Joint identification of plant rational models and noise distribution functions using binary-valued observations

System identification of plants with binary-valued output observations is of importance in understanding modeling capability and limitations for systems with limited sensor information, establishing relationships between communication resource limitations and identification complexity, and studying sensor networks. This paper resolves two issues arising in such system identification problems. First, regression structures for identifying a rational model contain non-smooth nonlinearities, leading to a difficult nonlinear filtering problem. By introducing a two-step identification procedure that employs periodic signals, empirical measures, and identifiability features, rational models can be identified without resorting to complicated nonlinear searching algorithms. Second, by formulating a joint identification problem, we are able to accommodate scenarios in which noise distribution functions are unknown. Convergence of parameter estimates is established. Recursive algorithms for joint identification and their key properties are further developed.