Filtering and fixed-point smoothing from an innovation approach in systems with uncertainty.
In this paper two recursive algorithms are proposed and compared as a solution of the least mean-squared error linear filtering problem of a wide-sense stationary scalar signal from uncertain observations perturbed by white and coloured additive noises. Considering that the state-space model of the signal is not available and that the variables modelling the uncertainty are not independent, the proposed algorithms are derived by using covariance information. The difference between both algorithms...
We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < ..., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent and the conditional distribution of y(ti) only depends on x(ti). When this conditional distribution has a specific form, we prove that the model ((x(ti),y(ti)), i≥1) is a computable filter in the sense that all distributions involved in filtering, prediction...