The Level Set Kalman Filter for State Estimation of Continuous-Discrete Systems

We propose a new extension of Kalman filtering for continuous-discrete systems with nonlinear state-space models that we name as the level set filter (LSKF). The LSKF assumes probability distribution can be approximated Gaussian and updates through time-update step measurement-update step. improves compared to existing methods, such cubature (CD-CKF), by reformulating underlying Fokker-Planck equation an ordinary differential Gaussian, thereby avoiding need explicit expression higher derivatives. Together carefully picked method, numerical experiments show has consistent performance improvement over CD-CKF range parameters. Meanwhile, simplifies implementation, no user-defined timestep subdivisions between measurements are required, spatial derivatives drift function not explicitly needed.