Air Traffic Management and Systems: Selected Papers of the by Electronic Navigation Research Inst

By Electronic Navigation Research Inst

The digital Navigation learn Institute (ENRI) held its third International Workshop on ATM / CNS in 2013 with the subject matter of "Drafting the destiny sky".

There is around the globe task occurring within the learn and development of sleek air site visitors administration (ATM) and its permitting applied sciences in Communication, Navigation and Surveillance (CNS).

Pioneering paintings is important to give a contribution to the worldwide harmonization of air site visitors administration and regulate. At this workshop, top experts in examine, and academia from worldwide met to share their principles and methods on ATM/CNS comparable topics.

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The wind prediction error represents uncertainty in the meteorological prediction, and for simplicity the only wind prediction error is considered. Because the Gaussian distributions are used for the uncertainties in this paper, Hermite polynomial basis functions collocated at Gauss-Hermite quadrature points are selected for the gPC method as suggested in the paper by Xiu [22]. The stochastic solution of the terminal time t f is calculated by using our proposed stochastic approach. In addition, to verify the effectiveness and performance of our proposed method, the stochastic solution is computed by using Monte Carlo method, one of the most commonly used methods for solving stochastic differential equations, and compared with the solution that is calculated by using our proposed approach.

In addition, the statistical information of the stochastic solution can be calculated by using the coefficients given by Eq. (11), and evaluates how the solution varies with the random variables. The expected value of the solution is described as the following equation. E[z(p)] ≈ E[zM (p)] = M ∑ Cm Φm (p) m=1 The variance is calculated by the following equation. ρ (p)d p = C1 (12) Probabilistic Conflict Detection in the Presence of Uncertainty 23 var[z(p)] = E[(z(p) − E[z(p)])2 ] ≈ E[(zM (p) − E[zM (p)])2 ] M ∑ Cm Φm (p) − C1 = 2 ρ (p)d p m=1 = M ∑ [Cm ]2 (13) m=2 By the theory of the gPC method, the stochastic solution including the statistical information (expected value and variance) is approximated and determined.

3. 2 Merging Scenario in Case 2 As shown in Fig. 3, the merging scenario of the three aircraft, labeled A, B, and C, flying at the same altitude (35,000 ft) and the same speed of V = 450 knots (true airspeed) is considered. The initial and terminal conditions of the aircraft A, B, and C are as follows. 5, π /2)T (21) where t f A , t f B , and t fC are the terminal time (or the time of arrival at the merging point) of the aircraft A, B, and C, respectively. Using our proposed stochastic approach described in Sect.

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