Probabilistic Estimation of the Number of Frequency-Hopping Transmitters

We present two probabilistic estimation techniques for identifying the most likely number of frequency-hopping transmitters for a range of different scenarios and compare their performances. In the first technique, cumulative estimation, a Gaussian approximation methodology is developed based on a single integrated measurement over the observation time window. In the second technique, time-distributed estimation, a maximum-likelihood formulation is adopted, and time-specific observation data is used. We give specific analytical consideration to the potential that not all transmitters that are present will be always detected, and explore the effects of the probability of misdetection on the overall estimation process. Simulation results confirm that the approaches presented here can lead with high probability to a correct decision regarding the number of transmitters.