A Ziv-Zakaï type bound for hybrid parameter estimation

Abstract

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. In this communication, we propose a new hybrid lower bound which, for the first time, includes the Ziv-Zakaï bound well known for its tightness in the Bayesian context (random parameters only). For the general case of parameterized mean model with Gaussian noise, closed-form expressions of the proposed bound are provided.

Fundamental Limitations and State-of-the-art Solutions for Target Node Localization in WSNs

“…Here as well, the main drawback of the HZZLB and HWWLB is the lack of tractability. It is noted that approximation of the HZZLB and HWWLB in a closed-form may exist under some specific assumptions [79].…”

A Hybrid Approach to Joint Estimation of Channel and Antenna impedance

“…329], because θ contains both random and deterministic parameters. Several authors have investigated hybrid estimation problems [14]- [18]. Estimators and Cramér-Rao-type bounds for hybrid estimation were formulated in [14] in the context of passive source localization.…”

“…ML estimator in (29) in the low-noise or high SNR limit. Finally, the last extreme case we consider is the singlepacket case, i.e., L = 1, where H = H ∼ CN (0, σ 2 H ) is a special case of (18). Under these assumptions, the sufficient statistic in (14) becomes V = [V 1 , V 2 ] T , and Theorem 1 leads to the single-packet joint MAP/ML solution,…”

Recursive Hybrid Cramér–Rao Bound for Discrete-Time Markovian Dynamic Systems

“…This initial characterization of hybrid estimation has been generalized by Reuven and Messer [2] who introduced the first "largeerror" hybrid bound, the so-called hybrid Barankin Bound (HBB), in order to handle the threshold phenomena and of which one limiting form yields the HCRB. This seminal work [2] has been lately extended to new "large-error" hybrid bounds [7] [11] [12] in order to improve the estimation of the transition region where the threshold phenomena occurs. Unfortunately, the computational cost of hybrid "large-error" bounds is prohibitive in most applications when the number of unknown parameters increases.…”