# Predict next set of coordinates in 3D space [closed]

Please forgive me if my question does not make sense - I am pretty new to stats and could use some guidance.

I would like to predict the next position of an object in 3D space. I have a list for each axis: xData, yData, zData - these lists contain the coordinates of the object. For example:

# | xData | yData | zData |
- | --------------------- |
1 | 1.245 | 2.452 | 5.125 |
2 | 3.256 | 4.357 | 7.425 |
n | ..... | ..... | ..... |


So, the first set of coordinates would be 1: {1.245, 2.452, 5.125}

I have thought about using a Kalman filter, but I am not sure what to do for the "predict" stage when following this tutorial.

A friend recommended building a multivariate dynamic linear model... but I don't know where to start.

Questions:

1. Would the Kalman filter work for this? (predicting the next set of coordinates xyz)
2. Would the multivariate dynamic linear model work better? If so, is it quicker to compute the next set of coordinates than the Kalman filter? (I need to keep computation times as low as possible)
3. Any recommended tutorials would be appreciated
• Is the position of the object random, or is it following a trajectory through space? The example data has two points so it's not possible to tell. If the object is following a trajectory - then the answer to your question is yes - one can use a Kalman filter to predict the next location. For my money the best book on Kalman filtering is (still) Applied Optimal Estimation by Gelb. – Keith Brodie Mar 20 '16 at 4:34
• @KeithBrodie The position is not random. For example, if the player in a 3D video game was the object, then I would like to predict the players next location. Thanks! – pookie Mar 20 '16 at 21:16
• So if there's no other forces acting on the object that we know of, the best prediction of the next position is to assume the same velocity observed in the last step. No KF is required unless there's noise on the position coordinates you already have. – Keith Brodie Mar 21 '16 at 7:08
• @KeithBrodie Thanks! I will go through the book you recommended as soon as I have some time! – pookie Mar 23 '16 at 17:49