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