sensors Article A Novel 3D Multilateration Sensor Using Distributed Ultrasonic Beacons for Indoor Navigation Rohan Kapoor 1, Subramanian Ramasamy 1, Alessandro Gardi 1,*, Chad Bieber 2, Larry Silverberg 2 and Roberto Sabatini 1 1 School of Engineering, RMIT University, Aerospace and Aviation Discipline Melbourne, Melbourne VIC 3000, Australia; [email protected] (R.K.); [email protected] (S.R.); [email protected] (R.S.) 2 Mechanical and Aerospace Engineering, NC State University, Raleigh, NC 27695, USA; [email protected] (C.B.); [email protected] (L.S.) * Correspondence: [email protected]; Tel.: +61-434-673-788 Academic Editors: Dipen N. Sinha and Cristian Pantea Received: 8 August 2016; Accepted: 27 September 2016; Published: 8 October 2016 Abstract: Navigation and guidance systems are a critical part of any autonomous vehicle. In this paper, a novel sensor grid using 40 KHz ultrasonic transmitters is presented for adoption in indoor 3D positioning applications. In the proposed technique, a vehicle measures the arrival time of incoming ultrasonic signals and calculates the position without broadcasting to the grid. This system allows for conducting silent or covert operations and can also be used for the simultaneous navigation of a large number of vehicles. The transmitters and receivers employed are first described. Transmission lobe patterns and receiver directionality determine the geometry of transmitter clusters. Range and accuracy of measurements dictate the number of sensors required to navigate in a given volume. Laboratory experiments were performed in which a small array of transmitters was set up and the sensor system was tested for position accuracy. The prototype system is shown to have a 1-sigma position error of about 16 cm, with errors between 7 and 11 cm in the local horizontal coordinates. This research work provides foundations for the future development of ultrasonic navigation sensors for a variety of autonomous vehicle applications. Keywords: navigation; overdetermined system; trilateration; ultrasonics; distributed sensing 1. Introduction In recent years, there has been an increasing research focus on developing and improving navigation systems for air, ground, and underwater vehicles. Navigation systems including the Global Navigation Satellite System (GNSS) are not possible to use underwater, and in several air and ground vehicle applications, it is prone to data degradations or the complete loss of signal due to multipath effects, interference, and antenna obscuration [1–5]. Hence, GNSS signals are not reliable in urban landscapes comprised of tall buildings and their performance further deteriorates in an indoor environment. Additionally, GNSS systems have an accuracy of a few meters, which is not suitable for most indoor navigation applications. Multilateration is a method used to determine the position of an object based on simultaneous range measurements from three or more anchors located at known positions [6]. If the number of anchors used is three, it becomes a case of trilateration. Trilateration has been implemented in ultrasonics-based localization systems like Active Bat [7], Cricket [8], Dolphin [9], and Millibots [10]. Alternate localization methods like Received Signal Strength (RSS), triangulation, and Time Difference of Arrival (TDOA) have been thoroughly investigated in the recent past. RSS has insufficient precision [11] and lower resolution [12] for an indoor environment. Triangulation requires expensive Sensors 2016, 16, 1637; doi:10.3390/s16101637 www.mdpi.com/journal/sensors Sensors 2016, 16, 1637 2 of 13 hardwareSensors like2016, directional16, 1637 antennas and the equations employed are more complex than trilateration2 of 13 equations [13]. TDOA computations require the sharing of data between receivers, which in turn dictatesrequires bandwidth expensive and hardware power like requirements directional ante [14nnas]. Furthermore,and the equations TDOA employed calculations are more complex involve the than trilateration equations [13]. TDOA computations require the sharing of data between receivers, intersection of hyperbolic surfaces, which increases the computational complexity. Ultrasonic sensors which in turn dictates bandwidth and power requirements [14]. Furthermore, TDOA calculations are relativelyinvolve the inexpensive intersection and of robusthyperbolic against surfaces, environmental which increases noise. the This computational makes them complexity. preferable to otherUltrasonic location techniques sensors are thatrelatively employ inexpensive visual, tactile, and robust and magneticagainst environmen systems [15tal]. noise. This makes Basedthem preferable on these to premises, other location this techniques research focuses that employ on thevisual, development tactile, and magnetic and testing systems of an [15]. in-door 3D ultrasonicBased positioning on these premises, system this using research multilateration focuses on the for development real-time dynamic and testing platform of an in-door applications. 3D The proposedultrasonic systempositioning is tested system for using positioning multilateration accuracy for real-time in relevant dynamic static platform and dynamic applications. case The studies, includingproposed both system numerical is tested simulations for positioning and experimentalaccuracy in relevant tests. static After and discussing dynamic thecase principles studies, of multilateration,including both a suitablenumerical iterative simulations algorithm and experimental is introduced tests.for After over-determined discussing the principles multilateration of multilateration, a suitable iterative algorithm is introduced for over-determined multilateration problems. The results of the numerical simulations and experiments corroborate the validity of problems. The results of the numerical simulations and experiments corroborate the validity of the the proposed sensor architecture. After discussing the key research findings, the paper sums up with proposed sensor architecture. After discussing the key research findings, the paper sums up with conclusionsconclusions and and recommendations recommendations for for future future work. work. 2. Multilateration2. Multilateration Principles Principles In 2DIn space, 2D space, trilateration trilateration requires requires at at least least threethree measured distances distances between between anchors anchors and anda node, a node, the locationthe location of which of which is to beis to determined. be determined. The anchorsThe anchors should should not not be collinearbe collinear and and their their position position should be fixedshould and be known fixed and for higherknown for accuracy. higher accuracy. After the Afte measurementsr the measurements are acquired, are acquired, the location the location of the ofnode can bethe determined node can be as determined the intersection as the of intersection three circumferences of three circumferences whose geometric whose centresgeometric coincide centres with the anchorcoincide positions. with the Theanchor measured positions. distance The measured is represented distance byis represented the radii from by the the radii anchors. from Figurethe 1 depictsanchors. the trilateration Figure 1 depicts principle the trilateration in 2D involving principle three in 2D anchors involving and three associated anchors spheres and associated of different spheres of different radii, depicting the range from each anchor. The confidence area, depicted in radii, depicting the range from each anchor. The confidence area, depicted in green, is the intersection green, is the intersection of all three circles. In 3D space, a minimum of four measurements are of allrequired three circles. for multilateration. In 3D space, The a minimum node is located of four at the measurements intersection of arespheres, required with anchors for multilateration. fixed at The nodetheir isgeometric located centres. at the intersection of spheres, with anchors fixed at their geometric centres. Figure 1. Multilateration position calculation. Figure 1. Multilateration position calculation. The fundamental principle adopted in multilateration systems is to measure the ranges between Thethe receiver fundamental (node) principleand simultaneously adopted inobserved multilateration transmitters systems (anchors). is to The measure equation the for ranges geometric between the receiverdistance (node) between and the simultaneously receiver and the transmitter observed transmitters can be written (anchors). as: The equation for geometric distance between the receiver and the transmitter can be written as: () = ( −) + ( −) + ( −) (1) q a 2 a 2 a 2 where ( , , ) arer (thet) = co-ordinates(x − x kof) the+ (receivery − yk )and+ ( z ,− zk, ) ) are the transmitter (1) coordinates. A purely analytical solution for position in 3D space can be found with a system of three a a a whereequations (xk, yk, z withk) are three the unknowns: co-ordinates of the receiver and (x , y , z ) are the transmitter coordinates. A purely analytical solution for position in 3D space can be found with a system of three equations () = ( − ) + ( −) + ( −) (n = 1,2,3) (2) with three unknowns: q a 2 a 2 a 2 rn (t) = (x − xk) + (y − yk) + (z − zk) (n = 1, 2, 3) (2) Sensors 2016, 16, 1637 3 of 13 This would provide a uniquely constrained system with two solutions. However, the navigation solution calculated with this system of equations does not account for measurement