Predicting the future state of a random dynamic signal based on corrupted, distorted, and partial observations is vital for proper real-time control of a system that includes time delay. Motivated by problems from Acoustic Positioning Research Inc., we consider the continual automated illumination of an object moving within a bounded domain, which requires object location prediction due to inherent mechanical and physical time lags associated with robotic lighting. Quality computational predictions demand high fidelity models for the coupled moving object signal and observation equipment pair. In our current problem, the signal represents the vector position, orientation, and velocity of a stage performer. Acoustic observations are formed by timing ultrasonic waves traveling from four perimeter speakers to a microphone attached to the performer. The goal is to schedule lighting movements that are coordinated with the performer by anticipating his/her future position based upon these observations using filtering theory.
Particle system based methods have experienced rapid development and have become an essential technique of contemporary filtering strategies. Hitherto, researchers have largely focused on continuous state particle filters, ranging from traditional weighted particle filters to adaptive refining particle filters, readily able to perform path-space estimation and prediction. Herein, we compare the performance of a state-of-the-art refining particle filter to that of a novel discrete-space particle filter on the acoustic positioning problem. By discrete space particle filter we mean a Markov chain that counts particles in discretized cells of the signal state space in order to form an approximated unnormalized distribution of the signal state. For both filters mentioned above, we will examine issues like the mean time to localize a signal, the fidelity of filter estimates at various signal to noise ratios, computational costs, and the effect of signal fading; furthermore, we will provide visual demonstrations of filter performance.