Detection of random and sinusoidal signals in hidden Markov noise

Noise which may be modeled as Z=AX, where A is a discrete positive valued random variable and X is a normally distributed random variable, has a discrete Gaussian mixture density. This model has been shown to apply to certain acoustic and radar data, and by using detection algorithms derived from this model the detection capability of radar operating against a background of sea clutter and thermal noise can be significantly enhanced in comparison with CFAR processing. In this article successive values of A have been assumed to be independent. However, for many applications, including detection in sea clutter, A may be correlated. In this study, A is modeled as a finite Markov process, and thus, Z is described by a hidden Markov model. Likelihood ratio and locally optimal detection statistics are derived for random and sinusoidal signals of unknown phase in hidden Markov noise. These algorithms are compared using radar data and Monte Carlo simulations.