Automatic determination of aircraft holding locations and holding durations from aircraft surveillance data
A method using airport surveillance data to output a location of a delay and an amount of time a vehicle is subjected to the delay during a movement of the vehicle between two locations, the delays being observed in the surveillance data as a knot of several data points. A first method is used to identify proposed knots based on distances between individual data points within the data. A second method is used to identify proposed knots based on the speed of the vehicle. Another method can be used to separate proposed knots have been incorrectly joined together. This method performs the separation by arranging the data points into a two-dimensional grid to form clusters of grid cells having data points. The location of the individual cells is then analyzed to determine whether clusters should be separated. Each of the remaining clusters defines a hold where the vehicle is delayed.
1. A method using airport surveillance data to output a location of a delay and an amount of time a vehicle is subjected to the delay during a movement of the vehicle between a first location and a second location, the method comprising:
obtaining a time-ordered sequence of data points representing the movement of the vehicle, each data point including an (x) position coordinate and a (y) position coordinate, at a particular time represented by a time stamp;
creating a vector (v) including a plurality of elements by performing the following steps for each data point (i) in the time ordered sequence, each of the elements corresponding to a respective one of the data points from the time ordered sequence, the steps comprising:
calculating a radial distance (r i,j ) between the (x) and (y) coordinates of the data point (i) and the (x) and (y) coordinates of each of the remaining data points (j), each radial distance (r i,j ) being equal to [(x i −x j ) 2 +(y i −y j ) 2 ] 1/2 ; and
recording one of a zero (0) entry and a number (N) entry as one element in the vector (v) corresponding to the data point (i), the zero (0) entry if there are no radial distances (r i,j ) that are less than a predetermined distance (r min ), the number (N) entry being the number of radial distances (r i,j ) that are equal to or less than the predetermined distance (r min );
replacing all of the number (N) entries in the vector (v) that have a value greater than a predetermined value (K) with a one (1) entry;
replacing all of the number (N) entries in the vector (v) that have a value equal to or less than the predetermined value (K) with a zero (0) entry;
replacing each zero (0) entry in the vector (v) with a one (1) entry if the zero (0) entry is a part of a sequence of consecutive zero (0) entries, the sequence of consecutive zero entries being less than a predetermined value (S);
defining a starting index and a stopping index within the vector (v) for each sequence of consecutive one (1) entries, each of the sequences of consecutive one (1) entries defining a proposed knot (ki);
performing the following steps for each proposed knot (ki):
finding a mean location (E(x), E(y)) for the proposed knot (ki), the mean location being the average of the (x) and (y) coordinates of the data points in the sequence of consecutive (1) entries in the proposed knot (ki);
calculating a radial distance (kr) between the mean location (E(x), E(y)) of the proposed knot and the (x) and (y) coordinates of each respective data point corresponding to the sequence of consecutive (1) entries in the proposed knot (ki); each radial distance (kr) being equal to [(x i −E(x)) 2 +(y i −E(y)) 2 ] 1/2 ;
computing a scale factor (m), where m=log e (length (r))/OSR, wherein OSR is a predetermined variable; and
dropping any data points from being associated with the proposed knot if its respective radial distance (kr) exceeds an average of all the radial distances (kr i,j ) for a given proposed knot+the scale factor (m)* a standard deviation of all the radial distances (kr) associated with the proposed knot;
eliminating any proposed knots that have less than a predetermined number (d) of data points remaining;
identifying the data points associated with any remaining proposed knot as being associated with the respective proposed knot; and
saving the data points identified onto a computer readable medium for at least one of review by an individual, production of a graphical display on a computer terminal, and production of a presentation document identifying those data points as being associated with one of the proposed knots.
2. The method according to claim 1 , wherein the predetermined distance (r min ) is between 15 feet and 30 feet.
3. The method according to claim 1 , wherein the predetermined distance (r min ) is 30 feet.
4. The method according to claim 1 , wherein the predetermined value (K) is between 5 and 15.
5. The method according to claim 1 , wherein the predetermined value (K) is 10.
6. The method according to claim 1 , wherein the predetermined value (S) is between 2 and 10.
7. The method according to claim 1 , wherein the predetermined value (S) is 5.
8. The method according to claim 1 , wherein the predetermined variable (OSR) is between 5 and 10.
9. The method according to claim 1 , wherein the predetermined variable (OSR) is 7.
10. The method according to claim 1 , wherein the predetermined number (d) is between 2 and 15.
11. The method according to claim 1 , wherein the predetermined number (d) is 5.
12. The method according to claim 1 , wherein the vehicle is an aircraft.