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IEEE Int Symp Circuits Syst Proc. 2013 May;2013:1304-1307.

Influence of Prior Knowledge on the Accuracy Limit of Parameter Estimation in Single-Molecule Fluorescence Microscopy.

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School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798.
Eric Jonsson School of Electrical Engineering and Computer Science, University of Texas at Dallas, Richardson, TX 75083-0688 USA.


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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