I have an internship measuring and analyzing telemetry data for the US military, and I've run into a phenomenon that I know can be represented as a mathematical equation. My current mathematical learning is not equipped to express it, however, so I would like some help.
First, we have an observed bearing, for example 094 relative to own instruments. Then we have an initial observable rate of change, or bearing rate, which for this example we'll use +0.5 degrees per minute. In addition we have an observable rate of change for the bearing rate itself, in this example we'll use +0.01 degrees per minute per minute. So at time 0 we have a bearing measurement of 094. At time +1 we have a measurement of 094.5. At time +2 we have a measurement of 095.01. At time +3 we have a measurement of 95.53 and so on. So if I want to calculate what bearing will measure at time +10 I take the initial bearing, add the bearing rate multiplied by ten then add the bearing rate change to that as it increases over time, in this case 0.01+0.02+0.03+0.04+0.05+0.06+0.07+0.08+0.09+0.1.
How can this be expressed as an equation? So far I've got something like y=a+bx+c... something, where y represents the final calculated measurement, a represents the initial bearing, b represents the initial bearing rate, x represents the time of the final calculated measurement and c(something) would represent the gradually increasing mathematical property of bearing rate rate. I'm guessing this is a function or an algorithm, but my current mathematical training is insufficient to put those into an equation. Any help would be much appreciated.