Uncertainty in Speed

Few topics generate more office-hours discussion in my photogrammetry course than assessing uncertainty. You’ve calculated a vehicle’s speed using video, but what range can you confidently apply to it?

Fortunately, several authors have addressed this issue, and as speed-from-video work continues to heat up, it's drawing more analysis and publication. It’s a deep topic and there are nuances that depend on your photogrammetry and frame timing methods, but a great place to start is the SAE paper Speed Analysis from Video: A Method for Determining a Range in the Calculations, by Gray Beauchamp, et al.

In video analyses, we’re generally calculating the average speed of the vehicle over a specific time interval. Sticking with the nomenclature of the paper, it’s simply: s = d/t. It’s no surprise the uncertainty in speed depends on the uncertainty in vehicle positioning and frame timing.

The authors use concepts from this error analysis textbook and present an equation to calculate uncertainty in speed. An algebraically simplified version of the equation is below:

Where:

δs = uncertainty in speed (ft/s, m/s)
δd1 = uncertainty in position 1 (ft, m)
δd2 = uncertainty in position 2 (ft, m)
d = travel distance between 1 and 2 (ft, m)
t = duration between 1 and 2 (s)
δt = uncertainty in timing, same for both positions (s)

Here is a basic Excel spreadsheet that makes the calculation, pre-loaded with the sample inputs from Appendix C so you can confirm it reproduces the paper's published results. Before using it for casework, run that check yourself and make sure you agree with the output.

​2021-01-0887 - Speed Uncertainty.xlsx​

The next question, of course, is how do you quantify uncertainty in positions and times? Sadly, that will have to be a topic for another day. Gotta keep these emails To the Point!

Thanks for reading, keep learning!

​Lou Peck
​Lightpoint | JS Forensics