We propose two nonlinear Kalman smoothers that rely on Student’s t distributions. The T-Robust smoother finds the maximum a posteriori likelihood (MAP) solution for Gaussian process noise and Student’s t observation noise, and is extremely robust against outliers, outperforming the recently proposed `1-Laplace smoother in extreme situations (e.g. 50% or more outliers). The second estimator, whi...

In this paper, we propose a new fixed-lag smoother that estimates the fixed-delayed state for a continuous-time stochastic system. The estimation error variance of the proposed smoother is minimized under the constraint that the estimated state converges to the real state exactly in finite time after noises or uncertainties disappear. For numerical computing, the proposed smoother is represente...

The nonlinear Gaussian Mixture Model Dynamically Orthogonal (GMM–DO) smoother for highdimensional stochastic fields is exemplified and contrasted with other smoothers by applications to three dynamical systems, all of which admit far-from-Gaussian distributions. The capabilities of the smoother are first illustrated using a double-well stochastic diffusion experiment. Comparisons with the origi...

A spatio-temporal linear dynamic model has been developed for patching short gaps in daily river runoff series. The model was cast in a state-space form in which the state variable was estimated using the Kalman smoother (RTS smoother). The EM algorithm was used to concurrently estimate both parameter and missing runoff values. Application of the model to daily runoff series in the Volta Basin ...

We employ the variational formulation and the Euler-Lagrange equations to study the steady-state error in linear non-causal estimators (smoothers). We give a complete description of the steady-state error for inputs that are polynomial in time. We show that the steadystate error regime in a smoother is similar to that in a filter of double the type. This means that the steady-state error in the...

The launch and impact points of a flight trajectory are estimated using U-D Kalman filter and Rauch-Tung-Striebel (R-T-S) smoother. Algorithms are implemented in PC MATLAB and validated using simulated data. The filter performance is evaluated in terms of state error, innovation sequence, and autocorrelation of residuals along with their theoretical bounds. The R-T-S smoother was found to gener...