# 11 – KALMAN QUIZ Parameter Update 01 RENDER V3

Suppose we multiply two Gaussians, as in Bayes rule, a prior and a measurement probability. The prior has a mean of Mu and a variance of Sigma square, and the measurement has a mean of Nu, and a covariance of r-square. Then, the new mean, Mu prime, is the weighted sum of the old means. The Mu is weighted by r-square, Mu is weighted by Sigma square, normalized by the sum of the weighting factors. The new variance term, I want to write Sigma square prime here for the new one after the update, is given by this equation over here. So, let’s put this into action. We have a weighted mean over here. Clearly, the prior Gaussian has a much higher uncertainty therefore Sigma square is larger and that means the nu is weighted much much larger than the Mu. So, the mean will be closer to the nu than the mu, which means it will be somewhere over here. Interestingly enough, the variance term is unaffected by the actual means, it just uses the previous variances. It comes up with a new one that’s even peak here, so the result might look like this. So, this is the common situation for the measurement update step where this is the prior, this is the measurement probability and this is the posterior. So, let’s practice these equations with a simple quiz. So, here are our equations again and suppose I use the following Gaussians. These are Gaussian with equal variance, but different means. They might look as follows. Compute for me the new mean after the update and the new sigma square.