Upenn-robotics 5: Robotics: Estimation and learning-week 2: Bayesian Estimation-target tracking

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The robot will not directly measure X unfortunately, but the robot may observe portions of X through it's sensors. this portion is labeled Z, where the relationship between the State and measurement is given by the mixing matrix, C.

 

 

Creditly both X and Z contain noise even in this model.

 

State X is noisy because the linear model does not capture all

 

Physical interactions.

 

Observation Z are noisy because sensors contain noise in their measurements.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In the next section, we will show how these two probability distributions

 

Can be fused to provide a better estimate of the true state.

 

 

 

 

 

 

 

 

 

 

From the dynamical system, the probability of the state given only the previous state can be represented with the prior information Alpha. Representing the information from our measurement model, BetaProvides observational evidence.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Upenn-robotics 5: Robotics: Estimation and learning-week 2: Bayesian Estimation-target tracking