On the Cram&amp;#x00E9;r-Rao bound of autoregressive estimation in noise

Weruaga, Luis; Melko, O. Michael

doi:10.1109/iscas.2011.5937580

Cited by 1 publication

(1 citation statement)

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“…We obtained the accuracy limit of the parameter estimates from the Cramér-Rao lower bound (CRLB) [5]–[7] for the case where no prior knowledge of the parameters is assumed [4]. Since in estimation theory that the use of prior knowledge may lead to a more accurate estimate [5], it is of interest to know how the accuracy limit presented in [4] may improve with prior knowledge of some of the parameters.…”

Section: Introductionmentioning

confidence: 99%

Influence of prior knowledge on the accuracy limit of parameter estimation in single-molecule fluorescence microscopy

Lin

Wong

Ober

2013

2013 IEEE International Symposium on Circuits and Systems (ISCAS2013)

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In estimation theory, it is known that prior knowledge of parameters can improve the Cramér-Rao lower bound (CRLB). In this paper, we study the influence of prior knowledge on the CRLB of the estimates of the parameters that describe the trajectory of a moving object (single molecule). Since the CRLB is obtained from the inverse of the Fisher information matrix, we present a general expression of the Fisher information matrix in terms of the image function, the object trajectory and the prior knowledge matrix. Applying this expression to an object moving linearly in a two-dimensional (2D) plane with two distinct cases of prior knowledge, explicit CRLB expressions are derived. From these expressions, we show that the improvement in the CRLB of the parameter estimates is dependent on which parameters are known.

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Section: Introductionmentioning

confidence: 99%