Now you understand how to integrate measurements, how to integrate motion, and perform a one-dimensional Kalman filter, but in reality we often encounter multi-dimensional situations.
This involves many factors, examples, and why estimation in more latitude state spaces is important.
Suppose you have a 2D space of x and y - say a camera image, or in our case we might take a car with a radar on it to detect
The position of the vehicle changes over time, at which time the two-dimensional Kalman filter is very suitable.
Here's how it works, assuming that at time t=0 you observe that the object of interest will be located at this coordinate
This could be another vehicle for Google's self-driving car project. You'll see it here after a while, t=1, and after a while, at t=2.
Where is t=3?
When you're making estimates and computing high latitude space, the Kalman filter not only helps you get into x and y space, but also lets you figure out exactly how fast the object is?
Then make a good prediction of the future based on the speed estimate, now notice that the sensor itself can only see the position, he can't see the actual speed, the speed is inferred from seeing multiple positions, so in the tracking application, Carl One of the most amazing features of the Mann filter is that he can derive the velocity of an object even if he doesn't measure it directly
Then based on the speed, predict the future position where the speed will occur. This is why the Kalman filter has become popular in artificial intelligence and control theory.
Kalman filter follow-up
You have now deployed a 1D Kalman filter and have some intuition about how a multidimensional Kalman filter works.
However, if we want to actually make (or even use) Kalman filters in a 2D or 3D world (or "state space" in robotics terms), we first need to have a deeper understanding of what the word "state" means.
But don't worry, we'll be back to our course on multidimensional Kalman filters soon!