Sequential Joint Detection And Estimation With An Application To Joint Symbol Decoding And Noise Power Estimation

Jointly testing multiple hypotheses and estimating a random parameter of the underlying model is investigated in a sequential setup. The optimal scheme is designed such that it minimizes the expected number of used samples while keeping the probabilities of falsely rejecting a hypothesis and the mean-squared estimation errors below a pre-set level. The underlying constrained problem is first converted to an unconstrained problem and then reduced to an optimal stopping problem, whose solution is characterized by a non-linear Bellman equation. The optimal cost coefficients are obtained by exploiting a connection between the derivatives of the cost function and the detection/estimation errors. The paper concludes with a numerical example, namely solving the problem of sequential joint amplitude-shift keying symbol decoding and noise power estimation.