Sequential estimation of probability of events

In many signal processing problems, it is important to estimate the probability that a signal is present in observed data. As opposed to standard Bernoulli experiments where the outcomes of the experiments clearly show when the event occurred, there are many situations where only probabilistic claims can be made about the occurrence of events. Examples of the latter include a variety of problems related to detection of signals in noise. A processing scheme for estimating the posterior probability density function of the probability of occurrence of an event is proposed. It is based on a sequential importance sampling method, which approximates the desired posterior density with a probability measure composed of particles and their associated weights. With the arrival of new experimental data, the weights of the particles are updated, and as a result, the overall posterior modified. A simulation result is provided that shows the performance of the proposed method.