Introducing the Laplace approximation in particle filtering

The situations where particle filtering fails (so-called weight degeneracy) can be detected with the asymptotic variance of the particle approximation. However, this asymptotic variance is in general intractable, and in the case of weight degeneracy, computing it by Monte Carlo sampling is inefficient. We propose to compute the asymptotic variance of the particle approximation via the Laplace method for multidimensional integrals. We present this method, and illustrate how it can be used to improve particle filtering robustness.