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The probability of lateral overlap in the ICAO model is based on the assumption that 50%
of large navigational errors would be detectable and correctable with ADS. The
parameter a in the double-double exponential distribution is adjusted to relate ADS effects
to the collision risk model.
The study estimated maximum track loading or maximum insertion rate into a single track
as the rough longitudinal equivalent of lateral separation between adjacent, parallel
oceanic tracks. While the lateral modeling expressions reflect probabilities of uncontrolled
EXISTING MODELS AND MODELING TOOLS
6-17
overlap,2 the longitudinal modeling uses explicit time buffers related to the tactical
intervention cycle in the following operational scenario.
1. An aircraft operates without intervention until its separation from the lead
aircraft decreases to or below a preset alarm distance. This alarm is a trigger
point for tactical intervention by the controller, not an operational error.
2. After analyzing the situation, a controller issues tactical control instructions.
The scenario assumes that the controller must use only speed control to
maintain separation.
3. On receiving the tactical instructions, the pilot acknowledges the commands
and executes the speed change maneuvers.
4. The time to implement the speed change includes the estimated response time
of the aircraft control system.
The total initial longitudinal separation is determined as the sum of three buffers (or
regions), expressed in terms of minutes: surveillance accuracy region, intervention rate
region, and tactical control region. Traffic densities depend on the initial separation, but
the initial longitudinal separation is not the minimum separation that the controller is
required to protect. A surveillance accuracy region is sized to provide a Minimum
Indicated Separation (MIS). This includes a minimum actual separation plus an allowance
for inaccuracies in the indicated positions displayed on the controller’s console. An
intervention rate region is sized to balance the need for closely spaced traffic with the
controller workload needed to deal with frequent tactical interventions. A tactical control
region is sized by probabilistic addition of delays attributable to controller scanning,
controller recognition, communication delay, pilot reaction, and aircraft response.
Main inputs and outputs
The starting points for this study are the same inputs and outputs used for the ICAO
Collision Risk Model. The estimates of ADS detectable and correctable errors were
determined by direct examination of all recorded navigational errors greater than 20
nautical miles in the North Atlantic airspace. With ADS and improved navigational
accuracy, the study estimates that lateral separations could be safely reduced to as little as
30 nm. Using the longitudinal analysis, the sum of the longitudinal buffer zones was also
just under 30 nm.
The factors in the intervention rate region are related as follows:
P IR P i P j a S l
i IR j i
( ) = ( ) * ( )
³ >
åå (2)
2 The form of the lateral equations anticipates uncontrolled overlap. As previously presented, the effect of
tactical intervention can be “hidden” by changing the parameters of the navigational error probability
function. Despite this, the lateral equations do not reveal the direct connection between intervention
performance parameters and the resulting changes in collision risk.
SEPARATION SAFETY MODELING
6-18
where,
IR = intervention rate region (in minutes),
Pa(IR) = probability of intervention alarm,
PS(i) = probability of Total Initial Longitudinal Separation of i minutes,
Pl(j) = probability of separation loss of j minutes.
The tactical control region is based on the sum of random variables representing the
various sources of delay. This is in contrast to making a worst-case allowance for each
source and adding up all of the worst-case buffers. The result is an operational worst-case
that takes into account that some delay from one source may be offset by less delay from
another source. Mathematically, this requires computing the convolution of the
probability density functions of an operational sequence that must take place in a given
order. The safety buffer is then set by choosing a target level on the combined, cumulative
probability distribution function.
The minimum indicated separation is based on the current oceanic system probability of
longitudinal overlap during maximum track loading and the probability density function
(PDF) f(x) expressing the accuracy of longitudinal position determination. The Minimum
Indicated Separation, Sx, is determined by numerically inverting the integral formula:
　
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