# Strapdown inertial navigation/spectrum red shift autonomous integrated navigation system and filtering method

## A technology of integrated navigation system and strapdown inertial navigation, which is applied in the field of autonomous integrated navigation system and filtering, can solve the problems of unable to obtain enough observation information, temporary interruption of measurement signal, and inability to obtain measurement information, etc., to improve navigation positioning accuracy and filtering Calculation accuracy, application of extended space, good concealment effect

Pending Publication Date: 2021-08-24
NORTHWESTERN POLYTECHNICAL UNIV
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## AI-Extracted Technical Summary

### Problems solved by technology

 However, with the single spectral redshift autonomous navigation method, during the attitude maneuvering process of the spacecraft, due to the inability to obtain sufficient observation information in a short period of time, or due to the interruption of observation information, the measurement informati...
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### Method used

In this algorithm, adopt stochastic weighted estimation method, according to the different sizes of each volume point estimation error, different weights are assigned to each volume point, according to eac...
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## Abstract

Application Domain

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• • • ## Examples

• Experimental program(1)

### Example Embodiment

 Example
 1. Mathematical model of SINS/SRS autonomous integrated navigation system
 (1) System state equation
 The East-North-Up geographic coordinate system is selected as the navigation coordinate system, and the system state equation is

 In formula (38), X(t) is the system state vector, F(t) is the state transition matrix, G(t) is the noise transition matrix, W(t) is the noise matrix.

 In formula (39), the velocity errors in the east, north and sky directions are respectively δv E , δv N , δv U; The latitude error, longitude error and height error are δL, δλ, δh respectively; the misalignment angle of the mathematical platform is φ E , φ N , φ U; The constant drift of the gyroscope on the three coordinate axes is ε x , ε y , ε z , and the constant value offsets on the three coordinate axes of the accelerometer are respectively
 The noise transfer matrix G(t) of the system is:

 The system noise vector consists of the random errors of the gyroscopes and accelerometers, expressed as

 The system state transition matrix F(t) is

 In formula (42), F N is the navigation parameter matrix;
 f s and F M They are:
 f M = 6×6 (43)
 In formula (43):

 In formula (44), q i (i=1,2,3,4) are the four elements of posture;
 (2) System measurement equation
 Transform the velocity information obtained by the spectral redshift into the navigation coordinate system, the attitude matrix As shown in the following formula:


 In formula (46), V n Indicates the velocity vector of the spacecraft in the navigation coordinate system, V b Indicates the velocity vector of the spacecraft in the body coordinate system;
 Taking the difference between the spectral redshift and the speed output by the inertial navigation system as the measurement, the speed measurement vector is:

 In formula (47), v E , v N and v U are the eastward velocity, northward velocity and skyward velocity of the spacecraft obtained by the inertial navigation system, v SE , v SN and v SU are the eastward velocity, northward velocity and skyward velocity of the spacecraft obtained from the spectral redshift, V v (t) is the speed measurement noise matrix;
 h v =[0 3×3 diag(111)0 3×9 ] 3×15 (48)
 In order to damp the divergence of the altitude channel of the inertial navigation system, a barometric altimeter is introduced. The difference between the altitude output by the barometric altimeter and the inertial navigation system is used as the quantity measurement, then the altitude measurement vector is:
 Z h =[h SINS -h H ] = H h X(t)+V h (t) (49)
 In formula (49), h SINS and h H are the altitude information output by the inertial navigation system and the barometric altimeter, V h (t) is the height measurement noise matrix.
 in:
 h h =[0 3×6 I 3×3 0 3×6 ] 3×15 T (50)
 The measurement equation of the SINS/SRS autonomous integrated navigation system is

 2. Adaptive Randomly Weighted Volumetric Kalman Filter (ARWCKF)
 In order to improve the filtering calculation accuracy of the SINS/SRS autonomous integrated navigation system, the present invention designs a high-precision, non-linear ARWCKF algorithm suitable for the SINS/SRS autonomous integrated navigation system.
 In this algorithm, the random weighted estimation method is adopted, and different weights are assigned to each volume point according to the different sizes of the estimation errors of each volume point. According to the state prediction value, observation prediction value, state error covariance prediction value, Autocorrelation covariance prediction value and cross-correlation covariance prediction value estimation error size, select different weight v i (i=1, 2,...m), by adjusting the weighting factor, the accuracy of prediction error estimation is improved, and then the accuracy of filtering calculation is improved.
 The main steps of the algorithm are:
 ①Initialization

 ②Calculation volume point and time update
 Record the covariance of state prediction at time k-1 as P k-1|k-1 , after Cholesky decomposition, P k-1|k-1 Expressed as:

 Calculate the volume point as follows:

 In formula (54), x i,k-1|k-1 (i=1,2,...,m) is the state quantity of the i-th volume point at time k-1, where S k-1|k-1 is a diagonal matrix.
Then, the state quantity of the i-th volume point from k-1 to k time is:

 ③Status prediction
 The state prediction of the i-th volume point from k-1 to k time is

 In formula (56), is q k-1 The arithmetic mean estimator of .
 Correspondingly, A random weighted estimate of

 In formula (57), is q k-1 A random weighted estimate of .
 State prediction covariance matrix P k|k-1 is described as:

 in, is Q k-1 The estimated arithmetic mean of .
 Correspondingly, P k|k-1 The random weighted estimate of

 In formula (59), is Q k-1 A random weighted estimate of .
 ④Measurement prediction
 The volume measurement of the i-th volume point from k-1 to time k is

 The measurement prediction of the i-th volume point from k-1 to k time is

 In formula (61), is r k The arithmetic mean estimate of .
 Correspondingly, A randomly weighted estimate of is expressed as:


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