Multiple Models — Fixed, Switching, Interacting
In dynamic models the dynamic and the observation equations are based on a known system model. The multiple model approach introduces uncertainties about the system model by a set of possible system models. In the multiple model approach for fixed models the true system does not change during the whole observation process, wheareas in the approach for switching models a jump from one model to another is allowed. In the later case the state estimation usually has to be approximated, e.g. by so-called interacting multiple models. The multiple model approach for fixed, switching and interacting models are presented and their application for GNSS ambiguity resolution is discussed, but open questions still remain.
KeywordsBayesian statistics ambiguity resolution model uncertainty recursive estimation multiple models interacting multiple models
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- Betti B, Crespi M, Sanso F (1993). A geometric illustration of ambiguity resolution in GPS theory and a Bayesian approach. Manuscripta Geodaetica 18: 317–330.Google Scholar
- Blom HAP (1984). An efficient filter for abruptly changing systems. In: Proc. 23rd IEEE Conf. Decision and Control, Las Vegas, NV, Dec. 1984.Google Scholar
- Brown RG, Hwang PYC (1983). A Kalman filter approach to precision GPS geodesy. Journal of The Institute of Navigation 30: 338–349.Google Scholar
- Chen G, Harigae M (2001). Precise DGPS positioning and carrier phase ambiguity resolution using IMM Kalman filters. In: Proc. of International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation (KIS 2001), Banff, Canada, June 5–8 2001, 339–346.Google Scholar
- Henderson P (2001). Flight test of a multiple filter approach for precise DGPS positioning and carrier-phase ambiguity resolution. ION GPS 2001, 11–14Google Scholar
- September 2001, Salt Lake City UT: 1565–1574.Google Scholar
- Koch KR (2000). Einführung in die Bayes—Statistik. Springer, Berlin Heidelberg New York.Google Scholar
- Magill DT (1965). Optimal adaptive estimation of sampled stochastic processes. IEEE Trans. Automatic Control, AC-10: 434–439, 1965.Google Scholar
- Teunissen (1994). A new method for fast carrier phase ambiguity estimation. In: Proceedings IEEE Position Location and Navigation Symposium, PLANS ‘84, 562–573, Las Vegas, Nevada.Google Scholar
- Wolfe JD, Williamson WR, Speyer IL (2001). Hypothesis testing for resolving integer ambiguity in GPS. ION GPS 2001, 11–14 September 2001, Salt Lake City UT: 15221531.Google Scholar