Model based Conflict Detection & Resolution

& Coordination of approach manoeuvres demo

Yannis Lymperopoulos & Yannis Lygeros

Systems and Measurements Laboratory

University of Patras

(in collaboration with A. Lecchini, W. Glover and J. Maciejowski,University of Cambridge)

Aircraft Trajectory Prediction(during take-off)

Formulation of the problemThe Aircraft ModelA first approach to the problemResults Future ideas

+DEMO: Coordination of approach manoeuvres using a “Roissy -Charles De Gaulle” set-up

Formulation of the problem

While taking off, there is great uncertainty about the future position of the aircraft.

Sources of uncertaintyInitial mass of the aircraft (undisclosed information)Wind and wind perturbations/disturbances (forecasts are approximations and account for very large areas)FMS settings (e.g. max thrust settings)

also:Model inaccuraciesHuman factors (pilots, controllers)

Improve on the prediction errors

When aircrafts are climbing or descending their future position is more unpredictable than when cruising

Uncertainty increases with look ahead time

Improve by measuring the position

Measure the position of the aircraft (every 6 or 12 seconds) with a RADARThe acquired trajectory encapsulates information about the missing parameters and the windUse this information to improve on your current estimation of the future

The aircraft model

Hybrid – combines continuous and discrete dynamicsConsiders the wind as a stochastic process, correlated in space and timeUses realistic flight plans from CFMUAcquires specific aircraft parameters from BADA (speed_profile, engine_type, mass, coefficients ...)Implements a Flight Management system (bank angle, flight path angle and thrust control)Includes nominal wind from RUC database.

Block Diagram of the model

State of the Aircraft Model

Continuous state (x)[Position (X1,X2,h)][True Airspeed V][Heading (psi)]

Inputs (u)Thrust (u1)Bank angle (phi)Flight path (gamma)

Discrete state FL: Flight LevelWP: Way point indexAM: Acceleration modeCM: Climb modeTrM: Troposphere modeSHM: Speed hold modeFP: Flight phaseRPM: Reduced power mode

CRM : Cruise mode

Goal

Use this model to predict the future positionof an aircraft, given the:

initial position in the RUNWAY (0.0 , 0.0)first way-point before starting cruisingunknown: aircraft_mass, wind evolution

Another problem arises: Measurement inaccuracyThe scale of the radar error is

small (comparable to the size of the aircraft) and such a distance

is covered in a fraction of a second

What is the current uncertainty?

What is the current uncertainty?

What is the current uncertainty?

Different scenarios give a maximum uncertainty of over 70.000 meters after 20 minutes from takeoff

Our prediction of aircraft position for more than 4 minutes breaks the line of safe separation(5nmi) by far and increasingly with time

A first approach to the problem

Create an “actual” trajectory using specific parameters and store the wind componentsImpose a Gaussian noise on this trajectory to represent measurement errors (we assume a RADAR accuracy of 60 meters).Implement an algorithm that uses the measurements to construct the posterior distribution of trajectories

Algorithm

I. Extract parameters: (m,w)(i) ~ g(m,w), i=1,...,N N=Number of configurations, m ~ Uniform, w ~ Gaussian

II. Simulate using (m,w)(i) to create a respective trajectory X(i)

III.Measure: Get a number of measurements Y1,...,YT, every 12 seconds, for the first 4 minutes (T=20) of the flight referring to the “actual” trajectory

IV.Weight each one of the trajectories to create the posterior:

P( X(i) | Y1:T ) => the probability, that this specific trajectory has

actually happened, given the measurements.

Weight the trajectories

weight(i) = P( m(i), w(i) | Y1:T ) => the probability that these parameters were the actual ones, given the measurements

oc L(m,w | Y1,...,YT) g(m,w) = L(m,w | Y1) L(m,w | Y2)......L(m,w | YT) g(m,w)

Calculate L(m,w | YK) = P(YK | m,w) => the probability that we got measurement YK using the specific parameters. That is, the probability, our Gaussian noise (N(0,400)) gave an error YK-XK.

Calculate g(m,w) => the probability that our prior distribution provided us with those parameters.

A possible problem - Degeneracy

Depending on the number of extractionsOne trajectory will have a huge weight, while all the others a weight close to zeroThis will be considered the most prominent to fit the actual trajectory, and the best prediction of future position available

Results

Horizontal and vertical distance

Trajectory prediction

Parameter identification

massestimated : 120800kgactual: 121940kg

wind initially there is informationon the effect of the wind fromthe measurements. As timeelapses and (1) no new measurements arrive, (2) thewind is less correlated to theprevious samples => the wind estimation worsens

Future ideas

Acquire real aircraft trajectories, to compare withCreate an aircraft model that moves to its next state stochastically (currently deterministic)Define a two stage process that estimates the position and identifies the parameters

Best candidate:

Sequential Monte Carlo Algorithm

I. Initialize X0(i) ~ P0(x0) i=1,...,N (set t = 1)II. Importance Sampling Step

I. Evolve X0:t(i) from X0:t-1

II. Evaluate the importance weights for each X0:t(i)

III.Selection StepI. Multiply/Discard particles with respect to high low

normalized importance weights to obtain N equally weighted particles X''0:t(i)

IV. Markov transition stepI. Sample X0:t(i) ~ M( X0:t(i) | X''0:t(i) ), where M( . | . ) is a

transition kernel of invariant distribution Pt(X0:t)II. Set t = t + 1 and go to step II

Conclusions

Greater ATM complexity requires more advanced DSTs (Decision Support Tools)The current ability for prediction of future aircraft positions will soon become insufficientThe uncertainty is really high during climb or descend proceduresGoal: Predict with high accuracy the location of an aircraft given a small amount of measurements (2-4 minutes)

Coordination of approach manoeuvres DEMO

A. Lecchini, W.Glover, J.Lygeros, J.MaciejowskiFind an optimal solution for the “trombone manoeuvre”

The method measures the performance of each of the feasible configurations (time of arrival)The constraint:

the trajectories should maintain safe separationthe aircraft must reach 1500ft before glide

MCMC simulation to achieve maximum performancegenerate trajectories for different parameters accept those that fit the constraint, with a probability for the ones with “superior performance”

Roissy - Charles De Gaulle IAF

Set-up for 2 aircrafts arriving simultaneously

nmi

Optimal configurations

Simulation DEMO

~interactive