# 10-27 Change MSE sign

I spent the last three weeks writing and improving my submission to SJF. I received feedback this weekend with which I can revise the report.

# Problem: Wrong sign in MSE

The function that calculates the mean squared error (MSE) has a mistake in it. The sign for one operation is wrong, it should be a - instead of a +. Since the MSE calculates the difference between the estimated radius and the determined distance based on the pythagorean theorem, it should look as follows:

Yet the formula I used was the following, note that the second minus is a plus.

For this reason all results I got and used in my report are wrong. Only one axis was probably correctly minimized, the other axis was mostly random. An artefact of this behaviour is probably the tent like structures with peaks about that I observed multiple times and the "superpositions" of the values in certain areas. By this I mean where the position bounced back and forth between two distinct clusters.

Many times during research, programming and unit-testing I was wondering whether it was correct, since it intuitively seemed to be wrong. But the source was from the MIT and written by a post-doctoral student, so I figured that perhaps it would be true because who am I compared to someone like that. In hindsight, I obviously should've trusted my common sense.

# Solution

Yesterday I conducted a test in a large room of the setup using the updated code. The mean RMSE was 0.899 and standard deviation of the RMSE values was 0.26m. This is considerably better than the values attained in an experiment of similar scope and settings but with the wrong function. There the mean RMSE was 1.11m and the standard deviation was 0.5839 meters. In that sense the mean RMSE was reduced by 19.3%. ).

There no longer are outliers, hence the plot is relatively flat (as suggested by the low stdev). Also noteworthy is that the bumps and valleys are largely random, as was initially expected.

# Next steps

This evening I will two more experiments, first using the coefficients from yesterday and another one using a smaller room. Then at least I will have three experiments I can base my whole paper on. Afterwards I probably have to already rewrite some parts and an addendum about how I noticed and corrected this fairly late on. I also will have to improve some stuff in the text anyway, so I don't have an unlimited amount of time to improve this.