In this paper, a probabilistic approach for estimating time and space-variant parameters of a system, based on sequentially received discrete-time signal values, is presented. The system description is the solution of a linear partial differential equation (PDE). The PDE describes for example the wave propagation of an acoustic wave in a localization system. The solution of the PDE is given by a time-variant and space-variant impulse response. This impulse response is characterized by the time and space-variant parameters in order to track an object, which emits for example an acoustic signal. For estimating the position of the object in an instantaneous way a Bayesian approach has to be used, which considers the dynamic behavior of the parameters in a system model and uncertainties in a stochastic manner by means of probability density functions. Hence, the new approach provides a probabilistic instantaneous model-based signal processing, where the sequentially measured signal values are processed directly and known reference signal sequences are interpreted as part of a time-variant nonlinear measurement equation.