Jason T. Isaacs

Optimal sensor placement for time difference of arrival localization

This paper addresses the problem of localizing a source from noisy time-of-arrival measurements. In particular, we are interested in the optimal placement of M planar sensors so as to yield the best expected source location estimate. The main result, on maximizing the expected determinant of the Fisher information matrix for truncated, radially-symmetric source distributions, shows two features not previously observed. First, the sensors should be placed as far from the expected source position as possible. Second, the sensors should be arranged in a splay configuration in which neighboring sensors are separated by equal angle increments. Specific examples are given for point, uniform, and truncated-Gaussian source density functions.

Algorithms for the traveling Salesman Problem with Neighborhoods involving a dubins vehicle

We study the problem of finding the minimum length curvature constrained closed path through a set of regions in the plane. This problem is referred to as the Dubins Traveling Salesperson Problem with Neighborhoods (DTSPN). Two algorithms are presented that transform this infinite dimensional combinatorial optimization problem into a finite dimensional asymmetric TSP by sampling and applying the appropriate transformations, thus allowing the use of existing approximation algorithms. We show for the case of disjoint regions, the first algorithm needs only to sample each region once to produce a tour within a factor of the length of the optimal tour that is independent of the number of regions. We present a second algorithm that performs no worse than the best existing algorithm and can perform significantly better when the regions overlap.

RF source-seeking by a micro aerial vehicle using rotation-based angle of arrival estimates

We investigate a computationally and memory efficient algorithm for radio frequency (RF) source-seeking with a single-wing rotating micro aerial vehicle (MAV) equipped with a directional antenna. The MAV is assumed to have no knowledge of its position and to have only an estimate of orientation through a magnetometer. A key novelty of our approach is in exploiting the rotation of the MAV and the directionality of its RF antenna to derive estimates of the angle of arrival (AOA) at each rotation. The MAV then follows the estimated direction until the next rotation is complete. We prove convergence of this greedy algorithm under rather weak assumptions on the noise associated with the AOA estimates, using recent results on the property of recurrence for systems governed by stochastic difference inclusions. These convergence results are supplemented by simulations quantifying the amount of excess travel, relative to the straight line distance to the source. Indoor experiments using Lockheed Martins Samarai MAV demonstrate the efficacy of the greedy algorithm both for static source-seeking, and for the more challenging problem of tracking a moving source.

Dubins Traveling Salesman Problem with Neighborhoods: A Graph-Based Approach

We study the problem of finding the minimum-length curvature constrained closed path through a set of regions in the plane. This problem is referred to as the Dubins Traveling Salesperson Problem with Neighborhoods (DTSPN). An algorithm is presented that uses sampling to cast this infinite dimensional combinatorial optimization problem as a Generalized Traveling Salesperson Problem (GTSP) with intersecting node sets. The GTSP is then converted to an Asymmetric Traveling Salesperson Problem (ATSP) through a series of graph transformations, thus allowing the use of existing approximation algorithms. This algorithm is shown to perform no worse than the best existing DTSPN algorithm and is shown to perform significantly better when the regions overlap. We report on the application of this algorithm to route an Unmanned Aerial Vehicle (UAV) equipped with a radio to collect data from sparsely deployed ground sensors in a field demonstration of autonomous detection, localization, and verification of multiple acoustic events.

Bayesian localization and mapping using GNSS SNR measurements

In urban areas, GNSS localization quality is often degraded due to signal blockage and multi-path reflections. When several GNSS signals are blocked by buildings, the remaining unblocked GNSS satellites are typically in a poor geometry for localization (nearly collinear along the street direction). Multi-path reflections result in pseudo range measurements that can be significantly longer than the line of sight path (true range) resulting in biased geolocation estimates. If a 3D map of the environment is available, one can address these problems by evaluating the likelihood of GNSS signal strength and location measurements given the map. We present two approaches based on this observation. The first is appropriate for cases when network connectivity may be unavailable or undesired and uses a particle filter framework that simultaneously improve both localization and the 3D map. This approach is shown via experiments to improve the map of a section of a university campus while simultaneously improving receiver localization. The second approach which may be more suitable for smartphone applications assumes that network connectivity is available and thus a software service running in the cloud performs the mapping and localization calculations. Early experiments demonstrate the potential of this approach to significantly improve geo-localization accuracy in urban areas.

Quadrotor control for RF source localization and tracking

Preliminary results on quadrotor control strategies enabling omnidirectional radio frequency (RF) sensing for source localization and tracking are discussed. The use of a quadrotor for source localization and tracking requires a tight coupling of the attitude control and RF sensing designs. We present a controller for tracking a ramp reference input in yaw (causing rotation of quadrotor) while maintaining a constant altitude hover or translation. The ability to track a ramp in the yaw angle is crucial for RF bearing estimation using received signal strength (RSS) measurements from a directional antenna as it avoids the need for additional gimbaling payload. This bearing or angle of arrival (AOA) estimate is then utilized by a particle filter for source localization and tracking. We report on extensive experiments that suggest that this approach is appropriate even in complex indoor environments where multipath fading effects are difficult to model.

On UAV routing protocols for sparse sensor data exfiltration

The problem addressed in this paper is data exfiltration from a collection of sensors that are unable to establish ad-hoc communication due to their widespread deployment, geographical constraints, and power considerations. Sensor data is exfiltrated by one or more uninhabited aerial vehicles (UAVs) that act as data mules by visiting each sensor in order to establish a communication link. In many applications, the sequence in which the UAVs visit the sensors can have large impact on the overall performance because some sensors have more informative data than others and because distant nodes take a long time to visit. One such application that we will focus on in this paper is the acoustic source localization problem in which the objective is to localize the source of a transient acoustic event as quickly as possible. We introduce two protocols, ACM and TTM, based on receding horizon optimization of the volume of the Cramer-Rao uncertainty ellipsoid and show significant performance benefits over several other routing protocols using a high-fidelity online simulation environment.

Localization with sparse acoustic sensor network using UAVs as information-seeking data mules

We propose and demonstrate a novel architecture for on-the-fly inference while collecting data from sparse sensor networks. In particular, we consider source localization using acoustic sensors dispersed over a large area, with the individual sensors located too far apart for direct connectivity. An Unmanned Aerial Vehicle (UAV) is employed for collecting sensor data, with the UAV route adaptively adjusted based on data from sensors already visited, in order to minimize the time to localize events of interest. The UAV therefore acts as a information-seeking data mule, not only providing connectivity, but also making Bayesian inferences from the data gathered in order to guide its future actions. The system we demonstrate has a modular architecture, comprising efficient algorithms for acoustic signal processing, routing the UAV to the sensors, and source localization. We report on extensive field tests which not only demonstrate the effectiveness of our general approach, but also yield specific practical insights into GPS time synchronization and localization accuracy, acoustic signal and channel characteristics, and the effects of environmental phenomena.

GPS-optimal micro air vehicle navigation in degraded environments

We investigate a computationally and memory efficient algorithm for radio frequency (RF) source-seeking with a single-wing rotating micro air vehicle (MAV) operating in an urban canyon environment. We present an algorithm that overcomes two significant difficulties of operating in an urban canyon environment. First, Global Positioning System (GPS) localization quality can be degraded due to the lack of clear line of sight to a sufficient number of GPS satellites. Second, the spatial RF field is complex due to multipath reflections leading to multiple maxima and minima in received signal strength (RSS). High quality GPS localization is maintained by observing the GPS signal to noise ratio (SNR) to each satellite and making inferences about directions of high GPS visibility (allowable) and directions of low GPS visibility (forbidden). To avoid local maxima in RSS due to multipath reflections we exploit the rotation of the MAV and the directionality of its RF antenna to derive estimates of the angle of arrival (AOA) at each rotation. Under mild assumptions on the noise associated with the AOA measurements, a greedy algorithm is shown to exhibit a global recurrence property. Simulations supplied with actual GPS SNR measurements indicate that this algorithm reliably finds the RF source while maintaining an acceptable level of GPS visibility. Additionally, outdoor experiments using Lockheed Martins Samarai MAV demonstrate the efficacy of this approach for static source-seeking in an urban canyon environment.

Multiple event localization in a sparse acoustic sensor network using UAVs as data mules

We report on a field demonstration of autonomous detection, localization, and verification of multiple acoustic events using sparsely deployed unattended ground sensors, unmanned aerial vehicles (UAV) as data mules, and a ground control interface. A novel algorithm is demonstrated to address the problem of multiple event acoustic source localization in the presence of false and missed detections. We also demonstrate an algorithm to route a UAV equipped with a radio to collect data from sparsely deployed ground sensors that takes advantage of the communication range of the aircraft while adhering to kinematic constraints of the UAV. A second UAV was utilized to provide video verification of localized events to a human operator at a ground control station.