A Sequential Smoothing Algorithm with Linear Computational Cost

In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method also overcomes some of the degeneracy problems we identify in many existing algorithms. Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and on the analysis of an athletics data set, that our new method also substantially outperforms the simple FilterSmoother (the only other smoother with computational cost that is linear in the number of particles).