Derivation of a sawtooth iterated extended Kalman smoother via the AECM algorithm

The iterated extended Kalman smoother (IEKS) is derived under expectation-m aximization (EM) algorithm formalism, providing insight into the behavior o f the suboptimal extended Kalman filter (EKF) and smoother (EKS). Through a n investigation of smoothing algorithms that result from variants of the EM algorithm, the sawtooth iterated extended Kalman smoother (SIEEKS) and its computationally inexpensive counterparts are proposed via the alternating expectation conditional maximization (AECM) algorithm. The SIEEKS is guaran teed to produce a sequence estimate that moves up the likelihood surface. N umerical simulations including frequency tracking examples display the supe rior performance of the sawtooth EKF over the standard EKF for a range of n onlinear signal models.