Optimal importance density for position location problem with non-Gaussian noise

State-space representation of positioning problems has enabled the use of particle filters to probabilistically estimate the location from the noisy sensor measurements. However, in particle filtering, the choice of the motion and sensor models, as well as the importance density used, are crucial for a good approximation. In this work, we have used Gaussian Mixtures to model the prior and likelihood densities, as they can be used for a wide range of distributions and can capture the multimodality of the densities. Additionally, with GMM prior and likelihood densities, we were able to evaluate and use the Optimal Importance Density for particle filters, which resolves the degeneracy of particles and sample impoverishment. We have provided simulation results based on field measurements to illustrate the validity of our models and the improvements made by using our proposed importance density.