Algorithms to detect athletic jumps and to determine in real-time performance parameters such as jump air time (AT), horizontal distance, height and drop, are developed in this work. These algorithms are customized to be implemented... more
Algorithms to detect athletic jumps and to determine in real-time performance parameters such as jump air time (AT), horizontal distance, height and drop, are developed in this work. These algorithms are customized to be implemented onboard action sports goggles developed by Recon Instruments Ltd. These goggles are equipped with low cost micro-electro-mechanical inertial sensors and a single point GPS receiver which feed raw data to the algorithms. The micro-LCD display system in the goggles displays jump statistics to the user wearing the goggles. Two novel methods, namely WMCM (Windowed Mean Canceled Multiplication) and PFAD (Preceding and Following Acceleration Dierence), are introduced for jump detection using accelerometer data. Four characteristic points in the resultant acceleration data are selected as the AT dening epochs for a jump. A novel threshold independent, probabilistic method using MADM (Multiple Attribute Decision Making) and the Closest Peak method are proposed to detect these characteristic points and determine the corresponding AT of a jump. A GPS/INS integration algorithm is developed to determine jump horizontal distance, height and drop. A novel sensor error compensation scheme is developed using sensor fusion and Linear Kalman Filters (LKF). The LKF parameters are varied to address the uctuating dynamics of the athlete during a jump. The Extended Kalman Filter (EKF) used for GPS/ INS integration has an observation vector augmented with sensor error measurements derived from sensor fusion. The performance of the proposed algorithms was evaluated through experimental eld tests. The proposed jump detection algorithm successfully detected 92% of the jumps performed by a snowboarder wearing the goggles whereas the current Recon algorithm only detects 60%. The AT determination algorithm exhibited an average error of 0.033 s (4.8%) which is well within the accuracy requirement of Recon, 0:1 s, and betters the current Recon algorithm which has an average error of 0.111 s (8.4%). For determination of jump horizontal distance, height and drop, the proposed algorithm has an error of 14.34 cm (5.55%), 1.56 cm (38.21%) and 6.71 cm (9.43%) respectively. The accuracy achieved is deemed to fulll expectations of both recreational and professional athletes.
We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$... more
We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$ our results cover other metrics like Skorokhod metric on the space of c\`{a}dl\`{a}g functions and uniform metrics on $C([0,1])$. We will show that these estimators are in an adaptive sense