daviddoji/Kalman-and-Bayesian-Filters-in-Python
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Fixed math for train.

Browse Source
This commit is contained in:
Roger Labbe 2015-05-23 09:27:56 -07:00
parent 4f1558b12a
commit 3cce5adf64
1 changed files with 1 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
01_g-h_filter.ipynb
View File

@ -1017,7 +1017,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's explore a few different problem domains to better understand this. Consider the problem of trying to track a train on a track. The track constrains the position of the train to a very specific region. Furthermore, trains are large and slow. It takes them many minutes to slow down or speed up significantly. So, if I know that the train is at kilometer marker 23km at time t and moving at 60 kph, I can be extremely confident in predicting its position at time t + 1 second. And why is that important? Suppose we can only measure its position with an accuracy of 500 meters. So at t+1 sec the measurement could be anywhere from 22.5 km to 23 km. But the train is moving at 60 kph, which is 16.6 meters/second. So if the next measurement says the position is at 23.4 we know that must be wrong. Even if at time t the engineer slammed on the brakes the train will still be very close to 23.0166 km because a train cannot slow down very much in 1 second. If we were to design a filter for this problem (and we will a bit further in the chapter!) we would want to design a filter that gave a very high weighting to the prediction vs the measurement. \n",
"Now let's explore a few different problem domains to better understand this. Consider the problem of trying to track a train on a track. The track constrains the position of the train to a very specific region. Furthermore, trains are large and slow. It takes them many minutes to slow down or speed up significantly. So, if I know that the train is at kilometer marker 23 km at time t and moving at 60 kph, I can be extremely confident in predicting its position at time t + 1 second. And why is that important? Suppose we can only measure its position with an accuracy of $\\pm$250 meters. The train is moving at 60 kph, which is 16.667 meters/second. So at t+1 second the train will be at 23.017 km and the measurement could be anywhere from 22.767 km to 23.267 km. So if the next measurement says the position is at 23.4 we know that must be wrong. Even if at time t the engineer slammed on the brakes the train will still be very close to 23.0166 km because a train cannot slow down very much in 1 second. If we were to design a filter for this problem (and we will a bit further in the chapter!) we would want to design a filter that gave a very high weighting to the prediction vs the measurement. \n",
"\n",
"Now consider the problem of tracking a thrown ball. We know that a ballistic object moves in a parabola in a vacuum when in a gravitational field. But a ball thrown on the surface of the Earth is influenced by air drag, so it does not travel in a perfect parabola. Baseball pitchers take advantage of this fact when they throw curve balls. Let's say that we are tracking the ball inside a stadium using computer vision. The accuracy of the computer vision tracking might be modest, but predicting the ball's future positions by assuming that it is moving on a parabola is not extremely accurate either. In this case we'd probably design a filter that gave roughly equal weight to the measurement and the prediction.\n",
"\n",