Multiple Optima in Identification of ARX Models Subject to Missing Data

Special system identification algorithms are required if there are significant amounts of data missing. Some such algorithms have been developed previously and typically result in iterative procedures for the parameter estimation. Since missing data can be viewed as irregular sampling (decimation) of the signals, it is obvious that there is a risk for aliasing. In system identification aliasing manifests itself as potential multiple global optima of the identification loss function. The aim of this paper is to investigate under what circumstances this may in fact occur. The focus of the paper is on periodic missing data patterns. It is shown that it is, in fact, not the fraction of missing data that is important, but rather what time lags of the input and output correlation and cross-correlation functions that can be estimated. For ARX models with all input data observed we verify that there is indeed only one global optimum.