An insight into the issue of dimensionality in particle filtering

Particle filtering is a widely used Monte Carlo method to approximate the posterior density in non-linear filtering. Unlike the Kalman filter, the particle filter deals with non-linearity, multi-modality or non Gaussianity. However, recently, it has been observed that particle filtering can be inefficient when the dimension of the system is high. We discuss the effect of dimensionality on the Monte Carlo error and we analyze it in the case of a linear tracking model. In this case, we show that this error increases exponentially with the dimension.