I have some vehicle based GNSS data. The data is GNSS time to a precision of 1 second and the corresponding lat and long coordinates in decimal degrees. The data sampling was inconsistent, ie not always 1hz.
I know how to establish the mean estimate for the vehicle speed by doing Δs/Δt.
If I were to continue on the basis that
- the time is correct and
- the Standard Dev in the Postional accuracy was 5 metres
How do I establish the uncertinity in the speed estimate by way of error propagation/some other method? The aim is to create a speed time graph to a confidence of 95% (2 SD).
Any help would be appreciated.
I tried to simply +/- the resultant Δs by 5 metres. However, as the speed is low at some point this can generate negative values. I don't know how to incorporate an uncertinty in the lat/long cordinates, which I am assuming is a better than method than applying the uncertinity to the calculated distance
If you assume a constant error in position, the faster the vehicle is traveling, the lower the percentage error will be.
Here is the problem, if you assume a +/- 5m error in positioning, your worst case scenario is a 10m difference between positions in one second for a stationary vehicle. That equates to a 10m/s speed, which is equivalent to 22mph, for a vehicle that is not even moving. I don't think you can assume 95% accuracy in speed estimation until the vehicle is reporting a speed of at least 90 m/s.