On the Existence of an MVU Estimator for Target Localization with Censored, Noise Free Binary Detectors

The problem of target localization with censored noise free binary detectors is considered. In this setting only the detecting sensors report their locations to the fusion center. It is proven that if the radius of detection is not known to the fusion center, a minimum variance unbiased (MVU) estimator does not exist. Also it is shown that when the radius is known the center of mass of the possible target region is the MVU estimator. In addition, a sub-optimum estimator is introduced whose performance is close to the MVU estimator but is preferred computationally. Furthermore, minimal sufficient statistics have been provided, both when the detection radius is known and when it is not. Simulations confirmed that the derived MVU estimator outperforms several heuristic location estimators.Comment: 25 pages, 9 figure

Detection Of A Non-Cooperative Transmitter In Rayleigh Fading With Binary Observations

The problem of distributed detection of a noncooperative target with non-coherent binary observations is considered. The propagation is assumed to be inversely proportional to a power of the distance from the target and the signal is assumed to be subject to Rayleigh fading and additive white Gaussian noise (AWGN). As the location and power of the target are unknown, the probability of detection and probability of false alarm are also not known for each individual detectors. Thus, the optimum Chair-Varshney fusion rule does not apply. Instead, a two stage method based on a generalized likelihood ratio test (GLRT) is derived and proposed. Monte Carlo simulations have been performed to evaluate the performance of the global fusion rule. The results show that the performance of this fusion scheme is significantly better than the intuitive counting rule. © 2012 IEEE

Detection of a non-cooperative transmitter in Rayleigh fading with binary observations

The problem of distributed detection of a noncooperative target with non-coherent binary observations is considered. The propagation is assumed to be inversely proportional to a power of the distance from the target and the signal is assumed to be subject to Rayleigh fading and additive white Gaussian noise (AWGN). As the location and power of the target are unknown, the probability of detection and probability of false alarm are also not known for each individual detectors. Thus, the optimum Chair-Varshney fusion rule does not apply. Instead, a two stage method based on a generalized likelihood ratio test (GLRT) is derived and proposed. Monte Carlo simulations have been performed to evaluate the performance of the global fusion rule. The results show that the performance of this fusion scheme is significantly better than the intuitive counting rule. © 2012 IEEE

On The Existence Of An Mvu Estimator For Target Localization With Censored, Noise-Free Binary Detectors

The problem of target localization with censored, noise-free binary detectors is considered. In this setting only the detecting sensors report their locations to the fusion center. It is proven that if the radius of detection is unknown to the fusion center, a minimum variance unbiased (MVU) estimator does not exist. Also it is shown that when the radius is known the center of mass of the possible target region is the MVU estimator among estimators that are invariant under Euclidean motion. In addition, a sub-optimum estimator is introduced whose performance is close to the MVU estimator but is preferred computationally. Moreover, for the case when the radius of detection is unknown a sub-optimum estimator is proposed that performs close to the Clairvoyant estimator. Furthermore, minimal sufficient statistics have been provided, both when the detection radius is known and when it is not. Simulations confirmed that the derived MVU estimator outperforms several heuristic location estimators

On Localization Of A Non-Cooperative Target With Non-Coherent Binary Detectors

Localization of a non-cooperative target with binary detectors is considered. A general expression for the Fisher information for estimation of target location and power is developed. This general expression is then used to derive closed-form approximations for the Cramér-Rao bound for the case of non-coherent detectors. Simulations show that the approximations are quite consistent with the exact bounds. © 2014 IEEE

Analysis Of Target Localization With Ideal Binary Detectors Via Likelihood Function Smoothing

This letter deals with noncooperative localization of a single target using censored binary observations acquired by spatially distributed sensors. An ideal, noise-free setting is considered whereby each sensor can perfectly detect if the target is in its close proximity or not. Only those detecting sensors communicate their decisions and locations to a fusion center (FC), which subsequently forms the desired location estimator based on censored observations. Because a maximum-likelihood estimator (MLE) does not exist in this setting, current approaches have relied on heuristic, centrality-based geometric estimators such as the center of a minimum enclosing circle (CMEC). A smooth surrogate to the likelihood function is proposed here, whose maximizer is shown to approach the CMEC asymptotically as the likelihood approximation error vanishes. This provides rigorous analytical justification as to why the CMEC estimator outperforms other heuristics for this problem, as empirically observed in prior studies. Since the Cramér-Rao Bound does not exist either, an upshot of the results in this letter is that the CMEC performance can be adopted as a benchmark in this ideal setting and also for comparison with other more pragmatic binary localization methods in the presence of uncertainty

Localization of a non-cooperative target with distributed binary observations

Thesis (Ph. D.)--University of Rochester. Department of Electrical and Computer Engineering, 2017This dissertation focus is on localization of a non-cooperative target with distrusted binary measurements. In a non-cooperative target localization unlike the cooperative one, we do not receive any assistance from the target on revealing its position. This type of localization has a lot of applications, for example, to identify the primary user in cognitive radio, spectrum cartography, identifying the location of an unauthorized user in a mobile network and identifying the location jammer in the battle field. However, the non-cooperative assumptions make many localization techniques including the ones requiring time reference synchronization impractical. Therefore, instead we rely on binary measurements of signal power from a large number of sensors scattered in the field which better lends itself to energy and complexity requirement of a Wireless Sensor Network realization. In other words, the location of the non-cooperative target would be carried out through processing of the data and locations of all sensors. In this setting, the estimate of the target location is being affected by two different sources of uncertainty. One is the uncertainty involved in each sensor decision which can be the result of noise, fading or other random process effects on the received signal and shows itself in terms of false alarm or missed detection. The other one is the intrinsic error resulting from estimating a source transmitter location through scattered binary measurements which involves the density of sensor deployment, actual power of transmitter and threshold selection to convert the received signal power value to binary decisions. The main contribution of this thesis is to provide a systematic approach to separately investigate the effects of these sources of error on the target location estimate. With that approach, it was possible to establish fundamental limits on performance and accuracy of a non-cooperative target localization through distributed binary measurements. A minimum variance unbiased (MVU) estimator for target estimation is also developed in noiseless regime which helped to establish a lower bound on the performance of all location estimators in the presence of noise and fading. The importance of such a development is that the usual Cram´er Rao Bounds derivation fails in this case due to the fact that the likelihood function becomes discontinuous. Furthermore, novel sub-optimal estimators have been developed based on the MVU estimator which performs close to optimal while requires much less resources to implement. Besides, the effects of density, power of transmission and threshold selection on the accuracy of location estimation have been investigated. In addition, the problem in the presence of noise and fading is investigated and it is shown that for any isotropic propagation the minimum mean square location error achievable by an efficient estimator would become independent from its performance for estimation of the source power. Moreover, formulas are derived to calculate the optimum threshold to be selected by the scattered binary sensors based on propagation characteristic to achieve the best performance for location estimation. Finally, methods are developed to quantify and compare how much location accuracy will be lost if the non-detecting sensors’ data are censored before the estimation process