Supplementary: A Nearly-Black-Box Online Algorithm for Joint Parameter and State Estimation in Temporal Models

Bootstrap particle filter as a subcase of APF Here we will show that when q is a delta function, APF recovers the bootstrap particle filter. The Dirac delta function can be considered as the limit of a Gaussian as the variance goes to zero, δ(θ − μ) = limσ2→0N (θ;μ, σ). Therefore, we can view q as an exponential family distribution. Specifically we are dealing with a Gaussian distribution with unknown mean and known variance (zero-variance). Then the moment matching integral required for assumed density filtering reduces to matching the means. If qi−1 = δ(θ−μi−1), then