Performance limitations and error calculations for parameter estimation
- 1 May 1970
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE
- Vol. 58 (5), 644-652
- https://doi.org/10.1109/proc.1970.7720
Abstract
Error calculations cannot be carried out precisely when parameters are estimated which affect the observation nonlinearly. This paper summarizes the available approaches to studying performance and compares the resulting answers for a specific case. It is shown that the familiar Cramér-Rao lower bound on rms error yields an accurate answer only for large signal-to-noise ratios (SNR). For low SNR, lower bounds on rms error obtained by Ziv and Zakai give easily calculated and fairly tight answers. Rate distortion theory gives a lower bound on the error achievable with any system. The Barankin lower bound does not appear to give useful information as a computational tool. A technique for approximating the error can be used effectively for a large class of systems. With numerical integration, an upper bound obtained by Seidman gives a fairly tight answer. Recent work by Ziv gives bounds on the bias of estimators but, in general, these appear to be rather weak. Tighter results are obtained for maximum-likelihood estimators with certain symmetry conditions. Applying these techniques makes it possible to locate the threshold level to within a few decibels of channel signal-to-noise ratio. Further, these calculations can be easily carried out for any system.Keywords
This publication has 14 references indexed in Scilit:
- A PPM/PM Hybrid Modulation SystemIEEE Transactions on Communications, 1969
- Bounds on the Bias of Signal Parameter EstimatorsBell System Technical Journal, 1969
- A Class of Signals for Analog Telemetry over a Coherent ChannelIEEE Transactions on Aerospace and Electronic Systems, 1969
- Some lower bounds on signal parameter estimationIEEE Transactions on Information Theory, 1969
- A useful form of the Barankin lower bound and its application to PPM threshold analysisIEEE Transactions on Information Theory, 1969
- An upper bound on average estimation error in nonlinear systemsIEEE Transactions on Information Theory, 1968
- An Extension of the Cramer-Rao InequalityThe Annals of Mathematical Statistics, 1959
- Telemetering and information theoryTransactions of the IRE Professional Group on Radio Telemetry and Remote Control, 1954
- On Minimum Variance EstimatorsThe Annals of Mathematical Statistics, 1952
- Locally Best Unbiased EstimatesThe Annals of Mathematical Statistics, 1949