A simple recursive algorithm for learning a Monotone Wiener system

This paper studies a recursive identification method (i.e. an adaptive filter, or online learning algorithm) - termed the RANKTRON - for learning a Monotone Wiener model from observed input-output pairs. Such a model consists of a sequence of an unknown Linear Time-Invariant (LTI) dynamic model, followed by an unknown monotone (in- or decreasing) static nonlinear function. The main contribution is the introduction of a technical argument which establish worst-case performance of the proposed algorithm. The same tool is then used to derive properties in case the Monotone Wiener assumption only holds approximatively, and to the case where the output nonlinearity is a quantization function. An application of the RANKTRON is reported for the identification of a 20e order LTI based on quantized observations, using a mere O(1000) samples.