Fast initialization of particle filters using a modified metropolis-Hastings algorithm: mode-hungry approach

As a recursive algorithm, the particle filter requires initial samples to track a state vector. These initial samples must be generated from the received data and usually obey a complicated distribution. The metropolis-Hastings (M-H) algorithm is used for sampling from intractable multivariate target distributions and is well suited for the initialization problem. Asymptotically, the M-H scheme creates samples drawn from the exact distribution. For the particle filter to track the state, the initial samples need to cover only the region around its current state. This region is marked by the presence of modes. Since the particle filter only needs samples around the mode, we modify the M-H algorithm to generate samples distributed around the modes of the target posterior. By simulations, we show that this "mode hungry" algorithm converges an order of magnitude faster than the original M-H scheme for both unimodal and multi-modal distributions.