Derivation of CRLB for Wireless Capsule Endoscope Localization Using Received Signal Strength

This paper presents a theoretical analysis for location estimation of a wireless capsule endoscope (WCE) in the small-intestine region. Under three different shadowing scenarios by assuming standard deviation of the shadowing with the constant variance, parameter-dependent variance, or correlated and parameter-dependent variance, analytical formulas are derived for the Cramér-Rao lower bound (CRLB) for capsule positioning when distance and azimuth angle measurements are employed to estimate the location of the capsule. The CRLB analysis can be employed to quantify the best achievable location estimation performance. We also present some numerical results to show the CRLB for three scenarios. The results show that in the most realistic scenario, when the shadowing is spatially correlated and distance dependent and the standard deviation of noise is 7 dB, the maximum square root of CRLB is 3.8 mm. Moreover, the square root of CRLB experiences its minimum value of 2 mm, when the capsule is away from its first location about half of the capsule length. Overall, the result of this paper suggests that it is possible to use received signal strength such as measured by a radar system for location estimation of a WCE.