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This paper considers a state estimation problem for discrete-time systems with Markov switching parameters. For this, the generalized pseudo-Bayesian second-order-extended Viterbi (GPB2-EV) and the interacting multiple-model-extended Viterbi (IMM-EV) algorithms are presented. The derivations of these new algorithms rely on a nontrival incorporation of some functional mechanisms of a new extended Viterbi algorithm into the GPB2 and the IMM methods for hypothesis reductions in order to improve computational efficiency and/or estimation performance. The IMM-EV (and the GPB2-EV) algorithm and the IMM (and the GPB2) algorithm have some common components, but their schemes for the calculation of weights and for the combination of the inputs and outputs are different. Indeed, the IMM-EV (and the GPB2-EV) algorithm spans the continuum from hard-decision methods with merged-hypothesis-tree style to the IMM (and the GPB2) algorithm inclusive. The proposed algorithms are well suited to state estimation problems in maneuvering target tracking. Simulations demonstrate that an IMM-EV algorithm can be an improvement to the IMM, the GPB2, and the variable-structure multiple model with likely-model set methods for tracking a target undergoing various types of maneuvers at some unknown times.