Recursive least-squares quadratic smoothing from measurements with packet dropouts

The least-squares quadratic filtering and fixed-point smoothing problems of discrete-time stochastic signals from observations with multiple packet dropouts are addressed. It is assumed that the packet dropouts occur randomly and the latest measurement received successfully is processed for the estimation in case that the current measurement is dropped-out. This situation is modelled by introducing in the observation model a sequence of Bernoulli random variables whose values – one or zero – indicate if the current measurement is received or dropped-out, respectively, and whose probability distributions are known. A recursive estimation algorithm is deduced without requiring full knowledge of the state-space model generating the signal process, but only information about the dropout probabilities and the moments of the signal and noise processes involved. Defining a suitable augmented observation model, the quadratic estimation problem is reduced to the linear estimation problem based on the augmented observations, which is solved by using an innovation approach.

► Algorithms for the quadratic estimators from packet dropouts are proposed.
► The algorithms, based on covariances, are derived using an innovation approach.
► The quadratic estimator is obtained as the linear one from the augmented observations.
► Recursive formulas for the estimation error covariance matrices are also proposed.