Performance evaluation for particle filters

Performance evaluation in particle filtering problems is commonly performed via point estimator comparison. However, in non-Gaussian cases, this can be not always meaningful and entire particle clouds need to be compared. The Kullback-Leibler divergence (KLD) can be used for such a particle cloud comparison. In contrast to KLD estimates commonly used in particle filtering applications, we present an estimator of the KLD being applicable to any cloud of particles. This estimator is applied to a performance evaluation scheme generally relevant to any particle filter, of which abilities are equal to no other known scheme in the literature. Through simulations and concrete examples, we will show that it is suitable to practically compare particle clouds, which have a limited number of particles, have a different size, are close to each other and have an high dimensionality.