Search

This work presents several algorithms that use vector observations in order to estimate the direction cosine matrix (DCM) as well as three constant biases and three time-varying drifts in body-mounted gyro output errors. All the algorithms use the matrix Kalman filter (MKF) paradigm, which preserves the natural formulation of the DCM state-space model equations. Focusing on the DCM estimation problem, the assumption of white noise in the gyro and in the vector observations errors yields reduced and efficient filter covariance computations. The orthogonality constraint on the DCM is handled via the technique of pseudomeasurement, which is naturally embedded in the MKF. Two additional known "brute-force" procedures are implemented for the sake of comparison. Extensive Monte-Carlo simulations illustrate the performances of the different estimators. When estimating only the DCM, it is shown that all the proposed orthogonalization procedures accelerate the estimation convergence. Nevertheless, the pseudomeasurement technique shows a smoother and shorter transient than the brute-force procedures, which on the other hand yield more accurate steady-states. The reduced covariance computations yield a more accurate steady-state than the full covariance computations but show a slower transient. When estimating the DCM as well as the gyro biases and drifts, enforcing orthogonalization seems to penalize the DCM estimation as long as the biases are not correctly identified. For the sake of computation savings during long duration missions, a mixed estimator, switching between long periods of DCM-only estimation and short periods of DCM-biases estimation, appears to be a promising strategy. [ABSTRACT FROM AUTHOR]

This paper presents a novel Kalman filter (KF) for estimating the attitude-quaternion as well as gyro random drifts from vector measurements. Employing a special manipulation on the measurement equation results in a linear pseudo-measurement equation whose error is state-dependent. Because the quaternion kinematics equation is linear, the combination of the two yields a linear KF that eliminates the usual linearization procedure and is less sensitive to initial estimation errors. General accurate expressions for the covariance matrices of the system state-dependent noises are developed. In addition, an analysis shows how to compute these covariance matrices efficiently. An adaptive version of the filter is also developed to handle modeling errors of the dynamic system noise statistics. Monte-Carlo simulations are carried out that demonstrate the efficiency of both versions of the filter. In the particular case of high initial estimation errors, a typical extended Kalman filter (EKF) fails to converge whereas the proposed filter succeeds. [ABSTRACT FROM AUTHOR]

A general discrete-time Kalman filter (KF) for state matrix estimation using matrix measurements is presented. The new algorithm evaluates the state matrix estimate and the estimation error covariance matrix in terms of the original system matrices. The proposed algorithm naturally fits systems which are most conveniently described by matrix process and measurement equations. Its formulation uses a compact notation for aiding both intuition and mathematical manipulation. It is a straightforward extension of the classical KF, and includes as special cases other matrix filters that were developed in the past. Beyond the analytical value of the matrix filter, it is shown through various examples arising in engineering problems that this filter can be computationally more efficient than its vectorized version. [ABSTRACT FROM AUTHOR]