4) in the corrected force information that compares and angular velocity information use hypercomplex number update algorithm to calculate the attitude matrix in this attitude algorithm cycle, thereby determine corresponding pitch angle, roll angle and course angle, the attitude after output is upgraded;

6) step 3) to 5) be an attitude algorithm cycle, repeating step 3) to 5) carry out the calculating in next attitude algorithm cycle, obtain pitch angle, roll angle and the course angle of corresponding attitude algorithm cycle carrier, until T.T. in cycle reaches step 1) in the aligning time T in determined each stage _i, complete fine alignment, export the attitude of last cycle renewal;

7) complete horizontal alignment and azimuthal alignment after alignment procedures finish, obtain accurate attitude angle, realize strapdown inertial navigation system autoregistration.

Described analytical method coarse alignment is:

Local latitude L is known quantity, and navigation coordinate system adopts sky, northeast coordinate system, gravity acceleration g and rotational-angular velocity of the earth ω _iecomponent in navigational system is all definite known, is expressed as:

g ⁿ＝[0?0?-g] ^T

${\mathrm{\ω}}_{\mathrm{ie}}^n={\left[\begin{array}{ccc}0& \mathrm{\Ω}\cos L& \mathrm{\Ω}\sin L\end{array}\right]}^T$

Wherein, g ⁿrepresent the projection of acceleration of gravity under navigation coordinate system, represent the projection of rotational-angular velocity of the earth under navigation coordinate system, Ω is earth rotation angular speed, the amplitude that g is acceleration of gravity;

Resolve coarse alignment and utilize known g ⁿ, estimate coarse alignment initial attitude matrix with the measured value of strapdown inertial navigation system sensor measurement value sensor is averaged to improve alignment precision, uses a ^bwith represent respectively accelerometer and gyrostatic measurement mean value;

Analytical method coarse alignment method adopts a kind of of following two kinds of methods:

(a) utilize three mutually orthogonal vectorial g, g * ω _ie(g * ω _ie) * g and three mutually orthogonal vectorial a ^b, a ^b* ω ^b(a ^b* ω ^b) * a ^bcalculate

${C^{\′}}_{b\left(0\right)}^n={\left[\begin{array}{c}{\left(g^n\right)}^T\\ {(g^n\×{\mathrm{\ω}}_{\mathrm{ie}}^n)}^T\\ {[(g^n\×{\mathrm{\ω}}_{\mathrm{ie}}^n)\×g^n]}^T\end{array}\right]}^{-1}\left[\begin{array}{c}{\left(a^b\right)}^T\\ {(a^b\×{\mathrm{\ω}}_{\mathrm{ie}}^b)}^T\\ {[(a^b\×{\mathrm{\ω}}_{\mathrm{ie}}^b)\×a^b]}^T\end{array}\right]$

To attitude matrix be normalized and obtain coarse alignment initial attitude matrix

$C_{b\left(0\right)}^n=C_{b\left(0\right)}^n{\left[{\left(C_{b\left(0\right)}^n\right)}^T{C}_{b\left(0\right)}^n\right]}^{-\frac{1}{2}}$

(b) by measured value, directly calculated

Will write as the form of column vector:

$C_{b\left(0\right)}^n=\left[\begin{array}{ccc}{C}_1& C_2& C_3\end{array}\right]$

C wherein ₁, C ₂, C ₃for forming three column vectors, and there is to each other orthogonality constraint;

If the measured value of k moment gyroscope and accelerometer is designated as respectively ω ^band a (k) ^b(k), sampling number is N time, adopts the least square method under orthogonality constraint to estimate three minutes column vectors:

$C_3=-\frac{1}{\mathrm{\λ}}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{a}^b\left(k\right)$

$C_2=\frac{1}{\mathrm{\η}}(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)+\mathrm{\ρ}\hat{z})$

$C_1=C_2\×C_3=\frac{1}{\mathrm{\η}}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)\×C_3$

$\mathrm{\λ}={\left[{\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{a}^b\left(k\right)\right)}^T\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{a}^b\left(k\right)\right)\right]}^{\frac{1}{2}}$

$\mathrm{\ρ}=\frac{1}{\mathrm{\λ}}{\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{a}^b\left(k\right)\right)}^T\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)\right)$

$\mathrm{\η}={[{\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)\right)}^T\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)\right)-{\mathrm{\ρ}}^2]}^{\frac{1}{2}}$

Now just obtained owing to being orthogonal matrix, so without orthogonalization.

Step 3) the acceleration correction amount described in $f_c^n={\left(\begin{array}{ccc}{f}_{\mathrm{cx}}^n& f_{\mathrm{cy}}^n& f_{\mathrm{cz}}^n\end{array}\right)}^T$ With rate correction amount ${\mathrm{\ω}}_c^n={\left(\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{cx}}^n& {\mathrm{\ω}}_{\mathrm{cy}}^n& {\mathrm{\ω}}_{\mathrm{cz}}^n\end{array}\right)}^T,$ Be calculated as follows:

Correction computing formula during horizontal alignment:

$\left\{\begin{array}{c}{\mathrm{\ω}}_{\mathrm{cx}}^n=\frac{K_2}{R}{\mathrm{\δV}}_N\\ {\mathrm{\ω}}_{\mathrm{cy}}^n=-\frac{K_2}{R}{\mathrm{\δV}}_E\\ {\mathrm{\ω}}_{\mathrm{cz}}^n=0\end{array}\right.,$ $\left\{\begin{array}{c}{f}_{\mathrm{cx}}^n=K_1{\mathrm{\δV}}_E\\ f_{\mathrm{cy}}^n=K_1{\mathrm{\δV}}_N\\ f_{\mathrm{cz}}^n=0\end{array}\right.$

Correction computing formula during azimuthal alignment:

$\left\{\begin{array}{c}{\mathrm{\ω}}_{\mathrm{cx}}^n=\frac{{K^{\′}}_2}{R}{\mathrm{\δV}}_N\\ {\mathrm{\ω}}_{\mathrm{cy}}^n=-\frac{{K^{\′}}_2}{R}{\mathrm{\δV}}_E\\ {\mathrm{\ω}}_{\mathrm{cz}}^n=\frac{{K^{\′}}_3}{{\mathrm{\ω}}_{\mathrm{ie}}\cos L(s+{K^{\′}}_4)}{\mathrm{\δV}}_N\end{array}\right.,$ $\left\{\begin{array}{c}{f}_{\mathrm{cx}}^n={K^{\′}}_1{\mathrm{\δV}}_E\\ f_{\mathrm{cy}}^n={K^{\′}}_1{\mathrm{\δV}}_N\\ f_{\mathrm{cz}}^n=0\end{array}\right.$

Wherein, R is earth radius, δ V _efor east orientation velocity error, δ V _nfor north orientation velocity error, L is latitude, ω _iefor rotational-angular velocity of the earth, s represents the integral element in alignment system.

The present invention utilizes analytical method to complete coarse alignment process, then carry out horizontal alignment and azimuthal alignment, azimuthal alignment is divided into three phases, thereby each stage selects different adjustment time and attenuation coefficient to determine corresponding alignment parameter according to the characteristic in this stage, based on these calculation of parameter acceleration correction amounts and rate correction amount, acceleration information and angular velocity information to input are revised, utilize revised information to carry out hypercomplex number and resolve and obtain initial attitude angle, complete three phases fine alignment process and obtained final initial attitude angle.

The present invention's advantage is compared with prior art:

(1) the present invention utilizes analytical method and compass method to complete initial alignment by gathering gyroscope and accelerometer data, and the method, without utilizing other sensor informations, guarantees security and the confidentiality of initial alignment.

(2) the present invention adopts azimuthal alignment procedure parameter sectional type method, for the alignment feature of different phase, select best adjustment time and attenuation coefficient, thereby calculate other alignment parameter, the method can improve the fast convergence of directrix curve and interference free performance.

Accompanying drawing explanation

Fig. 1 is strapdown inertial navigation system autoregistration process flow diagram of the present invention.

Fig. 2 is horizontal alignment of the present invention loop east orientation passage calcspar.

Fig. 3 is horizontal alignment of the present invention loop north orientation passage calcspar.

Fig. 4 is azimuthal alignment calcspar of the present invention.

Fig. 5 is self-alignment method for strapdown inertial navigation system schematic diagram of the present invention.

Fig. 6 is not segmentation autoregistration attitude error curve of embodiment of the present invention parameter.

Fig. 7 is the partial enlarged drawing of Fig. 6.

Fig. 8 is embodiment of the present invention parameter sectional type autoregistration attitude error curve.

Fig. 9 is the partial enlarged drawing of Fig. 8.

Embodiment

As Fig. 1, specific embodiment of the invention step is as follows:

1) aim at the front autoregistration fine alignment parameter of determining, comprise that each stage damping is than ξ, attenuation coefficient σ, adjustment time t _s, aim at time T and thus calculation of parameter go out other aim at other parameters in control loops;

2) utilize analytical method to carry out coarse alignment, determine initial attitude matrix and angle, initial heading initial pitch angle θ ₀with initial horizontal cradle angle γ ₀;

3) in step 2) start fine alignment process on the basis of coarse alignment, according to fine alignment institute stage by stage, each stage is by quasi loop being calculated to the lower acceleration correction information of navigation coordinate system with rate correction information described navigation coordinate is sky, northeast coordinate system;

4) by step 3) the middle acceleration correction information of calculating gained with rate correction information be transformed in carrier coordinate system, for the transition matrix of navigation coordinate to carrier coordinate, thus the specific force to the accelerometer in strapdown inertial navigation system with gyrostatic angular velocity revise,

5) utilize step 4) in the corrected force information that compares and angular velocity information use hypercomplex number update algorithm to calculate the attitude matrix in this attitude algorithm cycle, thereby determine corresponding pitch angle, roll angle and course angle, the attitude after output is upgraded;

6) step 3) to 5) be an attitude algorithm cycle, repeating step 3) to 5) carry out the calculating in next attitude algorithm cycle, obtain pitch angle, roll angle and the course angle of corresponding attitude algorithm cycle carrier, until T.T. in cycle reaches step 1) in the aligning time T in determined each stage _i, complete fine alignment, export the attitude of last cycle renewal;

7) complete horizontal alignment and azimuthal alignment after alignment procedures finish, obtain accurate attitude angle, realize strapdown inertial navigation system autoregistration.

The self aligned schematic diagram of strapdown inertial navigation system of the present invention is as Fig. 5, step 3) to step 5) complete an attitude algorithm cycle, cycle period, realizes autoregistration.

Analytical method coarse alignment of the present invention carries out in accordance with the following methods:

Coarse alignment is exactly the estimated value of setting up an approximate attitude matrix, i.e. initial attitude matrix thereby make system can carry out next step fine alignment.Coarse alignment is the known technology in strap-down inertial Initial Alignment Technique field, introduces wherein two kinds of methods here.

Local latitude L is known quantity, and navigation system adopts sky, northeast coordinate system, gravity acceleration g and rotational-angular velocity of the earth ω _iecomponent in navigation system is all definite known, can be expressed as:

g ⁿ＝[0?0?-g] ^T

${\mathrm{\ω}}_{\mathrm{ie}}^n={\left[\begin{array}{ccc}0& \mathrm{\Ω}\cos L& \mathrm{\Ω}\sin L\end{array}\right]}^T$

G wherein ⁿrepresent the projection of acceleration of gravity under navigation coordinate system, represent the projection of rotational-angular velocity of the earth under navigation coordinate system, Ω is earth rotation angular speed, the amplitude that g is acceleration of gravity.Resolving coarse alignment is exactly to utilize known g ⁿ, estimate with the measured value of strapdown inertial navigation system sensor represent that carrier coordinate is to the transition matrix of navigation coordinate, i.e. strapdown attitude matrix.Because the coarse alignment time is shorter, conventionally adopt the way that measurement value sensor is averaged to improve alignment precision.For expressing, write, use a ^bwith represent respectively accelerometer and gyrostatic measurement mean value.

Step 2) the analytical method coarse alignment method described in can adopt any of following two kinds of methods, is of equal value:

(a) utilize three mutually orthogonal vectorial g, g * ω _ie(g * ω _ie) * g and three mutually orthogonal vectorial a ^b, a ^b* ω ^b(a ^b* ω ^b) * a ^bcalculate

${C^{\′}}_{b\left(0\right)}^n={\left[\begin{array}{c}{\left(g^n\right)}^T\\ {(g^n\×{\mathrm{\ω}}_{\mathrm{ie}}^n)}^T\\ {[(g^n\×{\mathrm{\ω}}_{\mathrm{ie}}^n)\×g^n]}^T\end{array}\right]}^{-1}\left[\begin{array}{c}{\left(a^b\right)}^T\\ {(a^b\×{\mathrm{\ω}}_{\mathrm{ie}}^b)}^T\\ {[(a^b\×{\mathrm{\ω}}_{\mathrm{ie}}^b)\×a^b]}^T\end{array}\right]$

Wherein, g ⁿrepresent the projection of acceleration of gravity under navigation coordinate system, represent the projection of rotational-angular velocity of the earth under navigation coordinate system, a ^bthe measurement mean value that represents acceleration measuring value, the measurement mean value that represents gyroscope survey value;

To attitude matrix be normalized:

$C_{b\left(0\right)}^n={{C^{\′}}_{b\left(0\right)}^n\left[{\left({C^{\′}}_{b\left(0\right)}^n\right)}^T{C^{\′}}_{b\left(0\right)}^n\right]}^{-\frac{1}{2}}$

it is exactly the initial attitude matrix that coarse alignment obtains;

(b) by measured value, directly calculated

Will write as the form of column vector:

$C_{b\left(0\right)}^n=\left[\begin{array}{ccc}{C}_1& C_2& C_3\end{array}\right]$

C wherein ₁, C ₂, C ₃for forming three column vectors, and there is to each other orthogonality constraint.

If the measured value of k moment gyroscope and accelerometer is designated as respectively ω ^band a (k) ^b(k), sampling number is N time, adopts the least square method under orthogonality constraint to estimate three minutes column vectors:

$C_3=-\frac{1}{\mathrm{\λ}}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{a}^b\left(k\right)$

$C_2=\frac{1}{\mathrm{\η}}(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)+\mathrm{\ρ}\hat{z})$

$C_1=C_2\×C_3=\frac{1}{\mathrm{\η}}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)\×C_3$

$\mathrm{\λ}={\left[{\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{a}^b\left(k\right)\right)}^T\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{a}^b\left(k\right)\right)\right]}^{\frac{1}{2}}$

$\mathrm{\ρ}=\frac{1}{\mathrm{\λ}}{\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{a}^b\left(k\right)\right)}^T\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)\right)$

$\mathrm{\η}={[{\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)\right)}^T\left(\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}^b\left(k\right)\right)-{\mathrm{\ρ}}^2]}^{\frac{1}{2}}$

Now just obtained owing to being orthogonal matrix, so without orthogonalization.

What calculate above is initial attitude matrix, is first attitude algorithm cycle, and in follow-up attitude billing cycle, attitude matrix is identical with the computing method of initial attitude matrix, uses the sensor parameters that corresponding period measurement obtains to calculate.

Key character of the present invention is described fine alignment process definite aligning time and each alignment parameter stage by stage, specific as follows:

When design parameter, generally first select damping ratio ξ and adjust time t _s.

Adjusting time t _srefer to that unit-step response arrives and remain on the interior required shortest time of final value ± 5%, it is the composite target of reflection response speed and damping degree.T _ssimplification computing formula as follows:

$t_s\≈\frac{3}{{\mathrm{\ξ\ω}}_n}=\frac{3}{\mathrm{\σ}}$

Conventionally get damping ratio ξ=0.4～0.8 and be advisable, now overshoot appropriateness.The time of aiming at transition due to ratio of damping hour is long, a little less than the ability that when ratio of damping is large, system suppresses to disturb, therefore, chooses

For accelerating the aligning time, in fine alignment process, segmentation is carried out.The cardinal rule of every section of parameter selection is: adjust time t _selongated gradually.The first paragraph of fine alignment is adjusted the time can not be too short, otherwise there will be vibration during oscillating motion.The aligning time is that designed 1～2 times of adjustment time is comparatively suitable.

During design, to reasonably increase the number in fine alignment stage.Horizontal alignment of the present invention is divided into a stage, and alignment of orientation process divides three phases to complete.The parameter in each stage is chosen as follows:

The horizontal alignment stage: (the aligning time is T ₁=100s)

$\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.045， $t_s=\frac{3}{\mathrm{\σ}}=66.7$

The azimuthal alignment first stage: (aim at time T ₂=300s)

$\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.02， $t_s=\frac{3}{\mathrm{\σ}}=150$

Azimuthal alignment subordinate phase: (aim at time T ₃=300s)

$\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.015， $t_s=\frac{3}{\mathrm{\σ}}=200$

The azimuthal alignment phase III: (aim at time T ₄=300s)

$\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.01， $t_s=\frac{3}{\mathrm{\σ}}=300$

According to damping ratio ξ and attenuation coefficient σ, be calculated as follows other damping parameters of each stage:

Strapdown inertial navitation system (SINS) adopts sky, northeast coordinate system, according to the horizontal compass alignment system of strapdown inertial navitation system (SINS), as shown in Figures 2 and 3, obtains the damping parameter on each rank of horizontal alignment stage system:

K ₁＝3σ

$K_2=\frac{{\mathrm{\σ}}^2}{{\mathrm{\ω}}_s^2}(2+\frac{1}{{\mathrm{\ξ}}^2})-1$

$K_3=\frac{{\mathrm{\σ}}^3}{{\mathrm{g\ξ}}^2}$

According to strapdown inertial navitation system (SINS) azimuth compass alignment system, as described in Figure 4, obtain the damping parameter on each rank of azimuthal alignment stage system:

K′ ₁＝K′ ₄＝2σ

${K^{\′}}_2=\frac{{4\mathrm{\σ}}^2}{{\mathrm{\ω}}_s^2}-1$

${K^{\′}}_3=\frac{{4\mathrm{\σ}}^4}{g}$

Wherein, g is acceleration of gravity, and R is earth radius.

(3) accurate alignment method described in the present invention is as follows:

Fig. 2 is horizontal alignment loop east orientation passage calcspar, and Fig. 3 is horizontal alignment loop north orientation passage calcspar, and Fig. 4 is azimuthal alignment calcspar.Fig. 5 is fine alignment algorithm principle figure.

The accurate alignment method of employing based on level three loops, rank, fine alignment algorithm is divided into horizontal component and orientation part, ${\mathrm{\ω}}_c^n={\left(\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{cx}}^n& {\mathrm{\ω}}_{\mathrm{cy}}^n& {\mathrm{\ω}}_{\mathrm{cz}}^n\end{array}\right)}^T$ For rate correction amount, $f_c^n={\left(\begin{array}{ccc}{f}_{\mathrm{cx}}^n& f_{\mathrm{cy}}^n& f_{\mathrm{cz}}^n\end{array}\right)}^T$ For acceleration correction amount, computing method are as follows:

Correction computing formula during horizontal alignment:

$\left\{\begin{array}{c}{\mathrm{\ω}}_{\mathrm{cx}}^n=(\frac{K_2}{R}+\frac{K_3}{s}){\mathrm{\δV}}_N\\ {\mathrm{\ω}}_{\mathrm{cy}}^n=(-\frac{K_2}{R}+\frac{K_3}{s}){\mathrm{\δV}}_E\\ {\mathrm{\ω}}_{\mathrm{cz}}^n=0\end{array}\right.,$ $\left\{\begin{array}{c}{f}_{\mathrm{cx}}^n=K_1{\mathrm{\δV}}_E\\ f_{\mathrm{cy}}^n=K_1{\mathrm{\δV}}_N\\ f_{\mathrm{cz}}^n=0\end{array}\right.$

K ₁, K ₂, K ₃damping parameter for each rank of horizontal alignment stage system in Fig. 2 and Fig. 3:

Correction computing formula during azimuthal alignment:

$\left\{\begin{array}{c}{\mathrm{\ω}}_{\mathrm{cx}}^n=\frac{{K^{\′}}_2}{R}{\mathrm{\δV}}_N\\ {\mathrm{\ω}}_{\mathrm{cy}}^n=-\frac{{K^{\′}}_2}{R}{\mathrm{\δV}}_E\\ {\mathrm{\ω}}_{\mathrm{cz}}^n=\frac{{K^{\′}}_3}{{\mathrm{\ω}}_{\mathrm{ie}}\cos L(s+{K^{\′}}_4)}{\mathrm{\δV}}_N\end{array}\right.,$ $\left\{\begin{array}{c}{f}_{\mathrm{cx}}^n={K^{\′}}_1{\mathrm{\δV}}_E\\ f_{\mathrm{cy}}^n={K^{\′}}_1{\mathrm{\δV}}_N\\ f_{\mathrm{cz}}^n=0\end{array}\right.$

K ' ₁, K ' ₂, K ' ₃, K ' ₄damping parameter for each rank of azimuthal alignment stage system of introducing in Fig. 4 azimuthal alignment.

R is earth radius, δ V _efor east orientation velocity error, δ V _nfor north orientation velocity error, L is latitude, ω _iefor earth rotation angular speed, s represents the integral element in alignment system.。

The value that correction is converted under carrier coordinate system compensates acceleration information and angular velocity information under carrier system, thereby carry out hypercomplex number by the information after upgrading, calculates initial attitude angle.

The present invention adopt a kind of fast, parameter sectional type self-alignment method for strapdown inertial navigation system, below verify this beneficial effect of the invention under the three-axis swinging platform condition of laboratory.

The performance index of inertial sensor are as follows: gyroscope constant value drift: 0.04 °/h; Modelling of Random Drift of Gyroscopes: 0.04 °/h; Accelerometer bias: 50 μ g; Accelerometer is setovered at random: 50 μ g.Initial misalignment: 0.15 ° of pitching misalignment, 0.15 ° of rolling misalignment, 0.7 ° of course misalignment.

In experiment, the mode of motion of three-axis swinging is: the inside casing amplitude of oscillation is 15 °, and frequency is 0.125Hz; The center amplitude of oscillation is 8 °, and frequency is 0.15Hz; The housing amplitude of oscillation is 5 °, and frequency is 0.2Hz.Three axles carry out oscillating motion simultaneously, and with the applied environment of this motion status simulation naval vessel reality, 1000s is carried out in every group of test.

Fig. 6 and Fig. 7 have shown the unsegmented autoregistration attitude error of parameter curve, and Fig. 8 and Fig. 9 have shown the autoregistration attitude error curve of Parameter Subsection.Experimental result shows that the more traditional Alignment Method of parameter sectional type Alignment Method can shorten the aligning time, reduces vibration in alignment procedures and mean square deviation and the average of error angle, thereby alignment precision is improved.

Claims (1)

1. One kind fast, parameter sectional type self-alignment method for strapdown inertial navigation system, it is characterized in that being divided into coarse alignment and fine alignment two steps, first utilize analytical method to complete coarse alignment process, then carry out horizontal alignment and azimuthal alignment, based on fine alignment calculation of parameter acceleration correction information and rate correction information, acceleration information and angular velocity information to input strapdown inertial navigation system are revised, utilizing revised information to carry out hypercomplex number resolves and obtains initial attitude angle, complete fine alignment process, comprise the following steps:

   1) before aligning, first determine self aligned fine alignment parameter, comprise that each stage damping is than ξ, attenuation coefficient σ, adjustment time t _s, aim at time T _iand other damping parameters of each stage that gone out by described calculation of parameter;

   Fine alignment segmentation is carried out, and according to the different designs horizontal alignment of selecting alignment parameter, is a stage, and azimuthal alignment is three phases, and the cardinal rule of every section of parameter selection is: adjust time t _selongated gradually, specific as follows:

   The horizontal alignment stage: the aligning time is T ₁=100s

   $\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.045, $t_s=\frac{3}{\mathrm{\σ}}=66.7$

   The azimuthal alignment first stage: aim at time T ₂=300s

   $\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.02, $t_s=\frac{3}{\mathrm{\σ}}=150$

   Azimuthal alignment subordinate phase: aim at time T ₃=300s

   $\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.015, $t_s=\frac{3}{\mathrm{\σ}}=200$

   The azimuthal alignment phase III: aim at time T ₄=300s

   $\mathrm{\ξ}=\frac{1}{\sqrt{2}},$ σ＝0.01, $t_s=\frac{3}{\mathrm{\σ}}=300$

   According to damping ratio ξ and attenuation coefficient σ, be calculated as follows other damping parameters of each stage:

   Strapdown inertial navitation system (SINS) adopts sky, northeast coordinate system, according to the horizontal compass alignment principles of strapdown inertial navitation system (SINS), obtains the damping parameter on each rank of horizontal alignment stage system:

   $\begin{array}{c}{K}_1=3\mathrm{\σ}\\ K_2=\frac{{\mathrm{\σ}}^2}{{\mathrm{\ω}}_s^2}(2+\frac{1}{{\mathrm{\ξ}}^2})-1\\ K_3=\frac{{\mathrm{\σ}}^3}{{\mathrm{g\ξ}}^2}\end{array}$

   According to strapdown inertial navitation system (SINS) azimuth compass alignment principles, obtain the damping parameter on each rank of azimuthal alignment stage system:

   $\begin{array}{c}{K^{\′}}_1={K^{\′}}_4=2\mathrm{\σ}\\ {K^{\′}}_2=\frac{{4\mathrm{\σ}}^2}{{\mathrm{\ω}}_s^2}-1\\ {K^{\′}}_3=\frac{{4\mathrm{\σ}}^4}{g}\end{array}$

   Wherein, g is acceleration of gravity, and R is earth radius;

   2) utilize analytical method to carry out coarse alignment, determine initial attitude matrix and angle, initial heading initial pitch angle θ ₀with initial horizontal cradle angle γ ₀;

   3) in step 2) start fine alignment process on the basis of coarse alignment, according to fine alignment institute stage by stage, each stage is by quasi loop being calculated to the lower acceleration correction information of navigation coordinate system with rate correction information described navigation coordinate is sky, northeast coordinate system;

   4) by step 3) the middle acceleration correction information of calculating gained with rate correction information be transformed in carrier coordinate system, for the transition matrix of navigation coordinate to carrier coordinate, thus the specific force to the accelerometer in strapdown inertial navigation system with gyrostatic angular velocity revise, $f_{\mathrm{ib}}^{\′b}=f_{\mathrm{ib}}^b-f_c^b,{\mathrm{\ω}}_{\mathrm{ib}}^{\′b}={\mathrm{\ω}}_{\mathrm{ib}}^b-{\mathrm{\ω}}_c^b;$

   5) utilize step 4) in the corrected force information that compares and angular velocity information use hypercomplex number update algorithm to calculate the attitude matrix in this attitude algorithm cycle, thereby determine corresponding pitch angle, roll angle and course angle, the attitude after output is upgraded;

   6) step 3) to 5) be an attitude algorithm cycle, repeating step 3) to 5) carry out the calculating in next attitude algorithm cycle, obtain pitch angle, roll angle and the course angle of corresponding attitude algorithm cycle carrier, until T.T. in cycle reaches step 1) in the aligning time T in determined each stage _i, complete fine alignment, export the attitude of last cycle renewal;

   7) complete horizontal alignment and azimuthal alignment after alignment procedures finish, obtain accurate attitude angle, realize strapdown inertial navigation system autoregistration;

   Described analytical method coarse alignment is:

   Local latitude L is known quantity, and navigation coordinate system adopts sky, northeast coordinate system, gravity acceleration g and rotational-angular velocity of the earth ω _iecomponent in navigational system is all definite known, is expressed as:

   g ⁿ＝[0?0?-g] ^T

   ${\mathrm{\ω}}_{\mathrm{ie}}^n={\left[\begin{array}{ccc}0& \mathrm{\Ω}\cos L& \mathrm{\Ω}\sin L\end{array}\right]}^T$

   Wherein, g ⁿrepresent the projection of acceleration of gravity under navigation coordinate system, represent the projection of rotational-angular velocity of the earth under navigation coordinate system, Ω is earth rotation angular speed, the amplitude that g is acceleration of gravity;

   Resolve coarse alignment and utilize known g ⁿ, estimate coarse alignment initial attitude matrix with the measured value of strapdown inertial navigation system sensor measurement value sensor is averaged to improve alignment precision, uses a ^bwith represent respectively accelerometer and gyrostatic measurement mean value;

   Analytical method coarse alignment method adopts following methods:

   Utilize three mutually orthogonal vectorial g, g * ω _ie(g * ω _ie) * g and three mutually orthogonal vectorial a ^b, a ^b* ω ^b(a ^b* ω ^b) * a ^bcalculate

   $C_{b\left(0\right)}^{\′n}={\left[\begin{array}{c}{\left(g^n\right)}^T\\ {(g^n\×{\mathrm{\ω}}_{\mathrm{ie}}^n)}^T\\ {[(g^n\×{\mathrm{\ω}}_{\mathrm{ie}}^n)\×g^n]}^T\end{array}\right]}^{-1}\left[\begin{array}{c}{\left(a^b\right)}^T\\ {(a^b\×{\mathrm{\ω}}_{\mathrm{ie}}^b)}^T\\ {[(a^b\×{\mathrm{\ω}}_{\mathrm{ie}}^b)\×a^b]}^T\end{array}\right]$

   To attitude matrix be normalized and obtain coarse alignment initial attitude matrix

   $C_{b\left(0\right)}^n=C_{b\left(0\right)}^n{\left[{\left(C_{b\left(0\right)}^n\right)}^T{C}_{b\left(0\right)}^n\right]}^{-\frac{1}{2}}$

   Step 3) the acceleration correction information described in $f_c^n={\left(\begin{array}{ccc}{f}_{\mathrm{cx}}^n& f_{\mathrm{cy}}^n& f_{\mathrm{cz}}^n\end{array}\right)}^T$ With rate correction information ${\mathrm{\ω}}_c^n={\left(\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{cx}}^n& {\mathrm{\ω}}_{\mathrm{cy}}^n& {\mathrm{\ω}}_{\mathrm{cz}}^n\end{array}\right)}^T,$ Be calculated as follows:

   Update information computing formula during horizontal alignment:

   $\left\{\begin{array}{c}{\mathrm{\ω}}_{\mathrm{cx}}^n=\frac{K_2}{R}{\mathrm{\δV}}_N\\ {\mathrm{\ω}}_{\mathrm{cy}}^n=-\frac{K_2}{R}\mathrm{\δ}{V}_E\\ {\mathrm{\ω}}_{\mathrm{cz}}^n=0\end{array}\right.,\left\{\begin{array}{c}{f}_{\mathrm{cx}}^n=K_1{\mathrm{\δV}}_E\\ f_{\mathrm{cy}}^n=K_1{\mathrm{\δV}}_N\\ f_{\mathrm{cz}}^n=0\end{array}\right.$

   Update information computing formula during azimuthal alignment:

   $\left\{\begin{array}{c}{\mathrm{\ω}}_{\mathrm{cx}}^n=\frac{{K^{\′}}_2}{R}{\mathrm{\δV}}_N\\ {\mathrm{\ω}}_{\mathrm{cy}}^n=-\frac{{K^{\′}}_2}{R}{\mathrm{\δV}}_E\\ {\mathrm{\ω}}_{\mathrm{cz}}^n=\frac{{K^{\′}}_3}{{\mathrm{\ω}}_{\mathrm{ie}}\cos L(s+{K^{\′}}_4)}{\mathrm{\δV}}_N\end{array}\right.,\left\{\begin{array}{c}{f}_{\mathrm{cx}}^n={K^{\′}}_1{\mathrm{\δV}}_E\\ f_{\mathrm{cy}}^n={K^{\′}}_1{\mathrm{\δV}}_E\\ f_{\mathrm{cz}}^n=0\end{array}\right.$

   Wherein, R is earth radius, δ V _efor east orientation velocity error, δ V _nfor north orientation velocity error, L is latitude, ω _iefor rotational-angular velocity of the earth, s represents the integral element in alignment system.