Vehicle Tracking Based on Fusion of Magnetometer and Accelerometer Sensor Measurements with Particle Filtering Roland Hostettler, Petar M. Djuric´ This is a post-print of a paper published in IEEE Transactions on Vehicular Technology. When citing this work, you must always cite the original article: R. Hostettler and P. M. Djuric,´ “Vehicle tracking based on fusion of magnetometer and accelerometer sensor measurements with particle filtering,” Vehicular Technology, IEEE Trans- actions on, vol. 64, no. 11, pp. 4917–4928, November 2015 DOI: 10.1109/TVT.2014.2382644 Copyright: c 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. 1 Vehicle Tracking Based on Fusion of Magnetometer and Accelerometer Sensor Measurements with Particle Filtering Roland Hostettler, Member, IEEE, Petar M. Djuric,´ Fellow, IEEE Abstract—In this article, we propose a method for vehicle Target tracking is often formulated as a state estimation tracking on roadways using measurements of magnetometers problem where the position of the target as a function of time is and accelerometers. The measurements are used to build a considered a random process [17]. The measurements obtained low-cost, low-complexity vehicle tracking sensor platform for highway traffic monitoring. First, the problem is formulated by from the sensors are described as a function of the states, for introducing the process model for the motion of the vehicle example, of the range and bearing of a target [18]. In many on the road and two measurement models, one for each of cases, these measurements are highly nonlinear functions of the sensors. Second, it is shown how the measurements of the states which, for their processing, often require the use the sensors can be fused using particle filtering. The standard of approximating methods, such as the extended Kalman or sampling importance resampling (SIR) particle filter is extended for processing of multi-rate sensor measurements and models particle filters. It has been shown that the latter is a suitable that employ unknown static parameters. The latter are treated approach in many different applications; see [2] for a thorough by Rao-Blackwellization. The performance of the method is overview. demonstrated by computer simulations. It is found that it is In this work, we address vehicle tracking by combining feasible to fuse the two sensors for vehicle tracking and that the magnetometer and accelerometer measurements in a single proposed multi-rate particle filter performs better than particle filters that process only measurements of one of the sensors. sensor unit that is mounted on the road surface as illustrated The main contribution of this paper is the novel approach of in [16]. Even though tracking using individual sensors has fusing the measurements of road-mounted magnetometers and been addressed before [14]-[16], the combination of the two accelerometers for vehicle tracking and traffic monitoring. sensors has not been considered yet. An obvious major ad- Index Terms—Particle filters, sensor fusion, vehicle tracking vantage is that the two different sensors come at low costs and that they complement each other in the sense that they I. INTRODUCTION measure completely different phenomena. Furthermore, the sensors can be integrated in small, battery-powered sensor Target tracking is of importance in many different applica- nodes and require less computational power than, for example, tions ranging from air traffic control [2] to tracking of mobile video-based systems. phone users within a cellular network [3]. Another important Magnetometers are sensors measuring the strength of the application is in intelligent transportation systems that allows Earth’s magnetic field at a given point. They are often used in for tracking of vehicles on roadways. This is of interest for compass applications, for example, in mobile phones. Metallic obtaining insightful information about the traffic which can be objects like vehicles cause local distortions, and they can used, for example for understanding traffic patterns such as be measured by a magnetometer and exploited for target congestions [4], [5] or for predicting/preventing accidents [6] tracking [19]. Commonly, magnetometers are vector sensors (we note that the prevention of accidents requires very high measuring the Cartesian components of the vector field. Ac- accuracy of tracking). The gathered information (aggregate or celerometers are also used in a number of applications. An individual) can be broadcast to individual vehicles equipped accelerometer attached to the road surface measures vibrations with corresponding receiver equipment [4]. in the road caused by dynamic loads of vehicles passing in Popular approaches for vehicle tracking itself are often its proximity. The features of the vibrations can be used to based on vision systems [7]-[10], radar [11], or a combina- estimate vehicle parameters. tion of such techniques [12]. Recently, solutions that employ When these sensors are used for tracking purposes, there are low-cost, low-complexity sensors such as microphones [10], several important issues that need to be addressed carefully. [13], magnetometers [14], [15], or accelerometers [16] have First, the sensor measurements are highly nonlinear functions emerged. of the states. Second, the measurements depend on a set Copyright (c) 2014 IEEE. Personal use of this material is permitted. of unknown, target- or material-specific parameters which, if However, permission to use this material for any other purposes must be included in the estimation problem, make the problem even obtained from the IEEE by sending a request to [email protected]. R. Hostettler is with the Department of Computer Science, Electrical and more challenging. Third, due to the different measurement Space Engineering, Lulea˚ University of Technology, Lulea,˚ Sweden (e-mail: principles, the sensors have different properties including [email protected]). different sampling rates and operating clocks that usually are P. M. Djuric´ is with the Department of Electrical and Computer Engi- neering, Stony Brook University, Stony Brook, NY 11794 USA (e-mail: not synchronized. [email protected]). The solutions to this type of problems require fusion of 2 information from the sensors and multi-rate processing. A Thus, the motion is represented by a simple one-dimensional methodology that is suitable for these problems is particle constant velocity motion model given by filtering. Some solutions for generically similar settings have " T 2 # 1 Ts s been proposed in the literature. For example, a hybrid multi- xt = xt 1 + 2 ut; (1) rate Kalman-particle filter was proposed in [20]. There, it was 0 1 − Ts assumed that the measurements for the faster sensor depend | {z } | {z } ,A linearly on the state and hence, a Kalman filter was used ,B to update the particles when only the linear measurement where t = 1; 2;:::;T is a discrete time index, Ts is the were available. The method was also applied to a tracking sampling time, x problem where velocity and range measurements were avail- rt xt = x ; (2) able. In [21], particle filtering with multi-rate sensors in a r_t process industry context was considered. Similarly, [22] in- x x rt is the position on the road, and r_t is the vehicle’s velocity. troduced multi-rate particle filtering in conjunction with robot The symbol ut can be interpreted as a random acceleration localization based on a set of different sensors. An unscented term that accounts for small changes in the vehicles velocity information filter for estimating the position of a vehicle fusing due to the drivers input, drag, and so on. It is a random variable the measurements from a camera, laser range finder, and GPS with a distribution given by receiver was proposed in [23]. Finally, there is a large body of 2 work on vehicle tracking using particle filtering and different p(ut) = (ut; 0; σu ); (3) N t types of sensors. For example, Yin et. al. propose to combine a where (u ; 0; σ2 ) signifies normal distribution of a scalar particle filter with the CamShift algorithm for vehicle tracking N t ut with mean zero and variance σ2 . using video in order to achieve scale-invariability and account ut The initial position of the vehicle is the point where the for disturbances such as occlusion and background clutter [24]. vehicle is in the proximity of the sensor and where the Another video-based method that is especially robust to partial measurements start being taken. It is thus given through the occlusion of the target was proposed in [25]. Finally, [26] also sensor range plus some uncertainty. Hence, it is modeled uses particle filtering for video-based vehicle tracking where according to particles are clustered by analyzing the motion coherence in p(x ) = (x ; µ ;C ); (4) order to form convex shapes of the tracked objects. 0 N 0 x0 x0 The contributions of this paper are as follows. First, we where µx0 is the mean sensor range, Cx0 the spread, and propose a multi-rate particle filtering method for vehicle 1 tracking fusing the measurements of two passive sensors, (x0; µx0 ;Cx0 ) = N=2 1=2 N (2π) Cx0 (5) a magnetometer and an accelerometer, where the measure- 1 j j > −1 (x0 µ ) C (x0 µ ) ments are in general asynchronous. This is a novel approach e− 2 − x0 x0 − x0 × and has not been considered before. Second, the unknown is the normal distribution of an N 1 random variable x0 with parameters in the sensor models are handled through Rao- × mean µx0 and covariance Cx0 . Blackwellization, simplifying the tracking problem and im- Finally, the position of the target is defined by the vector proving the performance.