In order to estimate the collision risk in the process of airspace planning, a collision risk model based on distribution of initial time interval is proposed. In the collision risk model given some airspace planning parameters comprised of separation minimums, flight segment length, speeds of aircraft, the proportion of the aircraft type, flow rate, required navigation performance value, climb gradient or descend gradient are included. The influences of airspace planning parameters on collision risk can be characterized. The results show that vertical separation minimum have greater influences on the collision risk. A method to calculate the collision risk between intersecting flight tracks with planning parameters is developed. These would provide the method and theory to research the collision risk in the field of terminal airspace planning.

In this paper, Journe wavelet function is introduced as a wavelet generating function. The expression of reproducing kernel function for the image space of this wavelet transform is obtained based on the fact that the image space of the wavelet transform is a reproducing kernel Hilbert space. Then the isometric identity of Journe wavelet transform is obtained. The connections between the image space of the wavelet transform and the image space of the known reproducing kernel space are established by the theories of reproducing kernel. The properties and the structures of the image space of the wavelet transform can be characterized by the properties and the structures of the image space of the known reproducing kernel space. Using the ideas of reproducing kernel, we consider there are relations between the wavelet transform and the sampling theorem. Meanwhile, the approximations in sampling theorems is shown and the truncation error is given. This provides a theoretical basis for us to study the image space of the general wavelet transform and broadens the scope of application of theories of the reproducing kernel space.

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Practical sequential estimation algorithms inherently involve "iterated conditioning"; that is, the estimate at any algorithm step is conditioned o n information passed f r o m the previous step. Except in special cases, standard probability theory cannot deal with operations like iterated conditioning, so it is dificult even to formulate algorithms that make optimal use of the available information. The recently developed Product Space Conditional Event Algebra (PS-CEA) allows f o r the definition of '%onditional events" as regular events in a probability space, and thus f o r the extension of Bayesian analysis to cases of iterated conditioning. I n this paper, we describe the P S -C E A approach and give a n example of its use in deriving iterated image estimators when the information passed f r o m one stage to the next is the current image estimate.

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