Array shape calibration using sources in unknown locations--Part I: Far-field sources

Abstract

This paper deals with source localization using a two-dimensional array of sensors whose locations are not known precisely. If only a single source is observed, uncertainties in sensor location increase errors in source bearing and range by an amount which is independent of signal-to-noise ratio and which can easily dominate overall localization accuracy. Major performance gains could therefore result from successful calibration of array geometry. The paper derives Cramer-Rao bounds on calibration and source location accuracies achievable with far-field sources whose bearings are not initially known. The sources are assumed to radiate Gaussian noise and to be spectrally disjoint of each other. When the location of one sensor and Manuscript

On the Hybrid Cramér Rao Bound and Its Application to Dynamical Phase Estimation

“…We consider as an estimator of , where is the observation vector. The HCRB satisfies the following inequality on the MSE: (1) where is the so-called Hybrid Information Matrix (HIM) defined as [2] (2) where . When the deterministic and the random parts of the parameter vector are assumed to be independent, and after some algebraic manipulations, the HIM can be rewritten as (see [3, eq.…”

“…In other words, is now assumed to be a random vector with an a priori pdf . Based on the HIM definition given by (2) and expending the log-likelihood as , we obtain the following HIM:…”

“…At the end of the 1980s, an extension combining both the standard and the Bayesian CRBs was proposed [2]. Indeed, in some practical scenarios, it is natural to represent the parameter vector by a deterministic part and by a random part.…”

A constrained hybrid Cramér-Rao bound for parameter estimation

“…One can cite, for example, the Gaussian generalized linear model [9], array shape calibration [1], time-delay estimation in radar signal [4], phase estimation in binary phase-shift keying transmission in a nondata-aided context [10], phase estimation of QAM modulated signals [11], cisoid frequency estimation [12], joint estimation of the pair dynamic carrier phase/Doppler shift and the time-delay in a digital receiver [13], parameters estimation in long-code DS/CDMA systems [14], bearing estimation for deformed towed arrays in the fluid mechanics context [15]. It is therefore the aim of this paper to provide an extension of the deterministic CCRB [16] to the hybrid parameter context yielding the Constrained HCRB (CHCRB).…”

Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

“…Finally, when the parameter vector is made from both deterministic and random parameters, the so-called hybrid bounds have been developed [17] [18] [19] [20].…”