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

On the structural nature of cooperation in distributed network localization

We demonstrate analytically that the contribution of cooperation in improving the accuracy of distributed network localization has a fundamentally structural nature, rather then statistical as widely believed. To this end we first introduce a new approach to build Fisher Information Matrices (FIMs), in which the individual contribution of each cooperative pair of nodes is captured explicitly by a corresponding information vector. The approach offers new insight onto the structure of FIMs, enabling us to easily account for both anchor and node location uncertainties in assessing lower bounds on localization errors. Using this construction it is surprisingly found that in the presence of node location uncertainty and regardless of ranging error variances or network size, the Fisher information matrix (FIM) terms corresponding to the information added by node-to-node cooperation nearly vanish. In other words, the analysis reveals that the key contribution of cooperation in network localization is not to add statistical node-to-node information (in the Fisher sense), but rather to provide a structure over which information is better exploited

Low cost underwater acoustic localization

Over the course of the last decade, the cost of marine robotic platforms has significantly decreased. In part this has lowered the barriers to entry of exploring and monitoring larger areas of the earth's oceans. However, these advances have been mostly focused on autonomous surface vehicles (ASVs) or shallow water autonomous underwater vehicles (AUVs). One of the main drivers for high cost in the deep water domain is the challenge of localizing such vehicles using acoustics. A low cost one-way travel time underwater ranging system is proposed to assist in localizing deep water submersibles. The system consists of location aware anchor buoys at the surface and underwater nodes. This paper presents a comparison of methods together with details on the physical implementation to allow its integration into a deep sea micro AUV currently in development. Additional simulation results show error reductions by a factor of three.Comment: 73rd Meeting of the Acoustical Society of Americ

Performance Limits and Geometric Properties of Array Localization

Location-aware networks are of great importance and interest in both civil and military applications. This paper determines the localization accuracy of an agent, which is equipped with an antenna array and localizes itself using wireless measurements with anchor nodes, in a far-field environment. In view of the Cram\'er-Rao bound, we first derive the localization information for static scenarios and demonstrate that such information is a weighed sum of Fisher information matrices from each anchor-antenna measurement pair. Each matrix can be further decomposed into two parts: a distance part with intensity proportional to the squared baseband effective bandwidth of the transmitted signal and a direction part with intensity associated with the normalized anchor-antenna visual angle. Moreover, in dynamic scenarios, we show that the Doppler shift contributes additional direction information, with intensity determined by the agent velocity and the root mean squared time duration of the transmitted signal. In addition, two measures are proposed to evaluate the localization performance of wireless networks with different anchor-agent and array-antenna geometries, and both formulae and simulations are provided for typical anchor deployments and antenna arrays.Comment: to appear in IEEE Transactions on Information Theor

Cloud base height estimates from sky imagery and a network of pyranometers

Cloud base height (CBH) is an important parameter for physics-based high resolution solar radiation modeling. In sky imager-based forecasts, a ceilometer or stereographic setup is needed to derive the CBH; otherwise erroneous CBHs lead to incorrect physical cloud velocity and incorrect projection of cloud shadows, causing solar power forecast errors due to incorrect shadow positions and timing of shadowing events. In this paper, two methods to estimate cloud base height from a single sky imager and distributed ground solar irradiance measurements are proposed. The first method (Time Series Correlation, denoted as “TSC”) is based upon the correlation between ground-observed global horizontal irradiance (GHI) time series and a modeled GHI time series generated from a sequence of sky images geo-rectified to a candidate set of CBH. The estimated CBH is taken as the candidate that produces the highest correlation coefficient. The second method (Geometric Cloud Shadow Edge, denoted as “GCSE”) integrates a numerical ramp detection method for ground-observed GHI time series with solar and cloud geometry applied to cloud edges in a sky image. CBH are benchmarked against a collocated ceilometer and stereographically estimated CBH from two sky imagers for 15 min median-filtered CBHs. Over 30 days covering all seasons, the TSC method performs similarly to the GCSE method with nRMSD of 18.9% versus 20.8%. A key limitation of both proposed methods is the requirement of sufficient variation in GHI to enable reliable correlation and ramp detection. The advantage of the two proposed methods is that they can be applied when measurements from only a single sky imager and pyranometers are available