## Wednesday, June 29, 2011

### Computer Architecture # 02 : Data Representation: CASE STUDY: PATRIOT MISSILE DEFENSE FAILURE CAUSED BY LOSS OF PRECISION (16)

2.4 Case Study: Patriot Missile Defense Failure Caused by Loss of Precision
During the 1991-1992 Operation Desert Storm conﬂict between Coalition forces and Iraq, the Coalition used a military base in Dhahran, Saudi Arabia that was protected by six U.S. Patriot Missile batteries. The Patriot system was originally designed to be mobile and to operate for only a few hours in order to avoid detection.
The Patriot system tracks and intercepts certain types of objects, such as cruise missiles or Scud ballistic missiles, one of which hit a U.S. Army barracks at Dhahran on February 5, 1991, killing 28 Americans. The Patriot system failed to track and intercept the incoming Scud due to a loss of precision in converting integers to a ﬂoating point number representation.

A radar system operates by sending out a train of electromagnetic pulses in vari ous directions and then listening for return signals that are reﬂected from objects in the path of the radar beam. If an airborne object of interest such as a Scud is detected by the Patriot radar system, then the position of a range gate is determined, which estimates the position of the object being tracked during the next scan.
The range gate also allows information outside of its boundaries to be ﬁltered out, which simpliﬁes tracking. The position of the object (a Scud for this case) is conﬁrmed if it is found within the range gate.

The prediction of where the Scud will next appear is a function of the Scud’s velocity. The Scud’s velocity is determined by its change in position with respect to time, and time is updated in the Patriot’s internal clock in 100 ms intervals.

Velocity is represented as a 24-bit ﬂoating point number, and time is represented as a 24-bit integer, but both must be represented as 24-bit ﬂoating point numbers in order to predict where the Scud will next appear.
The conversion from integer time to real time results in a loss of precision that increases as the internal clock time increases. The error introduced by the conversion results in an error in the range gate calculation, which is proportional to the target’s velocity and the length of time that the system is running. The cause of the Dhahran incident, after the Patriot battery had been operating continuously for over 100 hours, is that the range gate shifted by 687 m, resulting in the failed interception of a Scud.
The conversion problem was known two weeks in advance of the Dhahran incident as a result of data provided by Israel, but it took until the day after the attack for new software to arrive due to the difﬁculty of distributing bug ﬁxes in a wartime environment. A solution to the problem, until a software ﬁx could be made available, would have been to simply reboot the system every few hours which would have the effect of resetting the internal clock. Since ﬁeld personnel were not informed of how long was too long to keep a system running, which was in fact known at the time from data provided by Israel, this solution was never implemented. The lesson for us is to be very aware of the limitations of relying on calculations that use ﬁnite precision