H.L. Van Trees (ed.) and K.L. Bell (ed.), Bayesian Bounds for parameter estimation and nonlinear filtering/tracking, Wiley & Sons Ltd, 2007 [Book review]

Parameter and random-process estimation play a central role in signal processing. A common requirement in the estimation problems is to predict and/or evaluate the error performance. This task is often complicated because the system and measurement models are typically non-linear with some inherent uncertainty. The error performance prediction is supposed to be theoretical - its goal is to establish the best achievable limit and is to be carried out even before one develops a suitable estimator. The error performance evaluation is usually done by Monte Carlo simulations once a candidate estimator has been built. Evaluation serves to assess the estimator quality by comparing its actual error with the theoretical prediction. The fundamental question in algorithm design is "Can we do better?" In this context, it is of paramount importance to find a theoretical bound on the error performance and compare it against the performance of various sub-optimal candidate estimators.