I need to determine location based upon N number of WIFI Access Points and their signal strengths. Is the best way to do this using a least-squares fit algorithm? How would I go about implementing such an algorithm?
Least Squares fitting should work if your noise in the signal strength is Gaussian, ie. follows a normal distribution.
What you are really looking for is the maximum likelihood estimator for the mean of the signal strength, and you hope that that estimation corresponds in some way to a distance.
"Least squares corresponds to the maximum likelihood criterion if the experimental errors have a normal distribution." -- http://en.wikipedia.org/wiki/Least_squares
So if your signal strength noise is not normally distributed (Gaussian) you are out of luck.
Of course you will also have a standard deviation of your estimate, which will let you know sure you can be of your location estimate. The more wifi signals, and more data points from each signal you can record, the better your estimate will be.
I have been trying to find time to do this too, please do tell how it turns out.