By L. T. Leondes

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**Extra resources for Advances in Aerospace Systems Dynamics and Control Systems/Part 1 of 3**

**Example text**

Its volume V is given by Eq. (14), that is, k V = c *' \S(k)\v\ n k 2 (23) nJ where c„ is the volume of the ^-dimensional unit hypersphere. Let the set of validated measurements at time k be denoted as z fc Z(fc) = {z (fc)}r= , i 1 (24) where m is the number of validated measurements. The cumulative set of measurements up to time k is denoted as k Z ={Z(j)} . k k j=1 Starting from here, one cycle of the P D A F algorithm is described next. (25) 42 C. PETER B. L Ü H et al. , m , and 9 (k) the event t ( fc 0 that none of the measurements is from the target.

However, since it is not known which of the m validated measurements is correct, the term P(k) defined in Eq. (36), which is positive semidefinite, increases the covariance of the updated state; this is the effect of measurement origin uncertainty. N o t e that P(k | k) depends on measurements, which is typical for nonlinear filters. T o go from time k to k + 1, we note that the conditional pdf of x(k + 1) given Z is a gaussian mixture, not gaussian. T o simplify the process, however, we adopt the fundamental assumption of the P D A F [Eq.

R. , "An Information Theoretic Approach to Dynamic System Modeling and Identification," IEEE Trans. Autom. Control AC-23, 61-66 (1978). 45. Y. B A R A M and N . R. , "Consistent Estimation of Finite Parameter Sets with Application to Linear Systems Identification," IEEE Trans. Autom. Control AC-23,451-454 (1978). 46. Κ. I. D. Dissertation, Rep. LIDS-TH-920, M I T Laboratory for Information and Decision Systems, Cambridge, Massachusetts, July 1979. 47. V B. V E N K A Y Y A and V. A. TISCHLER, "Frequency Control and Its Effects on Dynamic Response of Flexible Structures," AIAA J.