Cramer-Rao bounds in the estimation of time of arrival in fading channels

This paper computes the Cramer-Rao bounds for the time of arrival estimation in a multipath Rice and Rayleigh fading scenario, conditioned to the previous estimation of a set of propagation channels, since these channel estimates (correlation between received signal and the pilot sequence) are sufficient statistics in the estimation of delays. Furthermore, channel estimation is a constitutive block in receivers, so we can take advantage of this information to improve timing estimation by using time and space diversity. The received signal is modeled as coming from a scattering environment that disperses the signal both in space and time. Spatial scattering is modeled with a Gaussian distribution and temporal dispersion as an exponential random variable. The impact of the sampling rate, the roll-off factor, the spatial and temporal correlation among channel estimates, the number of channel estimates, and the use of multiple sensors in the antenna at the receiver is studied and related to the mobile subscriber positioning issue. To our knowledge, this model is the only one of its kind as a result of the relationship between the space-time diversity and the accuracy of the timing estimation.Peer ReviewedPostprint (published version

Error bounds for wireless localization in NLOS environments

An efficient and accurate method to evaluate the fundamental error bounds for wireless sen-sor localization is proposed. While there already exist efficient tools like Cram`er-Rao lower bound (CRLB) and position error bound (PEB) to estimate error limits, in their standard formulation they all need an accurate knowledge of the statistic of the ranging error. This requirement, under Non-Line-of-Sight (NLOS) environments, is impossible to be met a priori. Therefore, it is shown that collecting a small number of samples from each link and applying them to a non-parametric estimator, like the Gaussian kernel (GK), could lead to a quite accurate reconstruction of the error distribution. A proposed Edgeworth Expansion method is employed to reconstruct the error statistic in a much more efficient way with respect to the GK. It is shown that with this method, it is possible to get fundamental error bounds almost as accurate as the theoretical case, i.e. when a priori knowledge of the error distribution is available. Therein, a technique to determine fundamental error limits – CRLB and PEB – onsite without knowledge of the statistics of the ranging errors is proposed

Target Tracking in Confined Environments with Uncertain Sensor Positions

To ensure safety in confined environments such as mines or subway tunnels, a (wireless) sensor network can be deployed to monitor various environmental conditions. One of its most important applications is to track personnel, mobile equipment and vehicles. However, the state-of-the-art algorithms assume that the positions of the sensors are perfectly known, which is not necessarily true due to imprecise placement and/or dropping of sensors. Therefore, we propose an automatic approach for simultaneous refinement of sensors' positions and target tracking. We divide the considered area in a finite number of cells, define dynamic and measurement models, and apply a discrete variant of belief propagation which can efficiently solve this high-dimensional problem, and handle all non-Gaussian uncertainties expected in this kind of environments. Finally, we use ray-tracing simulation to generate an artificial mine-like environment and generate synthetic measurement data. According to our extensive simulation study, the proposed approach performs significantly better than standard Bayesian target tracking and localization algorithms, and provides robustness against outliers.Comment: IEEE Transactions on Vehicular Technology, 201

Localization in GPS denied environment

No abstract available