Abstract

In this talk I will provide an overview of some of the work we do when it comes to solving inference problems in nonlinear dynamical systems. A proper subtitle for the talk is “strategies and examples”, since I will only provide solution strategies and show that these strategies can successfully solve challenging applications. The first topic is parameter inference problems in nonlinear dynamical systems (a.k.a. nonlinear system identification). The maximum likelihood problem is solved using a combination of the expectation maximization (EM) algorithm and sequential Monte Carlo (SMC) methods (e.g., the particle filter and the particle smoother). The Bayesian problem is solved using a combination of Markov chain Monte Carlo (MCMC) and SMC . As an example, we show how to estimate a particular special case known as the Wiener model (a linear dynamical model followed by a static nonlinearity). The second topic is that of sensor fusion, which refers to the problem of inferring states (and possibly parameters) using measurements from several different, often complementary, sensors. The strategy is explained and (perhaps more importantly) illustrated using three of the industrial applications we are working with; 1. Navigation of fighter aircraft (using inertial sensors, radar and maps); 2. Indoor positioning of humans (using inertial sensors and maps); 3. Indoor pose estimation of a human body (using inertial sensors and ultra-wideband).