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The dynamic and unpredictable characteristics of wireless channels in harsh environments have resulted in a poor performance of localization systems. Conventional implementations rely on unrealistic assumptions driven by tractability requirements, such as linear models or Gaussian errors. In this paper, we present a framework for data fusion in localization systems based on determining likelihood functions that represent the relationship between measurements and distances. In this framework, such likelihoods are dynamically adapted to the propagation conditions. The subsequent usage of a particle filter (PF) leads to an adaptive likelihood particle (ALPA) filter that addresses the nonlinear and non-Gaussian behavior of measurements over time. The ALPA filter's performance is quantified by using received-signal-strength (RSS) and time-of-arrival (TOA) measurements collected with wireless local area network (WLAN) devices. We compare the accuracy obtained to the accuracy of conventional implementations and to the posterior Cramér-Rao lower bound (PCRLB). Both empirical and simulation results show that the proposed ALPA filter significantly improves the accuracy of conventional approaches, obtaining an error close to the PCRLB.