On Achievable Accuracy in Edge Localization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detection of abrupt changes: theory and application
Detection of abrupt changes: theory and application
An introduction to signal detection and estimation (2nd ed.)
An introduction to signal detection and estimation (2nd ed.)
Cramer-Rao bounds for deterministic signals in additive and multiplicative noise
Signal Processing - Special issue on higher order statistics
Cramer-Rao lower bound on locations of sudden changes in a steplikesignal
IEEE Transactions on Signal Processing
On the accuracy of estimating the parameters of a regular stationary process
IEEE Transactions on Information Theory
Analysis of multiscale products for step detection and estimation
IEEE Transactions on Information Theory
Parametric modeling of photometric signals
Signal Processing
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The paper addresses the problem of determining the Cramer-Rao lower bounds (CRLBs) for noise and change-point parameters, for steplike signals corrupted by multiplicative and/or additive white noise. Closed-form expressions for the signal and noise CRLBs are first derived for an ideal step with a known change point. For an unknown change-point, the noise-free signal is modeled by a sigmoidal function parametrized by location and step rise parameters. The noise and step change CRLBs corresponding to this model are shown to be well approximated by the more tractable expressions derived for a known change-point. The paper also shows that the step location parameter is asymptotically decoupled from the other parameters, which allows us to derive simple CRLBs for the step location. These bounds are then compared with the corresponding mean square errors of the maximum likelihood estimators in the pure multiplicative case. The comparison illustrates convergence and efficiency of the ML estimator. An extension to colored multiplicative noise is also discussed.