Underwater source localization problems are complicated and challenging: a) 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); b) the underwater acoustic signal travels much slower than the radio one in terrestrial environments, thus resulting into a significantly severe Doppler effect; c) energy-efficient techniques are urgently required and hence in favour of the design with a low computational complexity. Considering these issues, we propose a simple and efficient underwater source localization approach based on time difference of arrival (TDOA) and frequency difference of arrival (FDOA) 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.

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.

In Onur et al. ["Cooperative density estimation in random wireless ad hoc networks," IEEE Commun. Lett., vol. 16, no. 3, 269 pp. 331-333, Mar. 2012], two novel density estimation (DE) approaches in wireless random networks were introduced by Onur et al., which are carried out respectively in cooperative and individual fashions. Both of them were derived via the maximum likelihood (ML) method. However, an implicit but fatal error was made obtaining the individual DE (I-DE) approach. This letter comments on Onur et al. and points out the aforementioned error. By investigating the distance order statistics (DOS) distributions in the random networks, the correct I-DE approach is presented and discussed. Simulation results also show that the correct I-DE outperforms the wrong one. More importantly, a new method that can obtain any univariate or multivariate DOS distribution is demonstrated, which is expected to be helpful for the study of the wireless communications and networking.