Pole-based distance measure for change detection in linear dynamic systems

In this work, we derive a distance measure for the detection of changes in the behavior of linear dynamic single-input-single-output (SISO) systems based on input-output data. The distance is calculated as a function of the system poles, which are directly estimated from the given data. Poles represent a system as a set and have no identities, which is analogous to the nature of association-free multi-target tracking. This motivates the application of set distances known from multi-target tracking, namely the optimal subpattern assignment (OSPA) distance. Thus, the OSPA distance as well as a modification, the MAX-OSPA distance, are formulated as pole-distances between dynamic systems. In this formulation, the OSPA distance finds the optimal assingment by minimizing over the sum of distances between poles. The MAX-OSPA chooses an optimal assignment by minimizing the maximum distance between two poles. The proposed distances are evaluated in several simulations comparing the deterministic OSPA and MAX-OSPA to a state-of-the-art metric for autoregressive-moving-average (ARMA) processes, as well as OSPA and MAX-OSPA using the direct pole estimation and a two step-pole estimation utilizing recursive ARX (AutoRegressive model with eXogenous input) system identification.