text: The ability of robots to estimate their location is crucial for a wide variety of autonomous operations. In settings where GPS is unavailable, measurements of transmissions from fixed beacons provide an effective means of estimating a robot's location as it navigates. The accuracy of such a beacon-based localization system depends both on how beacons are distributed in the environment, and how the robot's location is inferred based on noisy and potentially ambiguous measurements. We propose an approach for making these design decisions automatically and without expert supervision, by explicitly searching for the placement and inference strategies that, together, are optimal for a given environment. Since this search is computationally expensive, our approach encodes beacon placement as a differential neural layer that interfaces with a neural network for inference. This formulation allows us to employ standard techniques for training neural networks to carry out the joint optimization. We evaluate this approach on a variety of environments and settings, and find that it is able to discover designs that enable high localization accuracy.
  @cite_0: By "intelligently" locating a sensor with respect to its envi ronment, it is possible to minimize the number of sensing operations required to perform many tasks. This is particu larly important for sensing media, such as tactile sensors and sonar, that provide only "sparse" data. In this paper, a sys tem is described that uses the principles of statistical decision theory to determine the optimal sensing locations for per forming recognition and localization operations. The system uses a Bayesian approach to utilize any prior object informa tion (including object models or previously acquired sensory data) in choosing the sensing locations.
  @cite_25: We address the problem of selecting sensors so as to minimize the error in estimating the position of a target. We consider a generic sensor model where the measurements can be interpreted as polygonal, convex subsets of the plane. This model applies to a large class of sensors including cameras. We present an approximation algorithm which guarantees that the resulting error in estimation is within a factor 2 of the least possible error. In establishing this result, we formally prove that a constant number of sensors suffice for a good estimate - an observation made by many researchers. In the second part of the paper, we study the scenario where the target's position is given by an uncertainty region and present algorithms for both probabilistic and online versions of this problem.
  @cite_12: We consider the problem of choosing a set of k sensor measurements, from a set of m possible or potential sensor measurements, that minimizes the error in estimating some parameters. Solving this problem by evaluating the performance for each of the (m k) possible choices of sensor measurements is not practical unless m and k are small. In this paper, we describe a heuristic, based on convex optimization, for approximately solving this problem. Our heuristic gives a subset selection as well as a bound on the best performance that can be achieved by any selection of k sensor measurements. There is no guarantee that the gap between the performance of the chosen subset and the performance bound is always small; but numerical experiments suggest that the gap is small in many cases. Our heuristic method requires on the order of m 3 operations; for m= 1000 possible sensors, we can carry out sensor selection in a few seconds on a 2-GHz personal computer.
summary: Our approach provides a way to trade-off localization accuracy with the number of beacons, similar to the performance-cost trade-offs considered by the more general problem of sensor selection @cite_0 @cite_25 @cite_12 . Some selection strategies are designed with specific inference strategies in mind. and use a greedy entropy-based approach to place sensors, tied to a Gaussian process (GP) model that is used for inference. However, this approach does not model the accuracy of the predictions at the selected locations. choose locations for a fixed sensor network that maximize mutual information using a GP model for phenomena over which inference is performed ( temperature). However, these formulations require that the phenomena be modeled as a GP, and are thus not suitable for the task of beacon-based localization.