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This paper presents a particle filter approach to spectral amplitude speech enhancement. Spectral amplitudes are known to exhibit inter-frame dependencies and non-Gaussian statistics; however, incorporating these properties makes closed-form solutions intractable. Using the particle filter framework allows the presented algorithm to model the speech spectral amplitudes as an autoregressive process with Laplace distributed excitation. Two variants of the standard algorithm are also presented: one that uses an interacting multiple model approach to account for transitions between active speech and silence intervals, and one that allows for phase differences between the clean speech and noise complex Fourier transform coefficients. All of the particle sampling distributions are constrained to take the measurement into account, improving sampling efficiency. In experiments using wideband speech and real recorded noise the proposed algorithm variants are shown to offer natural-sounding output speech, with objective evaluation results that compare favorably to existing particle filter speech enhancement algorithms. The multiple model variant is found to improve inter-speech noise reduction, while the phase variant improves performance when the signal-to-noise ratio is low.