Trajectory determination and analysis in sports by satellite and inertial navigation

This research presents methods for performance analysis in sports through the integration of Global Positioning System (GPS) measurements with Inertial Navigation System (INS). The described approach focuses on strapdown inertial navigation using Micro-Electro-Mechanical System (MEMS) Inertial Measurement Units (IMU). A simple inertial error model is proposed and its relevance is proven by comparison to reference data. The concept is then extended to a setup employing several MEMS-IMUs in parallel. The performance of the system is validated with experiments in skiing and motorcycling. The position accuracy achieved with the integrated system varies from decimeter level with dual-frequency differential GPS (DGPS) to 0.7 m for low-cost, single-frequency DGPS. Unlike the position, the velocity accuracy (0.2 m/s) and orientation accuracy (1 – 2 deg) are almost insensitive to the choice of the receiver hardware. The orientation performance, however, is improved by 30 – 50% when integrating four MEMS-IMUs in skew-redundant configuration. Later part of this research introduces a methodology for trajectory comparison. It is shown that trajectories based on dual-frequency GPS positions can be directly modeled and compared using cubic spline smoothing, while those derived from single-frequency DGPS require additional filtering and matching.

[1]  A. Schorderet,et al.  Synthèse modale et problème inverse en dynamique des structures , 1997 .

[2]  J. Slawinski,et al.  Use of Lumbar Point for the Estimation of Potential and Kinetic Mechanical Power in Running , 2004 .

[3]  Allison Kealy,et al.  A performance analysis of future global navigation satellite systems , 2004 .

[4]  Eric Dormegnie,et al.  Tyre Modelling for NVH Engineering in ADAMS , 2002 .

[5]  Michael S. Braasch,et al.  Performance comparison of multipath mitigating receiver architectures , 2001, 2001 IEEE Aerospace Conference Proceedings (Cat. No.01TH8542).

[6]  P. Veltink,et al.  Compensation of magnetic disturbances improves inertial and magnetic sensing of human body segment orientation , 2005, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[7]  Bernt Schiele,et al.  Design, Implementation and Testing of a Wearable Sensing System for Professional Downhill Skiing in Cooperation with Trainers , 2005 .

[8]  Mark G. Petovello,et al.  Twin IMU-HSGPS Integration for Pedestrian Navigation , 2008 .

[9]  K. P. Schwarz,et al.  Testing a decentralized filter for GPS/INS integration , 1990, IEEE Symposium on Position Location and Navigation. A Decade of Excellence in the Navigation Sciences.

[10]  James S. Meditch,et al.  Stochastic Optimal Linear Estimation and Control , 1969 .

[11]  Alain Schorderet,et al.  Structural Dynamics Optimization Based on a Hybrid Inverse Synthesis Method Using a Quadratic Approximation , 2004 .

[12]  R. C. Hansen.  Electrically Small Antennas , 2006 .

[13]  R. Hatch.  The synergism of GPS code and carrier measurements , 1982 .

[14]  Richard B. Langley,et al.  High-Accuracy Point Positioning with Low-Cost GPS Receivers: How Good Can It Get? , 2005 .

[15]  Kyle O'Keefe.  Availability and Reliability Advantages of GPS/Galileo Integration , 2001 .

[16]  J. Skaloud,et al.  An Eye for Landscapes - Rapid Aerial Mapping with Handheld Sensors , 2006 .

[17]  Jan Wendel,et al.  A Performance Comparison of Tightly Coupled GPS/INS Navigation Systems based on Extended and Sigma Point Kalman Filters , 2005 .

[18]  Alexei E. Zinoviev.  Using GLONASS in Combined GNSS Receivers: Current Status , 2005 .

[19]  Stéphane Guerrier.  Integration of Skew-Redundant MEMS-IMU with GPS for Improved Navigation Performance , 2008 .

[20]  Marie M. Largay,et al.  Comparative Analysis of GPS Clock Performance Using Both Code-Phase and Carrier-Derived Pseudorange Observations , 2004 .

[21]  F. Vernotte,et al.  A Bayesian method for oscillator stability analysis , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[22]  Kwang-Ho Bae,et al.  Edge and tree detection from three-dimensional unorganised point clouds from terretrial laser scanners , 2004 .

[23]  Pierre-Yves Gilliéron,et al.  Challenging EGNOS in the Swiss Alps , 2003 .

[24]  Eric Lantz,et al.  A new multi-variance method for the oscillator noise analysis , 1992, Proceedings of the 1992 IEEE Frequency Control Symposium.

[25]  Zhiqiang Xing,et al.  Modeling and bounding low cost inertial sensor errors , 2008, 2008 IEEE/ION Position, Location and Navigation Symposium.

[26]  John A. Marchant,et al.  Controllability and Observability: Tools for Kalman Filter Design , 1998, BMVC.

[27]  Hans B. Pacejka,et al.  THE MAGIC FORMULA TYRE MODEL , 1991 .

[28]  Hugh F. Durrant-Whyte,et al.  A Low-Cost, Redundant Inertial Measurement Unit for Unmanned Air Vehicles , 2000, Int. J. Robotics Res..

[29]  Michael Brady,et al.  Feature-based correspondence: an eigenvector approach , 1992, Image Vis. Comput..

[30]  Jonathan P. How,et al.  GPS estimation algorithms for precise velocity, slip and race-track position measurements , 2002 .

[31]  Florian Michahelles,et al.  Sensing and monitoring professional skiers , 2005, IEEE Pervasive Computing.

[32]  Antti Lehtinen.  Doppler positioning with GPS , 2002 .

[33]  D. Gingras,et al.  Comparison between the unscented Kalman filter and the extended Kalman filter for the position estimation module of an integrated navigation information system , 2004, IEEE Intelligent Vehicles Symposium, 2004.

[34]  C. Jekeli.  Inertial navigation systems with geodetic applications , 2000 .

[35]  R. Grover Brown,et al.  A Baseline GPS RAIM Scheme and a Note on the Equivalence of Three RAIM Methods , 1992 .

[36]  Joseph M. Strus,et al.  Development of a High Accuracy Pointing System for Maneuvering Platforms , 2007 .

[37]  I. Colomina,et al.  REDUNDANT IMUS FOR PRECISE TRAJECTORY DETERMINATION , 2004 .

[38]  W.J. Riley,et al.  Enhancements to GPS operations and clock evaluations using a "total" Hadamard deviation , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[39]  H Harry Asada,et al.  Wearable Conductive Fiber Sensors for Multi-Axis Human Joint Angle Measurements , 2005, Journal of NeuroEngineering and Rehabilitation.

[40]  Le Concept d"intégrité d"EGNOS , 2003 .

[41]  Jan Skaloud,et al.  Assessment of the Integration Strategy between GPS and Body-Worn MEMS Sensors with Application to Sports , 2007 .

[42]  G.R. Opshaug,et al.  Integrated GPS and UWB navigation system: (motivates the necessity of non-interference) , 2002, 2002 IEEE Conference on Ultra Wideband Systems and Technologies (IEEE Cat. No.02EX580).

[43]  Sergey G. Revnivykh,et al.  Status and development of GLONASS , 2004 .

[44]  Rudolph van der Merwe,et al.  Sigma-point kalman filters for probabilistic inference in dynamic state-space models , 2004 .

[45]  Olivier Staub.  Electrically small antennas , 2001 .

[46]  J. Oaks,et al.  NRL analysis of GPS on-orbit clocks , 2005, Proceedings of the 2005 IEEE International Frequency Control Symposium and Exposition, 2005..

[47]  K.P. Schwarz,et al.  Aided versus embedded-a comparison of two approaches to GPS/INS integration , 1994, Proceedings of 1994 IEEE Position, Location and Navigation Symposium - PLANS'94.

[48]  J. Skaloud,et al.  Accurate Trajectory and Orientation of a Motorcycle derived from low-cost Satellite and Inertial Measurement Systems , 2008 .

[49]  D. I NEICHEN,et al.  Enhancing the Swiss Permanent GPS Network ( AGNES ) for GLONASS , 2008 .

[50]  Jan Skaloud,et al.  Turning Point - Trajectory Analysis for Skiers , 2007 .

[51]  N. El-Sheimy,et al.  INS error model improvement for enhanced INS/GPS navigation during GPS signal blockage periods , 2006 .

[52]  James Fisher,et al.  A Study of Galileo Performance - GPS Interoperability and Discriminators for Urban and Indoor Environments , 2002 .

[53]  Yong Li,et al.  Low-cost tightly coupled GPS / INS integration based on a nonlinear Kalman filtering design , 2006 .

[54]  Fredrik Gustafsson,et al.  Particle filters for positioning, navigation, and tracking , 2002, IEEE Trans. Signal Process..

[55]  Yuanxi Yang,et al.  An Optimal Adaptive Kalman Filter , 2006 .

[56]  N. El-Sheimy,et al.  Improvement of MEMS-IMU/GPS performance using fuzzy modeling , 2006 .

[57]  Mark A. Sturza,et al.  Navigation System Integrity Monitoring Using Redundant Measurements , 1988 .

[58]  P.H. Veltink,et al.  Inclination measurement of human movement using a 3-D accelerometer with autocalibration , 2004, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[59]  Pierre Roduit.  Trajectory analysis using point distribution models , 2009 .

[60]  Hervé Gontran,et al.  Techniques GPS-RTK appliquées à la trajectographie , 2004 .

[61]  Chris Hide,et al.  Adaptive Kalman Filtering for Low-cost INS/GPS , 2002, Journal of Navigation.

[62]  B. Yegnanarayana,et al.  Artificial Neural Networks , 2004 .

[63]  Robin J. Y McLeod,et al.  Geometry and Interpolation of Curves and Surfaces , 1998 .

[64]  Mangesh Chansarkar.  Neural Networks in GPS Navigation , 2000, GPS Solutions.

[65]  G. Lachapelle,et al.  Augmentation of GPS for Ship Navigation in Constricted Water Ways , 1998 .

[66]  Jan Skaloud,et al.  Assessment of Timing and Performance based on Trajectories from low-cost GPS/INS Positioning , 2007 .

[67]  Chalermchon Satirapod,et al.  GPS Precise Point Positioning Software for Ground Control Point Establishment in Remote Sensing Applications , 2006 .

[68]  S. Julier,et al.  A General Method for Approximating Nonlinear Transformations of Probability Distributions , 1996 .

[69]  Yong Yang,et al.  Tightly coupled MEMS INS/GPS integration with INS aided receiver tracking loops , 2008 .

[70]  Aboelmagd Noureldin,et al.  Optimizing neuro-fuzzy modules for data fusion of vehicular navigation systems using temporal cross-validation , 2007, Eng. Appl. Artif. Intell..

[71]  A. Leick.  GPS satellite surveying , 1990 .

[72]  Günter W. Hein,et al.  From GPS and GLONASS via EGNOS to Galileo – Positioning and Navigation in the Third Millennium , 2000, GPS Solutions.

[73]  Paul Dierckx,et al.  Curve and surface fitting with splines , 1994, Monographs on numerical analysis.

[74]  Xiaoji Niu,et al.  Analysis and Modeling of Inertial Sensors Using Allan Variance , 2008, IEEE Transactions on Instrumentation and Measurement.

[75]  Jan Skaloud,et al.  GSM-Distributed RTK for Precise Analysis of Speed Skiing , 2004 .

[76]  J. Skaloud,et al.  Redundant MEMS-IMU integrated with GPS for performance assessment in sports , 2008, 2008 IEEE/ION Position, Location and Navigation Symposium.

[77]  Per Enge,et al.  GPS and UWB for indoor navigation , 2001 .

[78]  Akira Fukuda,et al.  Design of WiPS : WLAN-Based Indoor Positioning System , 2003 .

[79]  Jan Skaloud,et al.  DGPS-Calibrated Accelerometric System for Dynamic Sports Events , 2000 .

[80]  G. Strang,et al.  Linear Algebra, Geodesy, and GPS , 1997 .

[81]  A. H. Mohamed,et al.  Adaptive Kalman Filtering for INS/GPS , 1999 .

[82]  Jan Skaloud,et al.  Synergy of CP-DGPS, Accelerometry and Magnetic Sensors for Precise Trajectography in Ski Racing , 2003 .

[83]  Eric Lantz,et al.  Oscillator noise analysis: multivariance measurement , 1993 .

[84]  Haiying Hou,et al.  Modeling inertial sensors errors using Allan variance , 2004 .

[85]  Salah Sukkarieh,et al.  Low Cost, High Integrity, Aided Inertial Navigation Systems for Autonomous Land Vehicles , 2000 .

[86]  Rudolph van der Merwe,et al.  Efficient derivative-free Kalman filters for online learning , 2001, ESANN.

[87]  Nien Fan Zhang,et al.  The uncertainty associated with the weighted mean of measurement data , 2006 .

[88]  Ronald R. Hatch,et al.  GPS Multipath Mitigation in Measurement Domain and Its Applications for High Accuracy Navigation , 2004 .

[89]  A. Somieski,et al.  Precise Point Positioning with Single-Frequency Mass Market Receivers , 2008 .

[90]  Phillip Tomé,et al.  Improvement of Orientation Estimation in Pedestrian Navigation by Compensation of Magnetic Disturbances , 2008 .

[91]  C. Cobelli,et al.  A Markerless Motion Capture System to Study Musculoskeletal Biomechanics: Visual Hull and Simulated Annealing Approach , 2006, Annals of Biomedical Engineering.

[92]  Bernd Eissfeller,et al.  Real-Time Kinematic in the Light of GPS Modernization and Galileo , 2001 .

[93]  J. Richards,et al.  The measurement of human motion: A comparison of commercially available systems , 1999 .

[94]  Energy Management Optimization for a Solar Vehicle , 2006 .

[96]  Emma Frejinger,et al.  Route Choice Analysis: Data, Models, Algorithms and Applications , 2009 .

[98]  Jan Skaloud,et al.  Towards in-flight quality assessment of airborne laser scanning , 2008 .

[99]  Minh N. Do,et al.  Invariant Image Retrieval Using Wavelet Maxima Moment , 1999, VISUAL.

[100]  Andrew G. Dempster,et al.  A low-cost attitude heading reference system by combination of GPS and magnetometers and MEMS inertial sensors for mobile applications , 2006 .

[101]  Itzhack Y. Bar-Itzhack,et al.  REQUEST - A New Recursive Algorithm for Attitude Determination , 1996 .

[102]  Alexander Medvedev,et al.  Fault detection and isolation by a continuous parity space method , 1995, Autom..

[103]  I. Planovsky,et al.  GPS Antenna Phase Centre Position: precission, accuracy and time varaiability , 2002 .

[104]  Quentin Ladetto.  Capteurs et algorithmes pour la localisation autonome en mode pédestre , 2003 .

[105]  John Weston,et al.  Strapdown Inertial Navigation Technology , 1997 .

[106]  Kefei Zhang,et al.  Towards a Low-Cost, High Output Rate, Real-Time GPS Rowing Coaching and Training System , 2003 .

[107]  Jan Skaloud,et al.  Assessment of GPS/MEMS-IMU Integration Performance in Ski Racing , 2007 .

[108]  Sang Jeong Lee,et al.  An Assisted GPS Acquisition Method using L2 Civil Signal in Weak Signal Environment , 2004 .

[109]  Jon Rigelsford.  Handbook of Neural Network Signal Processing , 2003 .

[110]  Wyatt Page,et al.  Fusion motion capture: A prototype system using inertial measurement units and GPS for the biomechanical analysis of ski racing , 2008 .

[111]  Arthur J. Pejsa,et al.  Optimum Skewed Redundant Inertial Navigators , 1973 .

[112]  Michael S. Braasch,et al.  Evaluation of GNSS Receiver Correlation Processing Techniques for Multipath and Noise Mitigation , 1997 .

[113]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice , 1993 .

[114]  X. Pennec.  Computing the Mean of Geometric Features Application to the Mean Rotation , 1998 .

[115]  Michel Bierlaire,et al.  Capturing correlation with subnetworks in route choice models , 2007 .

[116]  Simon J. Julier,et al.  The scaled unscented transformation , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[117]  Simon J. Julier,et al.  The spherical simplex unscented transformation , 2003, Proceedings of the 2003 American Control Conference, 2003..

[118]  Richard G. Mach,et al.  New, improved GPS: The legacy accuracy improvement initiative , 2006 .

[119]  P. Savage.  Strapdown Inertial Navigation Integration Algorithm Design Part 1: Attitude Algorithms , 1998 .

[120]  David Törnqvist,et al.  Statistical Fault Detection with Applications to IMU Disturbances , 2006 .

[121]  Per Enge,et al.  GPS Modernization: Capabilities of the New Civil Signals , 2003 .

[122]  M. Shuster,et al.  Three-axis attitude determination from vector observations , 1981 .

[123]  Peter H. Veltink,et al.  Measuring orientation of human body segments using miniature gyroscopes and accelerometers , 2005, Medical and Biological Engineering and Computing.

[124]  Shaojun Feng,et al.  A measurement domain receiver autonomous integrity monitoring algorithm , 2006 .

[125]  Jaewoo Jung,et al.  Civilian GPS: The Benefits of Three Frequencies , 2000, GPS Solutions.

[126]  Salah Sukkarieh,et al.  Tightly Coupled INS/GPS with Bias Estimation for UAV Applications , 2004 .

[127]  K. Daly,et al.  FDI Performance of Two Redundant Sensor Configurations , 1979, IEEE Transactions on Aerospace and Electronic Systems.

[128]  Robert C. Williams,et al.  Speeds Associated With Skiing and Snowboarding , 2007, Wilderness & environmental medicine.

[129]  Naser El-Sheimy,et al.  Multi-sensor Inertial Navigation Systems Employing Skewed Redundant Inertial Sensors , 2006 .

[130]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[131]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[132]  Rudolph van der Merwe,et al.  The unscented Kalman filter for nonlinear estimation , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).

[133]  V. Klimov,et al.  GLONASS Status, Performance and Perspectives , 2005 .

[134]  Jean-Marie Bonnaz,et al.  L"analyse de performance sportive à l"aide d"un système GPS/INS low-cost: évaluation de capteurs inertiels de type MEMS , 2007 .

[135]  Thomas Blumenbach,et al.  GPS-Anwendungen in der Sportwissenschaft: Entwicklung eines Messverfahrens für das Skispringen , 2004 .

[136]  K. Schwarz,et al.  Differentiation for High-Precision GPS Velocity and Acceleration Determination , 1999, GPS Solutions.

[137]  Naser El-Sheimy,et al.  A combined algorithm of improving INS error modeling and sensor measurements for accurate INS/GPS navigation , 2006 .

[138]  Sergey Revnivykh,et al.  GLONASS Status and Progress , 2010 .

[139]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[140]  Hervé Gontran,et al.  Réalisation d"un serveur de corrections GPS accessible par GPRS , 2006 .

[141]  Ian Oppermann,et al.  UWB wireless sensor networks: UWEN - a practical example , 2004, IEEE Communications Magazine.

[142]  Jeremie Godet,et al.  Status of Galileo Frequency and Signal Design , 2002 .

[143]  Ulrich Vollath.  The Factorized Multi-Carrier Ambiguity Resolution (FAMCAR) Approach for Efficient Carrier-Phase Ambiguity Estimation , 2004 .

[144]  Zhaoying Zhou,et al.  A real-time articulated human motion tracking using tri-axis inertial/magnetic sensors package. , 2004, IEEE transactions on neural systems and rehabilitation engineering : a publication of the IEEE Engineering in Medicine and Biology Society.

[145]  Huamin Jia,et al.  A Review of Multisensor Fusion Methodologies for Aircraft Navigation Systems , 2005 .

[146]  M. E. Cannon,et al.  GPS/MEMS INS integrated system for navigation in urban areas , 2007 .

[147]  Alcherio Martinoli,et al.  A quantitative method for comparing trajectories of mobile robots using point distribution models , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[148]  Yang Gao,et al.  Kinematic Processing Analysis of Carrier Phase based Precise Point Positioning , 2002 .

[149]  Kefei Zhang,et al.  GNSS for sports - sailing and rowing perspectives , 2004 .

[150]  D. W. Allan,et al.  Statistics of atomic frequency standards , 1966 .

[151]  M. Esashi,et al.  Electrostatically levitated spherical 3-axis accelerometer , 2002, Technical Digest. MEMS 2002 IEEE International Conference. Fifteenth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.02CH37266).

[152]  K. C. Daly,et al.  Generalized Likelihood Test for FDI in Redundant Sensor Configurations , 1979 .

[153]  Gérard Lachapelle,et al.  Augmentation of DGNSS With Dynamic Constraints For Marine Navigation , 1999 .

[154]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[155]  Sylvain Pittet,et al.  UWB and MEMS Based Indoor Navigation , 2008, Journal of Navigation.