# Measurement and physics model fusion

I am combining two position measurements of a ball from two sensors in real time to obtain one triangulated position in x,y,z coordinates. As the data exchange of the measurements carries some latency, the data has to be extrapolated be able to obtain the current position. Due to extrapolation an error appears in the triangulated data.

I know that when the ball is in the air, the velocity of the ball should be constant in x and y directions and the velocity in the z direction should decay with g. The velocities in x and y however oscillate as function of time around a mean value which is the actual x respectively y velocity. The same goes for when I compute the acceleration in the z direction. It oscillates as function of time around g.

Given that I know how the ball should behave, i.e. that vx and vy should be constant and that the acceleration in the z direction should be z, how can I impose these conditions to better estimate the triangulated position?

• "that vx and vy should be constant" Are you throwing the ball in a vacuum chamber? – FooTheBar Jul 16 '15 at 8:07

## 1 Answer

Kalmnan filters are typically used for sensor fusion. You create a model for what you expect the process to look like, use your sensors as inputs, and the output is the filtered estimate. I'm not going to go over implementation in detail as there is plenty of information about these filters available online; I hope this points you in the right direction and if you have a specific question about it then by all means make a new question and I or someone else here can answer it.

I'm interested in your use of two sensors to triangulate (trilaterate) a ball. How are you using two sensors to fix a 3 dimensional coordinate?

• Thanks for your answer. I am having a look at how to implement Kalman filter to my setup, haven't figured it out quite yet. In my setup each sensor determines a 2D projection on a plane of the object to be triangulated. As the sensors are positioned a certain height from the projection plane, the 3D position of the object can be determined. – user2835098 Jun 19 '15 at 16:45
• You'll need a KF capable of handling nonlinear equations. Look into the extended Kalman filter and the unscented, both should fit your problem. What kind of sensors are you using? Cameras? – holmeski Jul 16 '15 at 15:16
• @holmeski - if you have a comment/question about the OP's question, please comment on the question, not my answer. – Chuck Jul 16 '15 at 15:23