A Local Unscented Transform Kalman Filter for Nonlinear Systems

This paper proposes an efficient data assimilation approach based on the sigma-point Kalman filter (SPKF). With a potential for nonlinear filtering applications, the proposed approach, designated as the local unscented transform Kalman filter (LUTKF), is similar to the SPKF in that the mean and covariance of the nonlinear system are estimated by propagating a set of sigma points-also referred to as ensemble members-generated using the scaled unscented transformation (SUT), while making no assumptions with regard to nonlinear models. However, unlike the SPKF, the LUTKF can reduce the influence of observations on distant state variables by employing a localization scheme to suppress spurious correlations between distant locations in the error covariance matrix. Moreover, while the SPKF uses the augmented state vector constructed by concatenating the model states, model noise, and measurement noise, the system state for the LUTKF is not augmented with the random noise variables, thereby providing an accurate state estimate with relatively few sigma points. In sensitivity experiments executed with a 40-variable Lorenz system, the LUTKF required only three sigma points to prevent filter divergence for linear/nonlinear measurement models. Comparisons of the LUTKF and the local ensemble transform Kalman filters (LETKFs) reveal the advantages of the proposed filter in situations that share common features with geophysical data assimilation applications. In particular, the LUTKF shows considerable benefits over LETKFs when assimilating densely spaced observations that are related nonlinearly to the model state and that have high noise levels-such as the assimilation of remotely sensed data from satellites and radars.