08. Filtering

Filtering

Forward vs. Inverse Measurement Model

Forward Measurement Model - P(z 1:t | x) : Estimating a posterior over the measurement given the system state.

Inverse Measurement Model - P(x | z 1:t ) : Estimating a posterior over the system state given the measurement.

The inverse measurement model is generally used when measurements are more complex than the system's state.

A robot is trying to measure its distance towards the closest wall, its position is known. What type of measurement model would you implement to solve this problem?

SOLUTION: Forward Measurement Model

What is the log odds ratio representation of p(A|B)? Select all that apply

SOLUTION:
  • log(\frac{P(A|B)}{1-P(A|B)})
  • log(\frac{P(A|B)}{P(\neg A|B)})

The advantage of using a log odds ratio representation is to avoid probability instabilities near 0 or 1. Another advantage relates to system speed, accuracy, and simplicity. Check out these two sources for more information on log probability and numerical stability:

  1. Log Probability
  2. Numerical Stability

Next Concept