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This work seeks to design a pilot signal, under a power constraint, such that the channel can be estimated with minimum mean square error. The procedure we derive does not assume Kronecker structure on the underlying covariance matrices, and the pilot signal is obtained in three main steps. Firstly, we solve a relaxed convex version of the original minimization problem. Secondly, its solution is projected onto the feasible set. Thirdly we use the projected solution as starting point for an augmented Lagrangian method. Numerical experiments indicate that this procedure may produce pilot signals that are far better than those obtained under the Kronecker structure assumption. QC 20140120

In this work, localization of a source within a lossy medium is considered. By a lossy medium we mean an environment where the signal power decays exponentially with distance. We assume no prior knowledge on the source location, but that the source is heard by nearby sensors when transmitting. The source position shall be estimated based on the power received by these sensors. Under these assumptions, our focus is to determine the Cramer-Rao Lower Bound (CRLB). Thus, we are not studying specific estimators, but rather the (theoretical) performance of an optimal one. We demonstrate that the CRLB greatly depends on the shadowing conditions, and also on the relative positions of the sensors and the source. This spatial variability of the CRLB is used to discuss favorable positioning of the sensors.

Exploiting prior knowledge, we use Bayesian estimation to localize a source heard by a fixed sensor network. The method has two main aspects: Firstly, the probability density function (PDF) of a function of the source location is approximated by a Gaussian mixture model (GMM). This approximation can theoretically be made arbitrarily accurate, and allows a closed form minimum mean square error (MMSE) estimator for that function. Secondly, the source location is retrieved by minimizing the Euclidean distance between the function and its MMSE estimate using a gradient method. Our method avoids the issues of a numerical MMSE estimator but shows comparable accuracy.

This paper considers the use of a sensor network to estimate the position of a transmitting radio based on the received signal strength at the sensors. A generic path loss model which includes the effects of spatially correlated shadowing is assumed. A weighted likelihood (WL) estimator is proposed, which can be seen as a simplified minimum mean square error (MMSE) estimator. This estimator can be used for localizing a source in a static scenario or it can provide the initial position estimate of a tracking algorithm. The performance of the WL estimator is simulated, and robustness to erroneous assumptions about path loss exponent, shadowing variance and correlation distance is demonstrated.