Traffic monitoring using an adaptive sensor power scheduling algorithm

Research Article Traffic monitoring using an adaptive sensor power scheduling algorithm Richard Tatum1 · Matthew Bays1 · John Hyland1 · Benjamin Hartman1 Received: 3 June 2019 / Accepted: 12 October 2019 / Published online: 5 November 2019 © This is a U.S. Government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019 Abstract Using sensors to monitor surface or subsurface traffic requires sensor placement, detection of traffic changes, and sensor power scheduling for improved efficiency. Of these capabilities, sensor power scheduling is one of the most important as the appropriate sensors must be selected for activation to respond to changes in the traffic. We present an adaptive power scheduling algorithm that uses the homogeneous equilibrium of a potential-field-based dynamical system to determine which sensors should be active. Our algorithm assumes a nearest neighbor topology, which makes additional assumptions about the placement of sensors. We formalize these conditions and construct a sensor placement algorithm to support our scheduling algorithm. To demonstrate the efficacy of our scheduling approach, we provide two distinctive traffic detection algorithms that we combine with our placement and scheduling algorithm to test via simulation. We provide the simulation results that show in both cases, the adaptive scheduling algorithm behaves efficiently as compared to an area coverage approach , as well as an all-active path coverage approach. Keywords Autonomous power scheduling · Traffic monitor · Nearest neighbor topology · Mixed-integer linear programming (MILP) · Potential field 1 Introduction The idea of using statically placed sensors to monitor geographical regions is well understood and has been applied to monitoring marine species [2], underwater vehicles [1], or more specifically, port security [16, 18]. Three facets to the problem of traffic monitoring are where to place the sensors, how to detect traffic distribution changes, and how to schedule sensors in response to traffic distribution changes. With respect to sensor placement, this problem is either solved as an area coverage problem [6, 7, 11, 19] or path coverage problem [14, 20]. As for the remaining facets, McIntyre and Hintz use information gain to determine sensor schedules for searching for unknown entities [17]. Others have considered the trade-off between accuracy and power with regard to scheduling sensors for tracking individual entities [12, 23]. Our scheduling approach, which we discuss in the next paragraph, considers detections from multiple entities. Our main contribution to the traffic monitoring problem is to focus on the scheduling facet of traffic monitoring. Simply stated, when a traffic distribution change is detected, a sensor scheduling algorithm must determine which sensors should be active and which should be inactive. Our approach, which uses statically placed sensors, borrows ideas from robotic path planning for mobile sensors [3, 15]. For mobile path planning, the velocity of the vehicle is proportional to the gradient of some potential function. Analogously, our approach assumes that the velocity of activating sensors is proportional to the gradient of an attractive potential field. Solving the resulting ordinary differential equation (ODE) for mobile path * Richard Tatum, | 1Naval Surface Warfare Center, Panama City Division, 110 Vernon Ave, Panama City, FL 32407, USA. SN Applied Sciences (2019) 1:1552 | https://doi.org/10.1007/s42452-019-1494-0 Vol.:(0123456789) Research Article SN Applied Sciences (2019) 1:1552 | https://doi.org/10.1007/s42452-019-1494-0 planning yields a path, while the solution of our ODE yields the indices of the sensors to be active. Thus, our approach combines elements of static and mobile sensors to create a new, unique sensor scheduling method. However, if sensors are not present where the traffic has shifted, then no scheduling of sensors can satisfactorily monitor the traffic. Thus, sensor placement clearly impacts the ability of any sensor schedule algorithm. In this paper, we more formally state placement assumptions and use them to construct a sensor placement algorithm to support our adaptive scheduling algorithm. In particular, our sensor placement algorithm uses a nearest neighbor topology, which is a modification of [20]; our placement approach considers the placement of only sensors. Sensor scheduling begins with detections of changes to traffic distributions. Without such indications, the sensor scheduling algorithm cannot proceed. Therefore, we provide two unique traffic change detection algorithms that we now describe. Our first traffic change detection approach relies on the following assumption: If traffic continuously shifts away from active sensors, then the total number of detections, which are the number of detections made by all active sensors, should decrease. To identify this event, we first use cubic b-splines as in [21] to smooth the noisy data of total detections. Using a uniform knot sequence, which guarantees C 2 smoothness of the b-spline everywhere over its domain [9], we are able to compute all of the inflection points and choose the inflection point with the highest number of detections. If the number of detections drops below the number of detections associated with the inflection point, we label that event as a traffic change event. Our second detection approach identifies a traffic change event as one in which the Hellinger distance between the previous and current detection distributions meets a specified threshold. The idea of using the Hellinger distance to compute the distance between distributions is an accepted technique as found in [13], in which the authors apply the Hellinger distance to distinguish distributions for classification problems. We combine our adaptive scheduling algorithm with the sensor placement approach and two traffic detection algorithms to form two completely distinctive traffic monitoring solutions. Figure 1 shows the conceptual behavior of these two traffic monitoring solutions. We compare these two methods with an area coverage approach found in [11] and an all-active path coverage approach found in [20] using a Monte Carlo simulation. In particular, we compare the probability of detections and the efficiency detections of all four monitoring solutions. Our paper is organized as follows. Section 2 describes the symbols that we use in this paper. Section 3 describes assumptions of our approach, while Sect. 4 describes the Vol:.(1234567890) Fig. 1  Ships (black diamonds) are generated from the traffic distribution (green arrows). The ships move from top to bottom, passing over sensors, which are either active (transparent blue circles) or not active (opaque blue circles) adaptive scheduling algorithm itself. In Sect. 5, we use the assumptions of 3 to construct a sensor placement algorithm. We describe two traffic detec (...truncated)