Ellipsoid bounding estimation for kinematic geodetic positioning |
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| Affiliation: | 1. School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212003, China;2. Automation School, Harbin Engineering University, Harbin, Heilongjiang 150001, China;1. Dept. of Information Technology and Electrical Engineering, University of Naples “Federico II”, via Claudio 21, 80125 Naples, Italy;2. Dept. of Electrical and Information Engineering, University of Cassino and Southern Lazio, via G. Di Biasio, 43, 03043 Cassino, Italy;1. Key Laboratory of Underwater Acoustic Communication and Marine Information Technology (Xiamen University), Ministry of Education, Xiamen 361005, China;2. College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China;1. School of Instrument Science and Opto-Electronic Engineering, Hefei University of Technology, Hefei 230009, China;2. College of Electronic and Information Engineering, Anhui JIANZHU University, Hefei 230601, China;1. AGH University of Science and Technology, Department of Electronics, Krakow, Poland;2. Silicon Creations, 49 Highway 23 NE, Suwanee, GA 30024, USA;3. Singulus Technologies AG, 63796 Kahl am Main, Germany;4. INESC-MN and IN, 1000-029 Lisbon, Portugal;5. Physics Department, Instituto Superior Tecnico, Universidade de Lisboa, Portugal;6. INL-International Iberian Nanotechnology Laboratory, Avenida Mestre José Veiga s/n, 4715-330 Braga, Portugal |
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| Abstract: | In kinematic position estimation, a Kalman filter procedure is often used to provide improved solution benefiting from the history information. However, the optimal Kalman filtering solutions are subject to precise function models and statistic knowledge of noises, which may be difficult to obtain in advance. As a result, Kalman filter does not necessarily provide better performance for kinematic positioning solutions. In real world situations, a bound of the noise distribution would be easily and more reasonably determined than noise statistics. This paper studies ellipsoid bounding estimation for kinematic position estimation. In this estimation, neither process nor measurement noise characteristics are necessary, as long as the noises at each sample points can be confined in a bound (ellipsoid). A general trace criteria is adopted to choose the optimal estimator. For a the special case that only scalar measurement is available, e.g., a position measurement, we designed a modified intersection approach to reduce the estimation conservatism. Numerical results are given in each estimation step to illustrate the algorithm. A flight trajectory data is processed and the estimation results are compared under three different measurement noise cases: Gaussian white noise, uniformly noise (non-Gaussian) and the real measurement noise. Kalman filter results are also given for comparison. Results demonstrate the ellipsoid estimation indeed offers improved kinematic position solution in the sense of robustness for non-Gaussian noises, and retains nearly the same estimation error variance. |
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| Keywords: | Ellipsoid estimation Kalman filter Constant velocity model |
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