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Re: Canarsie CBTC

Posted by RonInBayside on Sat Jun 18 10:44:55 2005, in response to Re: Canarsie CBTC, posted by Stephen Bauman on Sat Jun 18 09:42:30 2005.

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If you are traveling at 50 mph, that would be 50 x 5280 feet per mile = 264,000 feet per hour. Divide that by 3600 seconds per hour, and you get 73.33 feet per second.

But we want to try to measure that by GPS. So at time point 0 you are at point zero on the track. At time 1 you are, by GPS, somewhere between 58 feet and 88 feet down the track. The maximum error at that first time point is + or - 15/73 or 20.5%. At time 2 the error could go to +/- 30 feet or 41%; after 3 seconds 62%.

So let's say your true velocity is 73 feet per second. Between time point 0 and time point one GPS could estimate your velocity at between 58 and 88 feet per second; at time point two, your estimated velocity by GPS is between 58+43/2 = 50.5 feet per second and 88+ 103 feet per second/2 = 191/2 = 95.5 feet per second, which is 24-25% off one way or the other. This error then grows with succeeding time points.

So it's t1(p1*error factor) + t2(p2*error factor) = t3(p3*error factor)...tN(pN)*error factor) / t --> velocity estimate for time interval tN.

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