Unified performance measures in network localization

Abstract

With the evolving Internet of Things, location-based services have recently become very popular. For modern wireless sensor networks (WSNs), ubiquitous positioning is elementary. Hence, the demand of everlasting and low-cost sensor nodes is rapidly increasing. In terms of energy-efficiency, received signal strength (RSS)-based direction finding is a prospective approach providing location information in low-power sensor networks. Unfortunately, RSS-based direction finding is, as radio-based localization is in general, prone to multipath propagation of the wireless channel. Therefore, the impact of multipath fading as well as all other error source have to be modeled correctly and have to be considered in the design of a locating WSN.In this paper, we derive the classical Cramér-Rao Lower Bound (CRLB) for RSS-based direction-of-arrival (DOA). The drawbacks of the classical CRLB and its influence on the optimal network topology are discussed. The CRLB indicates that the minimum variance unbiased estimator (MVUE) does not exist for the problem of RSS-based DOA due to the nature of its measurement function. Hence, beyond the CRLB, we derive performance metrics for the maximum likelihood estimator (MLE) and compare position estimation errors for the MVUE and the MLE for different network topologies. Since both approaches, the CRLB and the maximum likelihood (ML) limits, are not capable of handling ambiguities, we introduce another measure for the variance of a measurement and its corresponding position estimate based on information theory. This way, the amount of information for a set of RSS measurements can be quantified exactly, even in the case of ambiguous probability densities. Thus, the proposed technique gives a holistic view on the information obtained from sensor measurements which can be utilized for network topology optimization.