Robust Sequential Monte Carlo

Standard SMC uses the assumed (often Gaussian) observation likelihood to weight particles. When an outlier arrives, Gaussian likelihoods assign it near-zero probability, causing weight collapse to a single particle. Robust SMC replaces the Gaussian likelihood with a heavier-tailed alternative (e.g., Student-t) or mixes it with an outlier component, so extreme observations still receive positive weight and the particle cloud remains diverse.

Particle degeneracy occurs when, after a weighting step, all of the importance weight concentrates on one or a few particles. Resampling draws a new set of N particles by sampling with replacement proportional to the weights, discarding low-weight particles and duplicating high-weight ones. This restores diversity but introduces sampling variance, so adaptive resampling (triggered only when effective sample size falls below a threshold) is preferred.

Use a Student-t likelihood when you suspect the observation noise has heavier tails than Gaussian — for example, financial returns, radar clutter, or ecological count data with overdispersion. The degrees-of-freedom parameter controls tail weight; values between 3 and 10 are common. A prior sensitivity analysis over this parameter is advisable.

Poorly: particle filters in general suffer from the curse of dimensionality. Above roughly 10-20 state dimensions, an astronomically large number of particles is needed for adequate coverage. In high-dimensional settings, Rao-Blackwellisation, auxiliary particle filters, or hybrid approaches combining SMC with Kalman-type updates are preferred.

No. A robust Kalman filter is a linearisation-based method that modifies the Kalman update equations to downweight outliers while retaining the Gaussian, linear-conjugate structure. Robust SMC makes no linearity or Gaussianity assumption and can handle fully nonlinear, non-Gaussian models, at the cost of higher computational expense.