A solution of the Bayesian recursive relations by the particle filter approach is treated. The stress is laid on the sample size setting as the main user design problem. The Cramér-Rao bound was chosen as a tool for setting the sample size for the three basic types of the state estimation, for filtering, prediction and smoothing. The mean square error matrices of particle filter state estimates...

In the parameter estimation problems, we obtain information about the parameter from a sample of data coming from the underlying probability distribution. A natural question is: how much information can a sample of data provide about the unknown parameter? This section introduces such a measure for information, and we can also see that this information measure can be used to find bounds on the ...

Wepropose a modified Bayesian Cramér-Rao lower bound (BCRLB) for nonlinear tracking applications where the prediction distribution conditioned on past measurements is used as the prior. The novelty of the proposed modified BCRLB comes from the fact that it utilizes past measurements, therefore it is specific to the current realization of the track which makes it a useful online tool that can be...

In an orthogonal-frequency-division multiplex (OFDM) system, the problem of sampling clock synchronization and channel estimation is analyzed. In such systems, when the number of sub-carriers is large, a sampling clock frequency mismatch between the transmitter and the receiver dramatically degrades the performance. Obviously, the channel-impulse response is unknown at the receiver and also nee...

We consider the problem of autonomously locating a number of asynchronous sensor nodes in a wireless network. A strong focus lies on reducing the processing resources needed to solve the relative positioning problem, an issue of great interest in resourceconstrained wireless sensor networks. In the first part of the paper, based on a well-known derivation of the Cramér-Rao lower bound for the a...

Rather than compute the exact error of a specific estimator, it is often more convenient to apply results which lower-bound the error of any estimator for a given problem. We present three such bounds and illustrate their applications to signal parameter estimation. The Cramèr-Rao bound is simple to compute and approximates the actual error under conditions of high signal-to-noise ratio. Howeve...

A Cramér-Rao bound (CRB) for semi-blind channel estimators in redundant block transmission systems is derived. The derived CRB is valid for any system adopting a full-rank linear redundant precoder, including the popular cyclicprefixed orthogonal frequency-division multiplexing system. Simple forms of CRBs for multiple complex parameters, either unconstrained or constrained by a holomorphic fun...