This paper proposes new recursive fixed-point smoother and filter using covariance information in linear discrete-time stochastic systems. In this paper, to be able to treat the estimation of the stochastic signal, a performance criterion, extended from the criterion in the H estimation problem, is newly proposed. The criterion is transformed equivalently into a min-max principle in game theory, and an observation equation in a Krein space is obtained as a result. The estimation accuracy of the proposed estimators are compared with the recursive least-squares (RLS) Wiener estimators, the Kalman filter and the fixed-point smoother based on the state-space model.

This paper proposes a measure of coefficient quantization errors for linear discrete-time state-space systems. The proposed measure of state-space systems agrees with the actual output error variance since it is derived from the exact evaluation of the output error variance due to coefficient deviation. The measure in this paper is represented by the controllability and the observability gramians and the state covariance matrix of the system. When the variance of coefficient variations is very small, the proposed measure is identical to the conventional statistical sensitivity of state-space systems. This paper also proposes a method of synthesizing minimum measure structures. Numerical examples show that the proposed measure is in very good agreement with the actual output error variance, and that minimum measure structures have a very small degradation of the frequency characteristic due to coefficient quantization.

We present a minimal lattice realization of MIMO linear discrete-time systems which interpolate the desired Markov and covariance parameters. The minimal lattice realization is derived via a recursive construction algorithm based on the state space description and it parametrizes all the interpolants.

We present a recursive algorithm for constructing linear discrete-time systems which interpolate the desired 1st-and 2nd-order information. The recursive algorithm constructs a new system and connects it to the previous system in the cascade form every time new information is added. These procedures yield a practical realization of all the interpolants.

The recursive least-squares filter and fixed-point smoother are designed in linear discrete-time systems. The estimators require the information of the system matrix, the observation vector and the variances of the state and white Gaussian observation noise in the signal generating model. By appropriate choices of the observation vector and the state variables, the state-space model corresponding to the ARMA (autoregressive moving average) model of order (n,m) is introduced. Here,some elements of the system matrix consist of the AR parameters. This paper proposes modified iterative technique to the existing one regarding the estimation of the variance of observation noise based on the estimation methods of ARMA parameters in Refs. [2],[3]. As a result, the system matrix, the ARMA parameters and the variances of the state and observation noise are estimated from the observed value and its sampled autocovariance data of finite number. The input noise variance of the ARMA model is estimated by use of the autocovariance data and the estimates of the AR parameters and one MA parameter.