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Extra info for Sensor and Data Fusion (2009)
CRC Press, 2001.  W. Koch. Fixed-Interval Retrodiction Approach to Bayesian IMM-MHT for Maneuvering Multiple Targets. In IEEE TAES, 36, No. 1, (2000).  W. Koch. On Adaptive Parameter Control for Phased-Array Tracking. Signal and Data Processing of Small Targets, SPIE Vol. 3809, pp. 444-455, Denver, USA, July 1999.  W. Koch and G. van Keuk. On Bayesian IMM-Tracking for Phased-Array Radar. In Proc. DGON/ITG International Radar Symposium, IRS ’98, Conference Proceedings, p. 715-723, Mnchen (1998).
Even if bounds exist on the antecedent fuzzy set, the extension will not have an adverse effect on the result. The conclusion function bounds are more important, however. As seen in Figure 6, the output bounds are exceeded. One of the most useful properties of fuzzy sets is that crisp values can be given a fuzzy representation. A crisp value in an antecedent fuzzy set can be represented as a simple discrete unit impulse. For the consequence membership functions, the crisp value is represented as the Dirac delta function.
This is no longer true for S-IMM. The resultant curves related to r = 2 (solid) and r = 3 (dashed) significantly differ from each other. The onset of maneuvers (Figure 5) strongly affects the mean update intervals and thus illustrates the adaptivity of the algorithm. Advanced Sensor and Dynamics Models with an Application to Sensor Management 25 Fig. 6. Revisit intervals for different filters: military cargo aircraft, medium bomber, fighter/attack aircraft, and anti-ship missile 2. 3. 4. The difference between the cases r = 2, 3 vanishes however, if IMM-MHT is used.