Jean-Rene Larocque, Ph. D. and William Ng, Ph.D. Candidate
MCMC (Markov Chain Monte Carlo) and MC Statistical Methods are very powerful statistical techniques for parameter estimation and related problems. They are particularly useful for the difficult nonlinear or non-Gaussian case. Using a large data set, these techniques can also be used to make inference on parameters, to integrate nuisance parameters, to evaluate functions numerically or to solve optimization problems.
We have applied these methods to several interesting problems: (J-R. Larocque)
- Joint model order detection and DOA estimation in coloured noise
Model order detection has always been a difficult problem in array signal processing w hen the noise is coloured. A novel reversible jump MCMC approach has been proposed to solve this problem (IEEE Trans Signal Processing, Feb., 2002). Download.
- Tracking of multiple targets using arrays of sensors
In this project, arrays of sensors are used to detect the number of targets and to jointly track their directions of arrival, using particle filters, or sequential Monte Carlo approaches. These methods approach real-time efficiency and show considerable advantages over previous techniques. A submission has been made to IEEE Trans. SP. Download.
- Applications to 3G
It is envisaged that third generation wireless systems will include an antenna array, at least at the base station and at the mobile not too long after. Channel modelling is required for these systems for calculation of outage,etc. Channel modelling in turn requires accurate measurement and estimation of the channel.
The Reversible Jump MCMC sampling scheme was applied to real-life outdoor propagation measurements for the purpose of channel estimation. An experimental wideband CDMA receiver was built for collecting propagation data. Excellent correspondence between the results estimated from the MCMC algorithm and geographical thruthing were obtained. A submission has been made to IEEE Trans. Vehicular Technology. Download.
The following work is being done by William Ng
Work is now in progress with the objective of using MCMC and sequential MC methods for restoration of signals using sensor arrays; i.e., we wish to extract a signal of interest from multiple interfering sources. This has been accomplished for the narrowband case, and work has been extended to the more difficult wideband case.
Details about these subjects can be downloaded from here.