The inverse Kalman filter

Abstract

We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman filter with the conjugate gradient algorithm, which substantially accelerates the computation of matrix inversion for a general form of covariance matrix, where other approximation approaches may not be directly applicable. We demonstrate the scalability and efficiency of the proposed approach through applications in nonparametric estimation of particle interaction functions, using both simulations and cell trajectories from microscopy data.

17 pages, 8 figures, 2 tables

References in corpus (7)

• Novel type of phase transition in a system of self-driven particles
• Large-scale collective properties of self-propelled rods
• A general framework for Vecchia approximations of Gaussian processes
• Nonparametric inference of interaction laws in systems of agents from trajectory data
• Nonparametric Bayes dynamic modeling of relational data
• Stochastic approximation of score functions for Gaussian processes
• Molecular-scale substrate anisotropy and crowding drive long-range nematic order of cell monolayers