Understanding the method of interval errors from the information theory perspective

Nonlinear parameter estimation often displays a threshold phenomenon, that is, below certain signal-to-noise ratio (SNR) the estimation mean-square error (MSE) increases dramatically. The method of interval errors (MIE) has been shown to provide accurate MSE prediction of related nonlinear techniques well into the estimation threshold region, yet relatively simple and robust in evaluation compared to a global performance bound. However those features have not been understood on a strict theoretical basis. This paper investigates numerical sensitivity of the MIE to parameter sampling resolution, aiming to understanding, from information theory perspective, the underlying mechanism leading to robust MSE approximation. A recently-developed information theory resolution bound is reinterpreted and applied to specify the parameter sampling resolution. Numerical evaluation of the relevant results for array-based bearing estimation supports the proposed connection between the resolution bound and the MIE.