Non-linear Estimation with Generalised Compressed Kalman Filter

The optimal estimation of dynamic random fields is a relevant problem in diverse areas of robotics application. The associated estimation process in these problems implicitly requires dealing with high dimensional multi-variate Probability Density Functions (PDFs) with unaffordable processing cost. The Generalised Compressed Kalman Filter (GCKF) with subsystem switching and proper information exchange architecture is capable of solving such problems with comparable performance to the optimal full Gaussian estimators but at a remarkably lower cost. In this paper, an explicit algorithm is proposed for replacing the Kalman Filter core with a suitable Gaussian Filter core to solve non-linear estimation problems. The computational advantages of GCKF are highlighted, where the computational complexities of different Gaussian Filters are compared against their compressed counterpart. The performance of the algorithm has been verified through its application in solving linear Stochastic Partial Differential Equations (SPDEs) with unknown parameters.