Inference: SLAM as a Maximum A Posterior Problem

Bayesian Equation

Consider the following example, because of the conditional independance of measurements given theta, the formula (1) can be broke down into the formula (2)

Least Square

Note that we did not solved Ax=b, in general no exact solution because of noise, instead we solved argmin (Ax-b)^2

Linear Example

Note that the smaller the variance, the larger the coefficient, which would influence the solution more