N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems
Automatica (Journal of IFAC) - Special issue on statistical signal processing and control
SIAM Review
A new autocovariance least-squares method for estimating noise covariances
Automatica (Journal of IFAC)
The application of kalman filter based human-computer learning model to chinese word segmentation
CICLing'13 Proceedings of the 14th international conference on Computational Linguistics and Intelligent Text Processing - Volume Part I
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Designing a state estimator for a linear state-space model requires knowledge of the characteristics of the disturbances entering the states and the measurements. In [Odelson, B. J., Rajamani, M. R., & Rawlings, J. B. (2006). A new autocovariance least squares method for estimating noise covariances. Automatica, 42(2), 303-308], the correlations between the innovations data were used to form a least-squares problem to determine the covariances for the disturbances. In this paper we present new and simpler necessary and sufficient conditions for the uniqueness of the covariance estimates. We also formulate the optimal weighting to be used in the least-squares objective in the covariance estimation problem to ensure minimum variance in the estimates. A modification to the above technique is then presented to estimate the number of independent stochastic disturbances affecting the states. This minimum number of disturbances is usually unknown and must be determined from data. A semidefinite optimization problem is solved to estimate the number of independent disturbances entering the system and their covariances.