Covariance-based estimation algorithms in networked systems with mixed uncertainties in the observations

• Uncertain observations with random transmission delays and dropouts are considered.
• Recursive LS linear prediction, filtering and smoothing algorithms are proposed.
• The algorithms, based on covariances, are derived using an innovation approach.
• Recursive formulas for the estimation error covariance matrices are also proposed.
• Non-stationary and stationary signal examples are given to illustrate the results.

In this paper a new observation model is proposed for networked systems subject to three sources of uncertainty. On the one hand, the measured outputs can be only noise (uncertain observations) and, on the other hand, one-step delays or packet dropouts may occur randomly during transmission; it is assumed that, at each sampling time, it is not known if some of these uncertainties have occurred. The random uncertainties are modelled by sequences of Bernoulli random variables. Under these assumptions, recursive least-squares linear estimation algorithms are derived by an innovation approach, without requiring knowledge of the signal evolution equation, but only the covariances of the processes involved in the observation model and the uncertainty probabilities.