Track algorithm

The original tracking algorithms were built into custom hardware that became common during World War II. This includes storage tubes used with planned position indicator displays, range height indicator displays, and pen-plotting boards used for civilian air traffic control and waterway management. It also includes custom analog computers, like the Mark I Fire Control Computer used with radar data to aim guns, missiles, and torpedoes associated with military air traffic control and waterway management.

Track algorithms were migrated from analog equipment to digital computers from the 1950s through the 1980s. This was necessary to eliminate limitations that include mid-air collisions and other problems linked with obsolete equipment that was socialized by PATCO and United States Department of Defense. Similar migration trends occurred in other countries throughout the world for similar reasons.

Modern civilian air traffic and military combat systems depend upon a custom track algorithms used with real-time computing slaved to displays and peripherals.

Limitation for modern digital computing systems are processing speed, input-output throughput rate, the number of input-output devices, and software compatibility with upgrade parts.

Tracking algorithms operate with a cartesian coordinate system. This is often called a rectangular coordinates, and is based on north–south, east–west, and altitude. Sensors operate using a polar coordinate system. This is often called spherical coordinates based on elevation, bearing, and range. Some common terminology is as follows.

Users are generally presented with several displays that show information from track data and raw detected signals.

• Plan position indicator
• Scrolling notifications for new tracks, split tracks, and join tracks
• Range amplitude display
• Range height indicator
• Angle error display
• Audible alerts (buzzer or voice)

The audible alert draws attention to the scrolling notification. This will present the track number for things like separation violation (impending collision) and lost track not located near a landing facility.

The scrolling notifications and audible alerts require no user action. Other displays activate to show additional information only when a track is selected by the user. The primary human interface for the tracking algorithm is a planned position indicator display. This typically puts up four pieces of information.

The track algorithm produces symbology that is displayed on the Plan Position Indicator.

Users have a pointing device with several buttons that provides access to the track file through the Plan Position Indicator. The typical pointing device is a track ball, which operates as follows.

Hook action turns off the cursor and displays additional information from the track algorithm. The user can perform actions while the hook is active, such as communicate with the vehicle or notify other users regarding the vehicle associated with the track.

The nearest neighbor track algorithm is described here for simplicity.

Each new detection reported from incoming sensor data is fed into the track algorithm, which is used to drive displays.[2]

Track algorithm operation depends upon a track file, which contains historical track data, and a computer program that periodically updates the track file.[3]

Sensors information (radar, sonar, and transponder data) is provided to the track algorithm using a polar coordinate system, and this is converted to cartesian coordinate system for the track algorithm. The polar to Cartesian conversion uses navigation data for sensors mounted on vehicles, which eliminates sensor position changes caused by ship and aircraft motion that would otherwise corrupt track data.

Track mode begins when a sensor produces a sustained detection in a specific volume of space.

The track algorithm takes one of four actions when this new sensor data arrives.

Each separate object has its own independent track information. This is called track history. This could be as much as an hour for airborne objects. Track history for underwater objects can extend back several weeks.

Each different kind of sensor produces different kinds of track data. A 2D radar with a fan beam produces no altitude information. A 4D radar with a pencil beam will produce radial Doppler velocity in addition to bearing, elevation, and slant range.

New sensor data is stored for a limited period of time. This occurs before track, capture and drop processing.

Stored data needs to be held for a limited time to allow time for comparison with existing tracks. Stored data must also be held long enough to complete processing required to develop new tracks.

Data quickly loses any purpose for sensor systems that use an M out of N detection strategy. Stored data is often dropped after N scans have expired with fewer than M detections within a specific volume.

Drop processing takes place only after track and capture processing takes place. Drop data may sometimes be extracted from main memory and recorded onto storage media along with the track file for offsite analysis.

The capture strategy depends upon the kind of sensor.

Capture processing takes place only after stored sensor data has been compared with all existing tracks.

All new sensor data is compared with existing tracks first before capture or drop processing takes place.

Track position and velocity information establishes a track volume at a future position. New sensor data that falls inside that track box is appended to the track history for that track and deleted from temporary storage.

${\displaystyle {\text{Append}}\;{\begin{cases}{\text{Size}}>\left\vert X_{s}-(X_{o}+V_{x}\cdot \Delta T)\right\vert \\{\text{Size}}>\left\vert Y_{s}-(Y_{o}+V_{y}\cdot \Delta T)\right\vert \\{\text{Size}}>\left\vert Z_{s}-(Z_{o}+V_{z}\cdot \Delta T)\right\vert \end{cases}}}$

During operation, XYZ sensor measurements for each vehicle are appended to the track file associated with that vehicle. This is the track history that is used to keep track of position and velocity. XYZ velocity is determined by subtracting successive values and dividing by the time difference between the two scans.

${\displaystyle {\text{Velocity}}\;{\begin{cases}Vx=(X_{1}-X_{0})/\Delta T\\Vy=(Y_{1}-Y_{0})/\Delta T\\Vz=(Z_{1}-Z_{0})/\Delta T\end{cases}}}$

Tracks where the vehicle continues to produces a detection are called active tracks. The track volume is much smaller than the capture volume.

The track is continued briefly in the absence of any detections. Tracks with no detections become coasted tracks. The velocity information is used to move the track volume through space briefly as the track volume is expanded.

New tracks that fall within the capture volume of a coasted track are cross correlated with the track history of the nearby coasted track. If position and speed are compatible, then the coasted track history is combined with the new track. This is called a join track.

A new track that begins in or near the capture volume of an active track is called a split track.

Coasted track, joined track, and split track trigger an operator alert. For example, a track coast can result from an aircraft collision, so the cause needs to be determined otherwise supervisory personnel need to be notified.

Civilian air traffic control personnel use leaders produced by the track algorithm to alert pilots when the future position of two tracks violate the separation limit.

Track data is usually recorded in the event that an investigation is required to establish the root cause for an aircraft loss.

This is a special case of the Kalman filter.