Recursive Bayesian Filtering Through a Mixture of Gaussian and Discrete Particles
Conventional solutions to nonlinear filtering problems fall into two categories, deterministic and stochastic approaches. While the former is heavily used due to low computational demand, approximation error is tied to their initialization, which causes difficulty during long term application. The latter circumvents this but at the cost of a significant increase in computation. An extremely popular stochastic filter termed the particle filter is especially notorious for this. However its superior performance (over the conventional nonlinear filters) and generality of use makes it ideal in environments where high nonlinearity plagues the state-space model. Estimation error and computational complexity for the particle filter are both related to the number of particles utilized. Yet, many researchers have observed that particles in the vicinity of one another, perhaps because they represent the same state, might be redundant. A new type of filter is proposed where particles in addition to a (linearized) Gaussian component are tracked. This can be seen as a parallel solution to the estimation problem, each component can be separately filtered and constituent outputs summed up to form the filtering distribution. This new filter is then used in two classical scenarios used to benchmark nonlinear filters.