@TECHREPORT{LehWil06PosteriorTR,
  author =      {Eric A. Lehmann and Robert C. Williamson},
  title =       {Posterior Cramér-Rao Bound for Acoustic Source Tracking in Reverberant Environments},
  type =        {{NICTA} Technical Report},
  number =      {ISSN 1833-9646},
  institution = {National ICT Australia},
  address =     {Canberra, Australia},
  month =       {December},
  year =        {2006},
  abstract =    {The research presented in this paper is motivated by the desire to determine a lower bound on the estimation error for acoustic source localisation and tracking (ASLT) algorithms operating in reverberant conditions. The present work makes use of the so-called posterior Cramér-Rao bound (PCRB), a generalisation of the well-known Cramér-Rao bound theory that is directly applicable to this kind of target-tracking situation. To this purpose, we propose to represent the considered ASLT problem with a system model that accounts for the effects of the temporal correlation existing between sound intensity values measured in a reverberant sound field by means of a microphone array beamformer. We then investigate the tracking results obtained with an acoustic source localisation algorithm, based on the concept of particle filtering (PF), used in conjunction with the proposed system model. As a result of the PCRB derivations implicitly assuming statistical whiteness when considering the system and observation noise processes, the lower bound derived in this work remains unaffected by the level of correlation existing in the ASLT model. On the other hand, the tracking accuracy of the particle filter clearly degrades as the level of correlation in the sound intensity measurements increases. This result leads to the conclusion that the PCRB does not completely capture the sort of performance one is interested in for practical applications, and highlights the need for a different type of lower bound that would account for potentially non-white noise processes in the system model.}
}