A very simple conditional probability calculation formula is modern foundation of mobile robotic perception, sensor fusion and object tracking. If you need to deal with an 'uncertain world', you must resort to probabilistic modeling whether in automated driving or robotics. And all these probabilistic methods is mostly based on the Bayes formula even if they do not explicitly tell it.
In most practical applications, the ultimate and primary aim is to estimate the state of the object: position of the car, position of the surrounding elementa around the car, shape and size of the object...we must estime the state using uncertain and cluttered measurements..given all measurements, please give me the accurate and robust estimate of my state. I would like to know where i am, what the things are around me, how fast I am...or i want to know the position of other objects...i want o know it instantly...maybe if i had all data at once and all the i need, i can come up with a very accurate estimate...with all data, i can eliminate the implausible-improbable states...but too much data means too much time to compute?
Then, what to do? I cannot store all measurements to decide at a given time..neither cars do not wait nor aircrafts. The obvious solution is that i do it recursively..i only store the information I need. Assuming Markov transition and independent measurements given the state, the past measurementa other than the previous time step is unnecessary...a lot of simplications and we can get the posterior pdf of the state given all measurements in a recursive manner: predict and update -correct-..
We go one step further. We assume linear object dynamics and linear sensor measurement models along with Gaussian noise processes, we end up Kalman filter: simple analytical formulas and also recursive. You just must propagate the mean and covariance of the Gaussian of over time since a Gaussian pdf is completely characterized by its mean and covariance...
What about non-linearities and multi target multi sensor scenarios? All these can be blundered into Bayesian? Please follow me.
