Joint Probability Density from two Gaussian Distributions

[Giri1]

I've been reading the following paper entitled "An Improved Algorithm to Generate a Wi-Fi Fingerprint Database for Indoor Positioning":

An Improved Algorithm to Generate a Wi-Fi Fingerprint Database for Indoor Positioning

In Part 3.3 (Step 6), it states: Use the fingerprint database to calculate the joint probability density for the received signal strengths (RSS) collected in the step 5.

At this point two Gaussian Distributions, which could either be regular Gaussians or Double Peaked Gaussians, have been calculated. The first is collected and stored in a database and depicts the "fingerprint" of a particular location. The second depicts the reading from a user at an unknown location.

The idea is that these two locations have to be compared using K Weighted Nearest Neighbour to determine whether the user's location corresponds to the location being compared to in the database.

My questions are:

1) How should I go about forming a Joint Probability Density from these two Gaussians? I also thought that the variables in a Joint Probability Density Function should be related somehow... but I don't see the relationship here..

2) What about the case where one of the Gaussians is double peaked and the other is just a regular Gaussian?

Sorry my statistics knowledge isn't great so I have just been trying to get an understanding of these concepts from the internet.

Thank you for your help!

 

[Valkarie]

The joint probability density of two Gaussians is formed by multiplying the two individual probability densities together. This is a basic property of probability theory.If one of the Gaussians is double-peaked, then it will be necessary to take into account both peaks when forming the joint probability density. To do this, you can simply multiply the two functions together, taking into account both peaks.