The inverse Kalman filter

We introduce the inverse Kalman filter (IKF), 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 IKF 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 IKF approach through applications in nonparametric estimation of particle interaction functions, using both simulations and real cell trajectory data.