APS Excellence in Physics Education Award
November 2019

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November 2011

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## Uncertainity post and replies

Uncertainity in Tracker
Magda Moscoso
3 Posts

How can I know the uncertainity in a measure that I did with tracker, for example position or velocity?

### Replies to Uncertainity in Tracker

Re: Uncertainity in Tracker -

Douglas Brown
353 Posts

Hi Magda,

There is no "automatic" way to estimate the uncertainty, but here are some factors to consider:

• how carefully the points are marked (how do they differ when another student marks them , etc)
• how clearly the positions can be seen on the video (are there changes in lighting, blurriness due to speed, etc?)
• how accurately the video is calibrated (this is often the source of large discrepancies)

Plus there are many more...  You really have to consider each experiment individually and make uncertainty estimates based on the above. It always helps to repeat the experiment to see how much variation occurs from one to the next.

Doug

Re: Re: Uncertainity in Tracker -
Magda Moscoso
3 Posts

Re: Re: Uncertainity in Tracker -
Magda Moscoso
3 Posts

Can you give any idea to meassure the  accurately of the video?

Thanks,
Magda

Re: Re: Re: Uncertainity in Tracker -
Ami B
9 Posts

Magda,
you can check the deviation of time measurments from the 1/FPS.
i.e. check how t is acturate.
if you have model   you can compare the measurements to the model ( x,y,vx,vy,ax,ay )
ami

Re: Uncertainity in Tracker -
Marta Wolak
1 Posts

I really enjoy using tracker but I always struggle with how to estimate uncertainty. Say one does the simplest free fall experiment. And let's say the tracking works really well for position time but what if I wanted to ass the error bars to the positions do you have a clear and straightforward advice on how to estimate them? then the same for velocity and then for the acceleration. It is very important in case I want to determine the acceleration from the slope of velocity time graph with uncertainty instead of using the rather noisy usually acceleration time graph. I have been struggling with this for last 5 years maybe someone has a nice and clear strategy to share? I will be so grateful

Re: Uncertainity in Tracker -

Douglas Brown
353 Posts

Hi Marta,

A good way to estimate an uncertainty is to perform the experiment multiple times and look at the variations in the results. For example, you might have several students analyze the same video and compare. To separate errors introduced by the calibration from those caused by the marking errors, you could have multiple students independently calibrate a video that is already marked, and other students mark a video that is already calibrated.  Multiple videos of the same event could also give you interesting data to compare.

> Re: Uncertainity in Tracker
>
> I really enjoy using tracker but I always struggle
> with how to estimate uncertainty. Say one does the
> simplest free fall experiment. And let's say the tracking
> works really well for position time but what if I
> wanted to ass the error bars to the positions do you
> have a clear and straightforward advice on how to
> estimate them? then the same for velocity and then
> for the acceleration. It is very important in case
> I want to determine the acceleration from the slope
> of velocity time graph with uncertainty instead of
> using the rather noisy usually acceleration time graph.
> I have been struggling with this for last 5 years
> maybe someone has a nice and clear strategy to share?
> I will be so grateful

Re: Uncertainity in Tracker -
Jens Biele
6 Posts

Doug is of course right.

But if you only have that one video? Not as good, but you can do something, I believe. here is my recipe:

- for position, use generally 0.1 (very good) to 1 px spatial resolution (x,y in image plane). This may correspond to varying real error bars, if your object is not always at the exact same distance. If camera lens distortion is not negligible, this will add a bias that can only be estimated if you have several known (world coordinates) static points in each image and compare that to the image x y coordinates.
- Estimate the uncertainty of your scale - this needs to be added as systematic uncertainty to anything
- Repeat tracker analysis for same video, but each time manually repeating the scale bar definition, and the tracking maybe with some different parameters of (auto-)tracker. Then you get an idea of the tracker analysis uncertainties. Add to above. This then is a priori error bar.
- Fit a theoretical curve or a reasonable curve through your data if you can (e.g. a parabola for the falling ball), fit rms should be comparable to the a priori estimate. of course do not over-fit ;-)
- For the uncertainty of the resulting derivatives, here velocity and acceleration, there are no closed formulae I think! The best you can do is to take your primary data (position vs. time) and their individual error bars, make N Monte Carlo copies of it (x_ij=x_i+sigma_x_i*randn_j, y_ij analogously; randn makes a normally distributed random number with average 0 and std 1). repeat fit and analytical derivatives each time, gives you a distribution of velocity and acceleration....