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.

翻译：本文提出了逆卡尔曼滤波器，该滤波器能够以线性计算成本，实现动态线性模型协方差矩阵与任意实值向量之间的精确矩阵-向量乘法。我们将逆卡尔曼滤波器与共轭梯度算法相结合，从而显著加速了一般形式协方差矩阵的求逆计算，而其他近似方法可能无法直接适用于此类矩阵。通过模拟实验和显微数据中的细胞轨迹，我们在粒子相互作用函数的非参数估计应用中，展示了所提方法的可扩展性和高效性。