ARS  Vol.3 No.2 , June 2014
Fundamental Properties and Optimal Gains of a Steady-State Velocity Measured α-β Tracking Filter
Abstract: This paper clarifies the steady-state properties and performance of an α-β filter for moving target tracking using both position and velocity measurements. We call this filter velocity measured α-β (VM-α-β) filter. We first derive the stability condition and steady-state predicted errors as fundamental properties of the VM-α-β filter. The optimal gains for representative motion models are then derived from the Kalman filter equations. Theoretical and numerical analyses verify that VM-α-β filters with these optimal gains realize more accurate tracking than conventional α-β filters when the filter gains are relatively large. Our study reveals the conditions under which the predicted errors of the VM-α-β filters are less than those of conventional α-β filters. Moreover, numerical simulations clarify that the variance of the tracking error of the VM-α-β filters is approximately 3/4 of that of the conventional α-β filters in realistic situations, even when the accuracy of the position/velocity measurements is the same.
Cite this paper: Saho, K. (2014) Fundamental Properties and Optimal Gains of a Steady-State Velocity Measured α-β Tracking Filter. Advances in Remote Sensing, 3, 61-76. doi: 10.4236/ars.2014.32006.

[1]   Ekstrand, B. (2012) Some Aspects on Filter Design for Target Tracking. Journal of Control Science and Engineering, 2012, Article ID: 870890.

[2]   Kalman, R.E. (1960) A New Approach to Linear Filtering and Prediction Problems. ASME Journal of Basic Engineering, 82, 35-45.

[3]   Niknejad, H., Takeuchi, A., Mita, S. and McAllester, D. (2012) On-Road Multivehicle Tracking Using Deformable Object Model and Particle Filter with Improved Likelihood Estimation. IEEE Transactions on Intelligent Transportation Systems, 13, 748-758.

[4]   Gross, J., Gu, Y., Gururajan, S. and Seanor, B. (2004) A Comparison of Extended Kalman Filter, Sigma-Point Kalman Filter, and Particle Filter in GPS/INS Sensor Fusion. Proceedings of the IEEE Intelligent Vehicles Symposium, Parma, 14-17 June 2004, 831-835.

[5]   Koteswara, S. (2005) Modified Gain Extended Kalman Filter with Application to Bearings-Only Passive Maneuvering Target Tracking. IEE Proceedings Radar, Sonar and Navigation, 152, 239-244.

[6]   Tenne, D. and Singh, T. (2002) Characterizing Performance of α-β-γ Filters. IEEE Transactions on Aerospace & Elec-tronic Systems, 38, 1072-1087.

[7]   Benedict, T. and Bordner, G. (1962) Synthesis of Optimal Set of Radar Track-While-Scan Smoothing Equations. IRE Transactions on Automatic Control, 7, 27-32.

[8]   Bridgewater, A. (1970) Analysis of Second and Third Order Steady State Tracking Filters. Proceedings of AGARD Strategies for Automatic Track Initiation, Ottawa, 9-1-9-11.

[9]   Navarro, A. (1977) General Properties of Alpha Beta, and Alpha Beta Gamma Tracking Filters. National Defence Re-search Organization, TNO.

[10]   Kalata, P.R. (1984) The Tracking Index: A Generalized Parameter for at and Target Trackers. IEEE Transactions on Aerospace and Electronic Systems, AES-20, 174-182.

[11]   Blackman, S.S. (1986) Multiple Target Tracking with Radar Applications. Artech House, Dedham.

[12]   Gray, J. and Murray, W. (1991) The Response of the Transfer Function of an Alpha-Beta Filter to Various Measurement Models. Proceedings of 23rd Southeastern Symposium on System Theory, Columbia, 10-12 March 1991, 389-393.

[13]   Hasan, A.H. and Grachev, A.N. (2013) Adaptive α-β-Filter for Target Tracking Using Real Time Genetic Algorithm. Journal of Electrical and Control Engineering, 3, 32-38.

[14]   Wu, C., Chang, C. and Chu, T. (2011) An Implementation of Target Tracking by New GA-Based α-β-γ-δ Filter with Its Parameters Optimized by the Taguchi Method Source. International Journal of Organizational Innovation, 4, 148-164.

[15]   Mohammed, D., Mokhtar, K., Abdelaziz, O. and Abdelkrim, M. (2009) A New IMM Algorithm Using Fixed Coefficients Filters (fastIMM). International Journal of Electronics and Communications, 64, 1123-1127.

[16]   Chernoguz, N. (2007) Adaptive-Gain Kinematic Filters of Orders 2-4. Journal of Computers, 2, 17-25.

[17]   Baratchi, M., Meratnia, N., Havinga, P.J.M., Skidmore, A.K. and Toxopeus, B.A.G. (2013) Sensing Solutions for Collecting Spatio-Temporal Data for Wildlife Monitoring Applications: A Review. Sensors, 5, 6054-6088.

[18]   Valenti, R.G., Dryanovski, I. and Xiao, J.Z. (2013) A Non-Inertial Acceleration Suppressor for Low Cost Inertial Measurement Unit Attitude Estimation. Proceedings of 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO), Shenzhen, 12-14 December 2013, 639-644.

[19]   Zheng, C. (2010) Tracking Vehicular Motion-Position Using V2V Communication. Master Thesis, The University of Waterloo.

[20]   Ramachandra, K.V., Mohan, B.R. and Geetha, B.R. (1993) A Three-State Kalman Tracker Using Position and Rate Measurements. IEEE Transactions on Aerospace and Electronic Systems, 29, 215-222.

[21]   Jonghyuk, K. and Salah, S. (2005) 6DoF SLAM Aided GNSS/INS Navigation in GNSS Denied and Unknown Envi-ronments. Journal of Global Positioning Systems, 4, 120-128.

[22]   Gazit, R. (1997) Digital Tracking Filters with High Order Correlated Measurement Noise. IEEE Transactions on Aerospace and Electronic Systems, 33, 171-177.

[23]   Fitzgerald, R.J. (1982) Simple Tracking Filters: Position and Velocity Measurements. IEEE Transactions on Aerospace and Electronic Systems, AES-18, 531-537.

[24]   Farina, A. and Pardini, S. (1979) Multiradar Tracking System Using Radial Velocity Measurements. IEEE Transactions on Aerospace and Electronic Systems, AES-15, 555-563.

[25]   Gelb, A. (1974) Applied Optimal Estimation. The M.I.T. Press, Cambridge.