Brief paper: Initial-value system for linear smoothing problems by covariance information
Automatica (Journal of IFAC)
A new initial-value method for on-line filtering and estimation (Corresp.)
IEEE Transactions on Information Theory
A view of three decades of linear filtering theory
IEEE Transactions on Information Theory
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The estimation problem of a signal is considered for the white Gaussian observation noise in linear continuous systems. At first, the recursive fixed-point smoother and filter are designed using the covariance information. The observation equation is given by y(t) = z(t) + v(t), z(t) = H(t)x(t), where y(t), x(t), v(t) and H(t) denote the observed value, the signal to be estimated, the white Gaussian observation noise and the observation matrix, respectively. It is assumed that the observed value, the autocovariance K"z(t, s) of z(t) and the variance R(t) of v(t) are known beforehand. Also, the spectral factorization problem is discussed on the system matrix F(t), the input matrix G(t) for the white Gaussian noise and the observation matrix H(t), and the parameter estimation algorithms for G(t) and H(t) are developed by using covariance information.