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.
One common instance of optimizing placement for coverage is the standard art-gallery visibility problem @cite_3 that seeks placements that ensure that all locations have line-of-sight to at least one beacon. This problem assumes a polygonal environment and that the beacons have an unlimited field-of-view, subject to occlusions by walls ( cameras). 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. Note that these methods treat occlusions as absolute, while in practice, obstructions often only cause partial attenuation---with points that are close but obstructed observing similar signal strengths as those that are farther away. provide an interesting alternative, and like us, use backpropagation to place WiFi access points---but again, only for the objective of maximizing coverage. consider localization accuracy for placing wireless access points to maximize receiver signal-to-noise ratios.
@cite_3
2099719044
This paper presents a novel approach to placing access points (APs) in wireless local area networks (WLAN). Unlike the traditional methods focusing on coverage maximization, we investigate how to place APs from the perspective of an indoor location system. We present a framework for linking the placement of APs and the positioning performance. Our algorithm, namely maximizing SNR (signal-to-noise ratio), aims at choosing a proper set of APs' locations so that the signal is maximized and the noise is minimized simultaneously. The proposed algorithm regards the location discriminant information as the signal and the degree of unstable measurements as the noise. Such numerical values provide a good theoretical formulation to measure the influence of the AP deployment. In our location system, we utilize such SNR ratio to deploy APs so as to reduce the positioning errors. Our location system is developed in a real-world WLAN environment, where the realistic measurements were collected. The experimental results show that the positioning accuracy is improved based on our deployment approach in different scenarios. Beacon placement strongly affects the quality of spatial localization, a critical service for context-aware applications in wireless sensor networks; yet this aspect of localization has received little attention. Fixed beacon placement approaches such as uniform and very dense placement are not always viable and will be inadequate in very noisy environments in which sensor networks may be expected to operate (with high terrain and propagation uncertainties). We motivate the need for empirically adaptive beacon placement and outline a general approach based on exploration and instrumentation of the terrain conditions by a mobile human or robot agent. We design, evaluate and analyze three novel adaptive beacon placement algorithms using this approach for localization based on RF-proximity. In our evaluation, we find that beacon density rather than noise level has a more significant impact on beacon placement algorithms. Our beacon placement algorithms are applicable to a low (beacon) density regime of operation. Noise makes moderate density regimes more improvable. In this work we consider the problem of an optimal geographic placement of content in wireless cellular networks modelled by Poisson point processes. Specifically, for the typical user requesting some particular content and whose popularity follows a given law (e.g. Zipf), we calculate the probability of finding the content cached in one of the base stations. Wireless coverage follows the usual signal-to-interference-and noise ratio (SINR) model, or some variants of it. We formulate and solve the problem of an optimal randomized content placement policy, to maximize the user's hit probability. The result dictates that it is not always optimal to follow the standard policy “cache the most popular content, everywhere”. In fact, our numerical results regarding three different coverage scenarios, show that the optimal policy significantly increases the chances of hit under high-coverage regime, i.e., when the probabilities of coverage by more than just one station are high enough. We consider the problem of localizing a robot in a known environment modeled by a simple polygon P. We assume that the robot has a map of P but is placed at an unknown location inside P. From its initial location, the robot sees a set of points called the visibility polygon V of its location. In general, sensing at a single point will not suffice to uniquely localize the robot, since the set H of points in P with visibility polygon V may have more than one element. Hence, the robot must move around and use range sensing and a compass to determine its position (i.e., localize itself). We seek a strategy that minimizes the distance the robot travels to determine its exact location. We show that the problem of localizing a robot with minimum travel is NP-hard. We then give a polynomial time approximation scheme that causes the robot to travel a distance of at most (k - 1)d, where k = |H|, which is no greater than the number of reflex vertices of P, and d is the length of a minimum length tour that would allow the robot to verify its true initial location by sensing. We also show that this bound is the best possible. The localization of sensor nodes is a fundamental problem in sensor networks and can be implemented using powerful and expensive beacons. Beacons, the fewer the better, can acquire their position knowledge either from GPS devices or by virtue of being manually placed. In this paper, we propose a distributed method to localization of sensor nodes using a single moving beacon, where sensor nodes compute their position estimate based on the range-free technique. Two parameters are critical to the location accuracy of sensor nodes: the radio transmission range of the beacon and how often the beacon broadcasts its position. Theoretical analysis shows that these two parameters determine the upper bound of the estimation error when the traverse route of the beacon is a straight line. We extend the position estimate when the traverse route of the beacon is randomly chosen in a real-world situation, where the radio irregularity might cause a node to miss some crucial coordinate information from the beacon. We further point out that the movement pattern of the beacon plays a pivotal role in the localization task for sensors. To minimize estimation errors, sensor nodes can carry out a variety of algorithms in accordance with the movement of the beacon. Simulation results compare variants of the distributed method in a variety of testing environments. Real experiments show that the proposed method is feasible and can estimate the location of sensor nodes accurately, given a single moving beacon. In this paper, we present a robust, decentralized approach to RF-based location tracking. Our system, called MoteTrack, is based on low-power radio transceivers coupled with a modest amount of computation and storage capabilities. MoteTrack does not rely upon any back-end server or network infrastructure: the location of each mobile node is computed using a received radio signal strength signature from numerous beacon nodes to a database of signatures that is replicated across the beacon nodes themselves. This design allows the system to function despite significant failures of the radio beacon infrastructure. In our deployment of MoteTrack, consisting of 20 beacon nodes distributed across our Computer Science building, we achieve a 50th percentile and 80th percentile location-tracking accuracy of 2 meters and 3 meters respectively. In addition, MoteTrack can tolerate the failure of up to 60 of the beacon nodes without severely degrading accuracy, making the system suitable for deployment in highly volatile conditions. We present a detailed analysis of MoteTrack's performance under a wide range of conditions, including variance in the number of obstructions, beacon node failure, radio signature perturbations, receiver sensitivity, and beacon node density. The visibility level set function introduced by allows for gradient based and variational formulations of many classical visibility optimization problems. In this work we propose solutions to two such problems. The first asks where to position n-observers such that the area visible to these observers is maximized. The second problem is to determine the shortest route an observer should take through a map such that every point in the map is visible from at least one vantage point on the route. These problems are similar to the art gallery and watchman route problems, respectively. We propose a greedy iterative algorithm, formulated in the level set framework as the solution to the art gallery problem. We also propose a variational solution to the watchman route problem which achieves complete visibility coverage of the domain while attaining a local minimum of path length. Camera placement has an enormous impact on the performance of vision systems, but the best placement to maximize performance depends on the purpose of the system. As a result, this paper focuses largely on the problem of task-specific camera placement. We propose a new camera placement method that optimizes views to provide the highest resolution images of objects and motions in the scene that are critical for the performance of some specified task (e.g. motion recognition, visual metrology, part identification, etc.). A general analytical formulation of the observation problem is developed in terms of motion statistics of a scene and resolution of observed actions resulting in an aggregate observability measure. The goal of this system is to optimize across multiple cameras the aggregate observability of the set of actions performed in a defined area. The method considers dynamic and unpredictable environments, where the subject of interest changes in time. It does not attempt to measure or reconstruct surfaces or objects, and does not use an internal model of the subjects for reference. As a result, this method differs significantly in its core formulation from camera placement solutions applied to problems such as inspection, reconstruction or the Art Gallery class of problems. We present tests of the system's optimized camera placement solutions using real-world data in both indoor and outdoor situations and robot-based experimentation using an all terrain robot vehicle-Jr robot in an indoor setting. During the last decades, location based services have become very popular and the developed indoor positioning systems have achieved an impressive accuracy. The problem though is that even if the only requirement is room-level localization, those systems are most of the times not cost-efficient and not easy to set-up, since they often require time-consuming calibration procedures. This paper presents a low-cost, threshold-based approach and introduces an algorithm that takes into account both the Received Signal Strength Indication (RSSI) of the Bluetooth Low Energy (BLE) beacons and the geometry of the rooms the beacons are placed in. Performance evaluation was done via measurements in an office environment composed of three rooms and in a house environment composed of six rooms. The experimental results show an improved accuracy in room detection when using the proposed algorithm, compared to when only considering the RSSI readings. This method was developed to provide context awareness to the international research project named SmartHeat. The projects aims to provide a system that efficiently heats a house, room by room, based on the habitants' habits and preferences. Many previous studies have examined the placement of access points (APs) to improve the community's understanding of the deployment and behavioral characteristics of wireless networks. A key implicit assumption in these studies is that one can estimate the AP location accurately from wardriving-like measurements. However, existing localization algorithms exhibit high error because they over-simplify the complex nature of signal propagation. In this work, we propose a novel approach that localizes APs using directional information derived from local signal strength variations. Our algorithm only uses signal strength information, and improves localization accuracy over existing techniques. Furthermore, the algorithm is robust to the sampling biases and non-uniform shadowing, which are common in wardriving measurements. We define and analyze a random coverage process of the @math -dimensional Euclidian space which allows one to describe a continuous spectrum that ranges from the Boolean model to the Poisson-Voronoi tessellation to the Johnson-Mehl model. Like for the Boolean model, the minimal stochastic setting consists of a Poisson point process on this Euclidian space and a sequence of real valued random variables considered as marks of this point process. In this coverage process, the cell attached to a point is defined as the region of the space where the effect of the mark of this point exceeds an affine function of the cumulated effect of all marks. This cumulated effect is defined as the shot noise process associated with the marked point process. In addition to analyzing and visualizing this continuum, we study various basic properties of the coverage process such as the probability that a point or a pair of points be covered by a typical cell. We also determine the distribution of the number of cells which cover a given point, and show how to provide deterministic bounds on this number. Finally, we also analyze convergence properties of the coverage process using the framework of closed sets, and its differentiability properties using perturbation analysis. Our results require a pathwise continuity property for the shot noise process for which we provide sufficient conditions. The model in question stems from wireless communications where several antennas share the same (or different but interfering) channel(s). In this case, the area where the signal of a given antenna can be received is the area where the signal to interference ratio is large enough. We describe this class of problems in detail in the paper. The obtained results allow one to compute quantities of practical interest within this setting: for instance the outage probability is obtained as the complement of the volume fraction; the law of the number of cells covering a point allows one to characterize handover strategies etc. We present the first constant-factor approximation algorithm for a nontrivial instance of the optimal guarding (coverage) problem in polygons. In particular, we give an @math -approximation algorithm for placing the fewest point guards on a 1.5D terrain, so that every point of the terrain is seen by at least one guard. While polylogarithmic-factor approximations follow from set cover results, our new results exploit the geometric structure of terrains to obtain a substantially improved approximation algorithm. We consider the problem of localizing a wireless client in an indoor environment based on the signal strength of its transmitted packets as received on stationary sniffers or access points. Several state-of-the-art indoor localization techniques have the drawback that they rely extensively on a labor-intensive 'training' phase that does not scale well. Use of unmodeled hardware with heterogeneous power levels further reduces the accuracy of these techniques. We propose a 'learning-based' approach, WiGEM, where the received signal strength is modeled as a Gaussian Mixture Model (GMM). Expectation Maximization (EM) is used to learn the maximum likelihood estimates of the model parameters. This approach enables us to localize a transmitting device based on the maximum a posteriori estimate. The key insight is to use the physics of wireless propagation, and exploit the signal strength constraints that exist for different transmit power levels. The learning approach not only avoids the labor-intensive training, but also makes the location estimates considerably robust in the face of heterogeneity and various time varying phenomena. We present evaluations on two different indoor testbeds with multiple WiFi devices. We demonstrate that WiGEM's accuracy is at par with or better than state-of-the-art techniques but without requiring any training. Maximizing network throughput while providing fairness is one of the key challenges in wireless LANs (WLANs). This goal is typically achieved when the load of access points (APs) is balanced. Recent studies on operational WLANs, however, have shown that AP load is often substantially uneven. To alleviate such imbalance of load, several load balancing schemes have been proposed. These schemes commonly require proprietary software or hardware at the user side for controlling the user-AP association. In this paper we present a new load balancing technique by controlling the size of WLAN cells (i.e., AP's coverage range), which is conceptually similar to cell breathing in cellular networks. The proposed scheme does not require any modification to the users neither the IEEE 802.11 standard. It only requires the ability of dynamically changing the transmission power of the AP beacon messages. We develop a set of polynomial time algorithms that find the optimal beacon power settings which minimize the load of the most congested AP. We also consider the problem of network-wide min-max load balancing. Simulation results show that the performance of the proposed method is comparable with or superior to the best existing association-based methods. Cellular networks are usually modeled by placing the base stations according to a regular geometry such as a grid, with the mobile users scattered around the network either as a Poisson point process (i.e. uniform distribution) or deterministically. These models have been used extensively for cellular design and analysis but suffer from being both highly idealized and not very tractable. Thus, complex simulations are used to evaluate key metrics such as coverage probability for a specified target rate (equivalently, the outage probability) or average sum rate. We develop general models for multi-cell signal-to-noise-plus-interference ratio (SINR) based on homogeneous Poisson point processes and derive the coverage probability, which is one minus the outage probability. Under very general assumptions, the resulting expressions for the SINR cumulative distribution function involve quickly computable integrals, and in some important special cases of practical interest these integrals can be simplified to common integrals (e.g., the Q-function) or even to exact and quite simple closed-form expressions. We compare our coverage predictions to the standard grid model and an actual base station deployment. We observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in urban cellular networks with highly variable coverage radii. Sensor nodes may be equipped with a "directional" sensing device (such as a camera) which senses a physical phenomenon in a certain direction depending on the chosen orientation. In this article, we address the problem of selection and orientation of such directional sensors with the objective of maximizing coverage area. Prior works on sensor coverage have largely focused on coverage with sensors that are associated with a unique sensing region. In contrast, directional sensors have multiple sensing regions associated with them, and the orientation of the sensor determines the actual sensing region. Thus, the coverage problems in the context of directional sensors entails selection as well as orientation of sensors needed to activate in order to maximize ensure coverage. In this article, we address the problem of selecting a minimum number of sensors and assigning orientations such that the given area (or set of target points) is k-covered (i.e., each point is covered k times). The above problem is NP-complete, and even NP-hard to approximate. Thus, we design a simple greedy algorithm that delivers a solution that k-covers at least half of the target points using at most M log(k|C|) sensors, where |C| is the maximum number of target points covered by a sensor and M is the minimum number of sensor required to k-cover all the given points. The above result holds for almost arbitrary sensing regions. We design a distributed implementation of the above algorithm, and study its performance through simulations. In addition to the above problem, we also look at other related coverage problems in the context of directional sensors, and design similar approximation algorithms for them. To deploy a multi-cell 802.11 wireless local area network (WLAN), access point (AP) placement and channel assignment are two primary design issues. For a given pattern of traffic demands, we aim at maximizing not only the overall system throughput, but also the fairness in resource sharing among mobile terminals. A novel method for estimating the system throughput of multi-cell WLAN is proposed. An important feature of this method is that co-channel overlapping is allowed. Unlike conventional approaches that decouple AP placement and channel assignment into two phases, we propose to jointly solve the two problems for better performance. The optimal solution can be found using exhaustive searching. Due to the high computational complexity involved in exhaustive searching, an efficient local searching algorithm, called patching algorithm, is designed. Numerical results show that for a typical indoor environment, patching algorithm can provide a close-to-optimal performance with much lower time complexity than exhaustive searching We present novel grid coverage strategies for effective surveillance and target location in distributed sensor networks. We represent the sensor field as a grid (two or three-dimensional) of points (coordinates) and use the term target location to refer to the problem of locating a target at a grid point at any instant in time. We first present an integer linear programming (ILP) solution for minimizing the cost of sensors for complete coverage of the sensor field. We solve the ILP model using a representative public-domain solver and present a divide-and-conquer approach for solving large problem instances. We then use the framework of identifying codes to determine sensor placement for unique target location, We provide coding-theoretic bounds on the number of sensors and present methods for determining their placement in the sensor field. We also show that grid-based sensor placement for single targets provides asymptotically complete (unambiguous) location of multiple targets in the grid. Many applications of wireless sensor networks (WSNs) require location information of the randomly deployed nodes. A common solution to the localization problem is to deploy a few special beacon nodes having location awareness, which help the ordinary nodes to localize. In this approach, non-beacon nodes estimate their locations using noisy distance measurements from three or more non-collinear beacons they can receive signals from. In this paper, the ranging-based localization task is formulated as a multidimensional optimization problem, and addressed using bio-inspired algorithms, exploiting their quick convergence to quality solutions. An investigation on distributed iterative localization is presented in this paper. Here, the nodes that get localized in an iteration act as references for remaining nodes to localize. The problem has been addressed using particle swarm optimization (PSO) and bacterial foraging algorithm (BFA). A comparison of the performances of PSO and BFA in terms of the number of nodes localized, localization accuracy and computation time is presented. This study investigated the impact of Bluetooth Low Energy devices in advertising beaconing mode on fingerprint-based indoor positioning schemes. Early experimentation demonstrated that the low bandwidth of BLE signals compared to WiFi is the cause of significant measurement error when coupled with the use of three BLE advertising channels. The physics underlying this behaviour is verified in simulation. A multipath mitigation scheme is proposed and tested. It is determined that the optimal positioning performance is provided by 10Hz beaconing and a 1 second multipath mitigation processing window size. It is determined that a steady increase in positioning performance with fingerprint size occurs up to 7 ±1, above this there is no clear benefit to extra beacon coverage.