Geometric Interpretation of Theoretical Bounds for RSS-based Source Localization with Uncertain Anchor Positions

The Received Signal Strength based source localization can encounter severe problems originating from uncertain information about the anchor positions in practice. The anchor positions, although commonly assumed to be precisely known prior to the source localization, are usually obtained using previous estimation algorithm such as GPS. This previous estimation procedure produces anchor positions with limited accuracy that result in degradations of the source localization algorithm and topology uncertainty. We have recently addressed the problem with a joint estimation framework that jointly estimates the unknown source and uncertain anchors positions and derived the theoretical limits of the framework. This paper extends the authors previous work on the theoretical performance bounds of the joint localization framework with appropriate geometric interpretation of the overall problem exploiting the properties of semi-definiteness and symmetry of the Fisher Information Matrix and the Cram{\`e}r-Rao Lower Bound and using Information and Error Ellipses, respectively. The numerical results aim to illustrate and discuss the usefulness of the geometric interpretation. They provide in-depth insight into the geometrical properties of the joint localization problem underlining the various possibilities for practical design of efficient localization algorithms.Comment: 30 pages, 15 figure

Fundamental Limits of Wideband Localization - Part II: Cooperative Networks

The availability of positional information is of great importance in many commercial, governmental, and military applications. Localization is commonly accomplished through the use of radio communication between mobile devices (agents) and fixed infrastructure (anchors). However, precise determination of agent positions is a challenging task, especially in harsh environments due to radio blockage or limited anchor deployment. In these situations, cooperation among agents can significantly improve localization accuracy and reduce localization outage probabilities. A general framework of analyzing the fundamental limits of wideband localization has been developed in Part I of the paper. Here, we build on this framework and establish the fundamental limits of wideband cooperative location-aware networks. Our analysis is based on the waveforms received at the nodes, in conjunction with Fisher information inequality. We provide a geometrical interpretation of equivalent Fisher information for cooperative networks. This approach allows us to succinctly derive fundamental performance limits and their scaling behaviors, and to treat anchors and agents in a unified way from the perspective of localization accuracy. Our results yield important insights into how and when cooperation is beneficial.Comment: To appear in IEEE Transactions on Information Theor

Power Optimization for Network Localization

Reliable and accurate localization of mobile objects is essential for many applications in wireless networks. In range-based localization, the position of the object can be inferred using the distance measurements from wireless signals exchanged with active objects or reflected by passive ones. Power allocation for ranging signals is important since it affects not only network lifetime and throughput but also localization accuracy. In this paper, we establish a unifying optimization framework for power allocation in both active and passive localization networks. In particular, we first determine the functional properties of the localization accuracy metric, which enable us to transform the power allocation problems into second-order cone programs (SOCPs). We then propose the robust counterparts of the problems in the presence of parameter uncertainty and develop asymptotically optimal and efficient near-optimal SOCP-based algorithms. Our simulation results validate the efficiency and robustness of the proposed algorithms.Comment: 15 pages, 7 figure

Dynamic Arrival Rate Estimation for Campus Mobility on Demand Network Graphs

Mobility On Demand (MOD) systems are revolutionizing transportation in urban settings by improving vehicle utilization and reducing parking congestion. A key factor in the success of an MOD system is the ability to measure and respond to real-time customer arrival data. Real time traffic arrival rate data is traditionally difficult to obtain due to the need to install fixed sensors throughout the MOD network. This paper presents a framework for measuring pedestrian traffic arrival rates using sensors onboard the vehicles that make up the MOD fleet. A novel distributed fusion algorithm is presented which combines onboard LIDAR and camera sensor measurements to detect trajectories of pedestrians with a 90% detection hit rate with 1.5 false positives per minute. A novel moving observer method is introduced to estimate pedestrian arrival rates from pedestrian trajectories collected from mobile sensors. The moving observer method is evaluated in both simulation and hardware and is shown to achieve arrival rate estimates comparable to those that would be obtained with multiple stationary sensors.Comment: Appears in 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). http://ieeexplore.ieee.org/abstract/document/7759357

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

Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation

Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large scale sensor networks, addressing four fundamental issues- connectivity, capacity, clocks and function computation. To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad-hoc network is modeled as a random graph and the critical range for asymptotic connectivity is determined, as well as the critical number of neighbors that a node needs to connect to. Next, given connectivity, we address the issue of how much data can be transported over the sensor network. We present fundamental bounds on capacity under several models, as well as architectural implications for how wireless communication should be organized. Temporal information is important both for the applications of sensor networks as well as their operation.We present fundamental bounds on the synchronizability of clocks in networks, and also present and analyze algorithms for clock synchronization. Finally we turn to the issue of gathering relevant information, that sensor networks are designed to do. One needs to study optimal strategies for in-network aggregation of data, in order to reliably compute a composite function of sensor measurements, as well as the complexity of doing so. We address the issue of how such computation can be performed efficiently in a sensor network and the algorithms for doing so, for some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE

Attention and Anticipation in Fast Visual-Inertial Navigation

We study a Visual-Inertial Navigation (VIN) problem in which a robot needs to estimate its state using an on-board camera and an inertial sensor, without any prior knowledge of the external environment. We consider the case in which the robot can allocate limited resources to VIN, due to tight computational constraints. Therefore, we answer the following question: under limited resources, what are the most relevant visual cues to maximize the performance of visual-inertial navigation? Our approach has four key ingredients. First, it is task-driven, in that the selection of the visual cues is guided by a metric quantifying the VIN performance. Second, it exploits the notion of anticipation, since it uses a simplified model for forward-simulation of robot dynamics, predicting the utility of a set of visual cues over a future time horizon. Third, it is efficient and easy to implement, since it leads to a greedy algorithm for the selection of the most relevant visual cues. Fourth, it provides formal performance guarantees: we leverage submodularity to prove that the greedy selection cannot be far from the optimal (combinatorial) selection. Simulations and real experiments on agile drones show that our approach ensures state-of-the-art VIN performance while maintaining a lean processing time. In the easy scenarios, our approach outperforms appearance-based feature selection in terms of localization errors. In the most challenging scenarios, it enables accurate visual-inertial navigation while appearance-based feature selection fails to track robot's motion during aggressive maneuvers.Comment: 20 pages, 7 figures, 2 table

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