Batch scheme Hartley modulating functions method for the detection and estimation of jumps in a class of convolvable nonlinear systems

Convolvable nonlinear continuous-time dynamical systems with parameters which may switch among a finite set of values are considered. A novel scheme, called the Hartley modulating functions (HMF) method, is proposed for the detection and estimation of physical parameter jumps given noisy observations. The HMF-method converts the nonlinear differential equation describing the convolvable nonlinear system into a Hartley spectrum equation using the frequency weighted least squares algorithm. During conversion the method retains identical relationship between physical parameter coefficients in differential equations and Hartley spectrum equations. Thus, it is suitable for estimation of physically-based nonlinear continuous-time systems. Preliminary illustrative results demonstrate the potential and performance of the approach.