Constrained filtering method for attitude determination using GPS and gyro

Abstract

I n attitude determination using the unit quaternion representation, the unit norm constraint results in singularity of thc covariancc matrix using classical filtering methods. To cope with this problem, a constrained filtering method is developcd. In this method, the constraint equations and the state equations are trcated as pscudo-iiieasLireiiient equations, so that they can be processed simultaneously with the rcal measurement equations. To illustrate thc application of the proposed scheme, a sccnario using GPS aiid gyro to pcrform attitudc determination is considcrcd. Software simulations show that the proposed scheme is sound, effcctive, and superior to existing methods.

Quaternion Estimation for attitude determination using multiple L1 GPS receivers

“…where Δ is the sampling, is the process noise, assumed to be Gaussian distributed with zero mean and covariance , and Ξ Ω , accordingly to [16]. The measurement model relates the baselines' coordinates with the quaternion elements estimated by the EKF and the known positions of the GPS antennas in the body fixed frame, accordingly to (23).…”

“…where is the covariance of the angular velocity noise and is the covariance of the angular velocity bias noise, [16]. These two parameters must be tuned in order to obtain the best solution, but since it is not used any rate gyro, it is assumed that the value of is close to zero.…”

Deducing the multi-trader population driving a financial market

“…As a result, we define H c k,j = ∂h c k ∂x k (x k|k,j−1 ) which gives us a local approximation to the direction of h c k . A stronger form for this solution can be found in past work, 4,5 where R c k will reflect the tightening of the covariance for the state prediction based on the new estimate at each iteration of j. We do not use this form and tighten the covariance matrix within these iterations, since in our form, we can change the number of equality constraints between iterations of j.…”

Real-time state observers based on multibody models and the extended Kalman filter

“…For example, in [2] it is shown that the descriptor dynamics give rise to singular measurement noise covariance, and an extended maximum-likelihood method is applied. This same idea is followed in [3], where the constraint (unit quaternion norm) is treated as a pseudo-measurement. In [4], the error from constraint linearization is treated in a separate step, after the EKF, increasing the computational complexity.…”