I am in the middle of a vehicle tracking project where I have to calculate the distance traveled by the vehicle in a given amount of time.
Data I am getting:
Speed : 30.2 km/hr 12.7 km/hr 15 km/hr 21.8 km/hr
Time : 11:00:00 11:00:22 11:00:45 11:01:10
That is I am getting the speed of the vehicle every 20-25 seconds. So what is the best way to calculate the distance traveled by the vehicle during this whole duration? Is taking the median of two speeds the best way to calculate the average speed here?
Best Answer
A simple approach is to vary the speed linearly with time and integrate that to get distance. Of course in real life a lot can happen in 25 seconds so this will not give good results. The more closely spaced points the better.
Look up numerical integration and choose a scheme of your liking, like trapezoidal, simpsons rule, guassian quadrature, romberg's method, and more.
What tools to you have available for doing data processing and number crunching, and how many data points to do have? The choise depends on what you are familiar with, also.
I strongly adivse to tighten up the sample intervals, and to control the measurement error as much as possible. What is your target error in distance?
I did an example calculation, with trapezoidal rule at 11:00:45 you have traveled 212.1 meters, but with a higher order method the result is 204.1 meters (4% difference is huge).