In this letter, a new estimation filtering is proposed when a delay between signal generation and signal estimation exists. The estimation filter is developed under a maximum likelihood criterion using only the finite observations on the delay interval. The proposed estimation filter is represented in both matrix form and iterative form. It is shown that the filtered estimate has good inherent properties such as time-invariance, unbiasedness and deadbeat. Via numerical simulations, the performance of the proposed estimation filtering is evaluated by the comparison with that of the existing fixed-lag smoothing, which shows that the proposed approach could be appropriate for fast estimation of signals that vary relatively quickly. Moreover, the on-line computational complexity of the proposed estimation filter is shown to be maintained at a lower level than the existing one.

This paper discusses the least-squares linear filtering and fixed-lag smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of not necessarily independent Bernoulli variables. It is assumed that the observations are perturbed by white noise and the autocovariance function of the signal is factorizable. Using an innovation approach we obtain the filtering and fixed-lag smoothing recursive algorithms, which do not require the knowledge of the state-space model generating the signal. Besides the observed values, they use only the matrix functions defining the factorizable autocovariance function of the signal, the noise autocovariance function, the marginal probabilities and the (2,2)-element of the conditional probability matrices of the Bernoulli variables. The algorithms are applied to estimate a scalar signal which may be transmitted through one of two channels.

This paper treats the least-squares linear filtering and smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables. Using an innovation approach we obtain the filtering algorithm and a general expression for the smoother which leads to fixed-point, fixed-interval and fixed-lag smoothing recursive algorithms. The proposed algorithms do not require the knowledge of the state-space model generating the signal, but only the covariance information of the signal and the observation noise, as well as the probability that the signal exists in the observed values.