Anders Hansson (Linköping University)
System Identification with Missing Data
In this talk we will discuss system identification when some of the data is missing. Mainly two different approaches will be discussed. The first one is based on maximum likelihood estimation. We will see that the an equivalent criterion is to minimize the Euclidean norm of the prediction error vector scaled by a particular function of the covariance matrix of the observed output data. We also provide insight into when simpler and in general sub-optimal schemes are indeed optimal. An efficient implementation is obtained by recognizing that the problem is a separable least squares problem. The second approach is based on a subspace formulation and uses the nuclear norm heuristic for structured low-rank matrix approximation, with the missing input and output values as the optimization variables. Here the key to an efficient implementation is to employ the alternating direction method of multipliers.