CN110646012A - Unit position initial alignment optimization method for inertial navigation system - Google Patents

Abstract

The invention belongs to an optimization method, and particularly relates to an inertial navigation system unit initial alignment optimization method. An inertial navigation system unit position initial alignment optimization method comprises the following steps: the method comprises the following steps: externally inputting the measured values of the gravity vector under a body coordinate system and a reference coordinate system, and performing the second step: taking as a weight coefficient; step three: calculating each intermediate variable, and the fourth step: calculating a loss function construction matrix; step five: calculating the eigenvalue λ of K_iAnd a feature vector q_iAnd step six: iteration is carried out; step seven: and ensuring iterative convergence and obtaining an optimal posture solution. The invention has the beneficial effects that: the comparison test shows that the method can simultaneously optimize the speed of north, east and sky directions, and has high optimization efficiency and good optimization effect.

Description

Unit position initial alignment optimization method for inertial navigation system

Technical Field

The invention belongs to an optimization method, and particularly relates to an inertial navigation system unit initial alignment optimization method.

Background

The initial alignment of the inertial navigation system is one of the key technologies affecting the use performance of the system, and the accuracy and speed of the alignment are directly related to the accuracy and starting characteristics of the inertial system. According to the principle of the inertial navigation system, multi-position alignment calculation is required to completely eliminate errors, but in most cases, the requirement cannot be met, and alignment can be performed only at one position. Therefore, the method has important application value for improving the unit initial alignment precision.

The traditional unit alignment method adopts an accelerometer to measure horizontal attitude and measures course through compass effect, and the method has long alignment time, is easy to be interfered, can not align under dynamic condition and is basically eliminated at present. The most common method at present is an alignment method based on gravity vectors, which is to calculate the rotation angle of the gravity vectors in the inertial space to obtain the initial attitude of the inertial navigation system, and select t_mAnd t_nThe two groups of acceleration integral values at the moment smooth the gravity integral, reduce the interference of the acceleration generated by the carrier swing, but do not fully utilize the gravity information and do not belong to the optimal algorithm.

Disclosure of Invention

The invention aims to provide an optimal method for unit initial alignment of an inertial navigation system, aiming at the defects of the prior art.

The invention is realized by the following steps: an inertial navigation system unit initial alignment optimization method comprises the following steps:

the method comprises the following steps:

external input

Andand

is the measured value of the gravity vector under the body coordinate system and the reference coordinate system,

step two:

take alpha_iIs a weight coefficient, and

n coefficients corresponding to n sets of gravity vector measurements, α_iIs inputted from the outside

Step three:

the intermediate variables are calculated by the following formula,

S＝B+B^T (4)

where tr denotes the trace of the matrix and x denotes the anti-symmetric matrix, i.e. a vector is changed into a 3 by 3 matrix;

step four:

from equations (1) to (4), the following loss function construction matrix is calculated

I is a unit diagonal matrix;

step five:

calculating the eigenvalue λ of K_iAnd a feature vector q_iWherein i is 1,2,3,4,

step six:

the largest one λ of all eigenvalues of K_max，λ_maxThe theoretical value is 1, so 1 can be used as an initial value to calculate lambda by iterative calculation_maxWill be λ_max,0Iteration is performed as 1 with equation (6) to yield:

λ_max,i+1＝λ_max,i-p(λ_i)/p′(λ_i),i＝0,1,... (6)

wherein

Step seven:

to ensure iterative convergence, let:

[(λ+σ)I-S]^-1＝γ^-1(αI+βS+S²) (8)

can obtain alpha ═ lambda²-σ²+ κ, β ═ λ - σ, γ ═ α (λ + σ) - Δ; where κ ═ tr (adj (S))), Δ ═ S |, tr denotes the traces of the matrix, adj denotes the adjoint matrix

Substitution of α, β and γ into formula (12) can give:

p(λ)＝λ⁴-(a+b)λ²-cλ+(ab+cσ-d)＝0 (9)

wherein a ═ σ²-κ，

This gives:

the attitude-optimal solution thus obtained is:

wherein:

the inertial navigation system unit position initial alignment optimization method further comprises the following steps,

step eight:

attitude cosine matrix A and attitude quaternion

Has a conversion relation of

Wherein

To achieve an optimal estimation of the attitude pair, the following loss function is defined:

then there are:

g(A)＝1-L(A)＝tr[AB^T] (15)

to achieve the minimum loss function, it is only necessary to satisfy g (A) max,

bringing (12) into (15) makes available:

elements of quaternions have unique constraints

To find the maximum for equation (16) under the constraint of equation (17), the equation is reconstructed:

order to

Can obtain the product

As can be seen from the above formula analysis, λ is a characteristic root of K,

the corresponding feature vector and therefore the result of (11) is an optimal estimate.

The invention has the beneficial effects that: the comparison test shows that the method can simultaneously optimize the speed of north, east and sky directions, and has high optimization efficiency and good optimization effect.

Drawings

FIG. 1 is a lake trial alignment process attitude curve.

Detailed Description

An inertial navigation system unit initial alignment optimization method comprises the following steps:

the method comprises the following steps:

external input

And

and

the measured values of the gravity vector in the body coordinate system and the reference coordinate system.

Step two:

take alpha_iIs a rightA coefficient of gravity of

And n coefficients are provided, and the n coefficients correspond to n groups of gravity vector measurement values. Alpha is alpha_iIs inputted from the outside

Step three:

each intermediate variable is calculated by the following formula.

S＝B+B^T(23)

Where tr denotes the trace of the matrix and x denotes the anti-symmetric matrix, i.e. a vector is changed into a 3 by 3 matrix;

step four:

from equations (20) to (23), the following loss function construction matrix is calculated

I is a unit diagonal matrix;

step five:

calculating the eigenvalue λ of K_iAnd a feature vector q_iWherein i is 1,2,3, 4.

Step six:

the largest one λ of all eigenvalues of K_max。λ_maxThe theoretical value is 1, so 1 can be used as an initial value to calculate lambda by iterative calculation_max. Will be lambda_max,0Iteration is performed as 1 with equation (6) to yield:

λ_max,i+1＝λ_max,i-p(λ_i)/p′(λ_i),i＝0,1,... (25)

wherein

Step seven:

to ensure iterative convergence, let:

[(λ+σ)I-S]^-1＝γ^-1(αI+βS+S²) (27)

can obtain alpha ═ lambda²-σ²+ κ, β ═ λ - σ, γ ═ α (λ + σ) - Δ; where κ ═ tr (adj (S))), Δ ═ S |, tr denotes the traces of the matrix, adj denotes the adjoint matrix

Substitution of α, β and γ into formula (12) can give:

p(λ)＝λ⁴-(a+b)λ²-cλ+(ab+cσ-d)＝0 (28)

wherein a ═ σ²-κ，

This gives:

the attitude-optimal solution thus obtained is:

wherein:

step eight:

attitude cosine matrix A and attitude quaternion

Has a conversion relation of

Wherein

To achieve an optimal estimation of the attitude pair, the following loss function is defined:

then there are:

g(A)＝1-L(A)＝tr[AB^T] (34)

to achieve the minimum loss function, it is only necessary to satisfy g (a) max.

Bringing (31) into (34) makes available:

elements of quaternions have unique constraints

To solve equation (35) for the maximum under the constraint of equation (36), the equation is reconstructed:

order to

Can obtain the product

As can be seen from the above formula analysis, λ is a characteristic root of K,

is corresponding toSo the result of (30) is an optimal estimate.

The precision indexes of the optical fiber strapdown inertial navigation system for lake trial production are as follows: the gyro drifts 0.05 degree/h and walks randomly

Accelerometer zero 100 μ g, random walk

The lake trial alignment attitude error is shown in figure 1.

Alignment accuracy pairs for the three bars are shown in table 1.

TABLE 1 statistical table of lake test speed error (unit: m/s, 1. sigma.)

Claims (2)

1. An inertial navigation system unit initial alignment optimization method is characterized by comprising the following steps:

the method comprises the following steps:

external input

And and

is the measured value of the gravity vector under the body coordinate system and the reference coordinate system,

step two:

take alpha_iIs a weight coefficient, and

n coefficients corresponding to n sets of gravity vector measurements, α_iIs inputted from the outside

Step three:

the intermediate variables are calculated by the following formula,

S＝B+B^T (4)

where tr denotes the trace of the matrix and x denotes the anti-symmetric matrix, i.e. a vector is changed into a 3 by 3 matrix;

step four:

from equations (1) to (4), the following loss function construction matrix is calculated

I is a unit diagonal matrix;

step five:

calculating the eigenvalue λ of K_iAnd a feature vector q_iWherein i is 1,2,3,4,

step six:

the largest one λ of all eigenvalues of K_max，λ_maxThe theoretical value is 1, so 1 can be used as an initial value to calculate lambda by iterative calculation_maxWill be λ_max,0Iteration is performed as 1 with equation (6) to yield:

λ_max,i+1＝λ_max,i-p(λ_i)/p′(λ_i),i＝0,1,...(6)

wherein

Step seven:

to ensure iterative convergence, let:

[(λ+σ)I-S]^-1＝γ^-1(αI+βS+S²) (8)

can obtain alpha ═ lambda²-σ²+ κ, β ═ λ - σ, γ ═ α (λ + σ) - Δ; where κ ═ tr (adj (S))), Δ ═ S |, tr denotes the traces of the matrix, adj denotes the adjoint matrix

Substitution of α, β and γ into formula (12) can give:

p(λ)＝λ⁴-(a+b)λ²-cλ+(ab+cσ-d)＝0 (9)

wherein a ═ σ²-κ，

This gives:

the attitude-optimal solution thus obtained is:

wherein:

2. the method for optimizing the unit initial alignment of the inertial navigation system according to claim 1, wherein: the method also comprises the following steps of,

step eight:

attitude cosine matrix A and attitude quaternion

Conversion relation ofIs composed of

Wherein

To achieve an optimal estimation of the attitude pair, the following loss function is defined:

then there are:

g(A)＝1-L(A)＝tr[AB^T] (15)

to achieve the minimum loss function, it is only necessary to satisfy g (A) max,

bringing (12) into (15) makes available:

elements of quaternions have unique constraints

To find the maximum for equation (16) under the constraint of equation (17), the equation is reconstructed:

order to

Can obtain the product

As can be seen from the above formula analysis, λ is a characteristic root of K,

the corresponding feature vector and therefore the result of (11) is an optimal estimate.