Source localization based on signal strength measurements has become very popular due to its practical simplicity. However, the severe nonlinearity and non-convexity make the related optimization problem mathematically difficult to solve, especially when the transmit power or the path-loss exponent (PLE) is unknown. Moreover, even if the PLE is known but not perfectly estimated or the anchor location information is not accurate, the constructed data model will become uncertain, making the problem again hard to solve. This paper particularly focuses on differential received signal strength (DRSS)-based localization with model uncertainties in case of unknown transmit power and PLE. A new whitened model for DRSS-based localization with unknown transmit powers is first presented and investigated. When assuming the PLE is known, we introduce two estimators based on an exact data model, an advanced best linear unbiased estimator (A-BLUE) and a Lagrangian estimator (LE), and then we present a robust semidefinite programming (SDP)-based estimator (RSDPE), which can cope with model uncertainties (imperfect PLE and inaccurate anchor location information). The three proposed estimators have their own advantages from different perspectives: the A-BLUE has the lowest complexity; the LE holds the best accuracy for a small measurement noise; and the RSDPE yields the best performance under a large measurement noise and possesses a very good robustness against model uncertainties. Finally, we propose a robust SDP-based block coordinate descent estimator (RSDP-BCDE) to deal with a completely unknown PLE and its performance converges to that of the RSDPE using a perfectly known PLE.Index Terms-Source localization, differential received signal strength (DRSS), path-loss exponent (PLE), least squares, Lagrangian multiplier, semidefinite programming (SDP), convex optimization, block coordinate descent. 1053-587X
Since the global positioning system (GPS) is not applicable underwater, source localization using wireless sensor networks (WSNs) is gaining popularity in oceanographic applications. Unlike terrestrial WSNs (TWSNs) which uses electromagnetic signaling, underwater WSNs (UWSNs) require underwater acoustic (UWA) signaling. Received signal strength (RSS)-based source localization is considered in this paper due to its practical simplicity and the constraint of low-cost sensor devices, but this area received little attention so far because of the complicated UWA transmission loss (TL) phenomena. In this paper, we address this issue and propose two novel semidefinite programming (SDP) approaches which can be solved more efficiently. The numerical results validate our proposed SDP solvers in underwater environments, and indicate that the placement of the anchor nodes influences the RSS-based localization accuracy similarly as in the terrestrial counterpart. We also highlight that adopting traditional terrestrial RSS-based localization methods will fail in underwater scenarios.
The migration rates of both medium and very large dunes in a part of the North Sea are determined from high resolution multi-beam echo soundings. From the bathymetric maps, crest positions are determined and compared. From changes in the position of these crests relative to fixed markers, the migration rates within a tidal cycle and on a seasonal time scale are calculated. The sediment transport rates derived from the migration of the bedforms compare well with theoretical estimates of the residual transport in the area.
The path-loss exponent (PLE) is one of the most crucial parameters in wireless communications to characterize the propagation of fading channels. It is currently adopted for many different kinds of wireless network problems such as power consumption issues, modeling the communication environment, and received signal strength (RSS)-based localization. PLE estimation is thus of great use to assist in wireless networking. However, a majority of methods to estimate the PLE require either some particular information of the wireless network, which might be unknown, or some external auxiliary devices, such as anchor nodes or the Global Positioning System. Moreover, this external information might sometimes be unreliable, spoofed, or difficult to obtain. Therefore, a self-estimator for the PLE, which is able to work independently, becomes an urgent demand to robustly and securely get a grip on the PLE for various wireless network applications. This paper is the first to introduce two methods that can solely and locally estimate the PLE. To start, a new linear regression model for the PLE is presented. Based on this model, a closed-form total least squares (TLS) method to estimate the PLE is first proposed, in which, with no other assistance or external information, each node can estimate the PLE merely by collecting RSSs. Second, to suppress the estimation errors, a closed-form weighted TLS method is further developed, having a better performance. Due to their simplicity and independence of any auxiliary system, our two proposed methods can be easily incorporated into any kind of wireless communication stack. Simulation results show that our estimators are reliable, even in harsh environments, where the PLE is high. Many potential applications are also explicitly illustrated in this paper, such as secure RSS-based localization, kth nearest neighbor routing, etc. Those applications detail the significance of self-estimation of the PLE.Index Terms-Lognormal shadowing, path-loss exponent (PLE), radio propagation channel, security, total least squares (TLS).
Underwater source localization problems are complicated and challenging: 1) the sound propagation speed is often unknown and the unpredictable ocean current might lead to the uncertainties of sensor parameters (i.e., position and velocity); 2) the underwater acoustic signal travels much slower than the radio one in terrestrial environments, thus resulting into a significantly severe Doppler effect; and 3) energy-efficient techniques are urgently required and hence in favor of the design with a low computational complexity. Considering these issues, we propose a simple and efficient underwater source localization approach based on the time difference of arrival and frequency difference of arrival measurements, which copes with unknown propagation speed and sensor parameter errors. The proposed method mitigates the impact of the Doppler effect for accurately inferring the source parameters (i.e., position and velocity). The Cramér-Rao lower bounds (CRLBs) for this kind of localization are derived and, moreover, the analytical study shows that our method can yield the performance that is very close to the CRLB, particularly under small noise. The numerical results not only confirm the above conclusions but also show that our method outperforms other competing approaches.INDEX TERMS Underwater localization, algebraic solution, sound propagation speed uncertainty, sensor node uncertainty, time difference of arrival (TDOA), frequency difference of arrival (FDOA).
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