Real-Time Estimation of Parameter Maps

Abstract

System parameters might have a distinct operating point dependency that is unknown. Nonlinear state observers or Kalman Filters can be applied to estimate such parameters in real-time, revealing the unknown parameter value in the vicinity of the current operating point. Commonly, these methods are prone to forget the revealed dependence continuously when a different operating point is approached. This paper provides a procedure to preserve past estimates and reveal the hidden parameter map during operation of the system. Parameter dependencies are approximated via adjustable interpolants. In particular, ready-to-use formulae for piecewise linear and cubic Hermite interpolants are provided. An existing approach as well as a newly derived approach to embed these interpolants within an Unscented Kalman Filter are presented and discussed. While the first approach utilizes the parameter map estimation directly within the Kalman Filter scheme, the new approach expands the Kalman Filter steps by a recursive map adaption scheme and is thereby far less computationally expensive. Both methods are compared and validated via numerical simulations, where a superior performance is achieved compared to the standard parameter estimation within the Kalman Filter approach.