Algorithms for obtaining sub-optimal filtering, fixed-point smoothing, and fixed-lag smoothing estimates of the state of a non-linear system given noisy discrete time measurements are presented. The filtering problem involves obtaining estimates of the states x(kT) and x((k −1)T), and the smoothing algorithms generate an estimate of the state x((k — N)T) for either (k — N) orNconstant, whereTis the time increment between receiving measurements andk= 0, 1,…, is the discrete time index. An example is included to illustrate the utility of the smoothing algorithms for obtaining estimates superior to filtering results.