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_3: We address the problem of placing a sensor network so as to minimize the uncertainty in estimating the position of targets. The novelty of our formulation is in the sensing model: we focus on stereo sensors where the measurements from two sensors must be combined for an estimation. We study two versions of this problem. In the first version, which we call the placement problem, we are given a workspace and an error threshold. The objective is to place a minimum number of cameras so that no matter where the target is located in the workspace, the uncertainty in localizing it is less than the threshold. For this problem, we present an approximation algorithm and prove that the deviation of its performance from the optimal value is bounded by a constant. In the second version, called the deployment problem, we study the problem of relocating a mobile sensor team to minimize the uncertainty in localizing possibly moving targets. We present a distributed, discrete-time algorithm which explicit addresses communication and motion constraints and show how to compute the optimal move within the time-step for a given target sensor-pair assignment. The utility of the algorithm is demonstrated with simulations
summary: Meanwhile, beacon allocation traditionally relies on coverage as a heuristic to guide placement in a specific environment. When the environment is polygonal and beacons have an unlimited field-of-view subject to occlusions by walls (e.g., cameras), coverage corresponds to the standard art-gallery visibility problem @cite_3 . Related, propose a greedy landmark-based method that solves for the placement of the minimum number of beacons (within a @math factor) necessary to cover all but a fraction of a given polygonal environment. However, a beacon's sensing geometry is often complex as a result of partial attenuation due to the environment, beacon noise, and signal interference. Interference varies according to the placement of other beacons and channel allocation, which most coverage algorithms do not reason over. These factors are particularly important for RF-based localization, which is sensitive to the effects of aliasing, further complicating the relationship between allocation and inference.