Hybrid Bayesian Approach for Fusing Range-based and Sourceless Localization Estimates Under Non-Stationary Observability

The paper proposes a hybrid Bayesian approach for multi-sensor data fusion for 3D localization. The approach addresses the problem of fusing range-based and sourceless localization estimates under conditions of varying observ ability in the range-based sub-system. The proposed localization app roach uses a mixture of Single-Hypothesis-Tracking (e.g. Kalmanfilter) and Multi-Hypothesis-Tracking (MHT) (e.g. Particle Filte rs) Bayesian filtering to improve tracking accuracy under condi tions of varying observability. Under conditions of sufficient (or no) range measurements a single hypothesis approach is used. Un der the condition of insufficient range measurements (i.e, 1 or 2 ranges), MHT is used, since it more accurately models the distribution of real error in the estimated positions by means of Gaussian mixtures rather that a single Gaussian. The result s show up to 10% improvement in 3D position estimation as compared to Single-Constraint-at-a-Time (SCAAT) approach and upto24% improvement compared to an Extended Kalman Filter approach for intermittent 3 second partial range occlusions when tracking human arm movements. I. I NTRODUCTION Motion capture (Mocap) and motion tracking are of interest in applications ranging from entertainment industry to hea lthcare [1]. Range-based Mocap systems employ multiple range measurements at wearable sensors to estimate 3D position [2 ]. Typically, range is measured between fixed transmitters and wearable sensors or vice versa. Range can either be measured directly using ultrasonic [3] or UltraWideBand [4] signals or estimated indirectly based on measurements from optical sensors [5]. These systems provide accurate absolute posit ion estimates but generally suffer from Non-Line-of-Sight (NL OS) or occlusion problems. Anther class of Mocap systems are sourceless. Typically these self-contained systems rely o n Inertial Measurement Units (IMUs) to measure linear and angular acceleration. While sourceless systems do not have NLOS problems, they do suffer from rapid growth in error when position is estimated by dead reckoning. This is due to IMU bias instability and inaccurate gravity compensation. Hyb rid Mocap systems offer a more accurate and robust solution [6], [7]. Hybrid systems solve the NLOS, drift and calibration problems by incorporating range-based and sourceless subsystems and fusing the data. The conventional approach to data fusion is through a series of prediction-correction st ep . The sourceless system parameters form the basis of the motio n prediction model and the range measurements are used in the correction step. During the correction step, the measur d ranges can be incorporated sequentially or as a single vecto r. The accuracy of the correction step depends on the number of transmitter-receiver pairs that have Line Of Sight (LOS). T he nature of the transmitter-receiver occlusion pattern for a fixed infrastructure based system depends on the type of movement s being performed. Herein, we are interested in occlusions occurring in applications in which rehabilitation, sports or fitness exercise s are monitored. The work presented in this paper addresses the problem of location estimation in cases of temporary partia l occlusion of the ranging subsystem in hybrid Mocap systems. By temporary partial occlusion, we mean that for short time periods only 1 or 2 range estimates are available due to NLOS conditions between the other transmitters and receivers. W e assume that 3 or more range estimates are available before partial occlusion occurs. Herein we propose a novel method that operates via selective transition between a MultipleHypothesis-tracking (MHT) and Single-Hypothesis-Tracki ng (SHT). The proposed method was found to provide higher accuracy than previously published algorithms, in terms of 3D position estimation, for the considered occlusion scenari os. In a dition, the computational complexity of the proposed filt er is lower than a conventional particle filter because it uses a lesser number of particles. The remainder of the paper is organized as follows. Section II gives a mathematical description of the problem and also details the envisioned occlusion scenarios which the mobil e d vice encounters during dynamics of the motion. Section II I outlines previous work reported on 3D localization using ra nge nd inertial measurements, particularly emphasizing meth ods that use a mixture of two or more bayesian techniques. Section IV introduces the proposed approach and discusses the shortcomings of conventional approaches under particu lar scenarios. Section V presents 3D localization results usin g the proposed method and compares the results with other candidate approaches. Finally Section VI draws conclusion s and discusses potential future work. II. PROBLEM DESCRIPTION Mocap systems determine the Position and Orientation (P&O) of multiple sensors units placed on landmarks on the human body. Herein, we focus on 3D position estimation of a single sensor unit. A single sensor unit in our case is compos ed of an ultrasonic receiver and an IMU unit. The problem of localization of the sensor unit is modeled in a dynamic nonlinear state space model. The initial state is sampled from t he Gaussian distribution given by: