Passive Multipath Time Delay Estimation Using MCMC Methods

Passive time delay estimation in multipath environments is studied in this paper. A novel restrained maximum likelihood (ML) estimator is proposed to estimate the multiple time delays. Unlike traditional ML function which has P global maximum values, restraint conditions limit the ML function of P paths time delays signal with only one global maximum value. Markov chain Monte Carlo (MCMC) algorithm is used to find the global maximum of the restrained likelihood function to avoid traditional complex multidimensional grid search, initialization-dependent iterative methods or methods using interpolation to enhance performance. Indeed, MCMC sampling technique for ML function has a lower computational complexity than importance sampling (IS), which needs to compute the required realizations before sampling. Furthermore, Cramer–Rao lower bound of this model is derived. Finally, simulations results and theoretical analysis demonstrate that MCMC-based approach has the same performance as IS-based algorithm and the lower computational complexity than IS-based technique.