Multipath propagation makes the use of received signal strength (RSS) unreliable as a signal propagation model for localization of a radio source based on RSS data. An approach to mitigation of this problem is the use of a Hidden Markov model (HMM) to represent the relationship between RSS and the radio source location by incorporating an environment prior and RSS source dynamics. The HMM structure forces a geometric form for the distribution for the sojourn time. This, combined with missing data problems, reduces confidence in location estimation. It is found, in this paper, that Hidden semi-Markov Models (HsMMs), with a more flexible sojourn time distribution are more able to represent source dynamics while retaining the advantages of HMMs for environmental constraints and improving resilience to missing measurements. The performance of the proposed HsMM algorithm is compared with a standard HMM via experiments and simulations involving indoor radio source localization using RSS data. Simulations use a ray tracing software-based simulator and the experiments for transmitter localization with RSS data are collected by software defined radios.