[arungovindneelan]

Could you explain exact difference between moving least square (MLS) and weighted least square (WLS). I personally feel that moving least square is a sub case of weighted least square.

My understanding :

Lets say we are using linear polynomial as our base and I'm assuming we are having four points within "Support Radius" (area where we are using non-zero weight). To fit one linear polynomial we need only two points, but we are having four points, so we can use least square approach to approximate the polynomial. Another better approach is giving more weight to the nearest points (WLS), so we can include a weighting function as a function of distance (eg. Gaussian weight), then we can calculate the coefficient and we can do interpolation. If we do the same process for next evaluating point, the weight will vary based on the distance between evaluating point and points within the "support radius". Since the weight and co-efficient are changing based on, changing ( or moving) evaluating point this method is called as MLS. Actually Its a kind of WLS.

Is there is any fixed rule that distinguish MLS and WLS?

Please correct me if I'm wrong .

Thank you




[1]: http://www.math.iit.edu/~fass/603_ch7.pdf
[2]: http://www.azdhs.gov/lab/documents/l...sion-calib.pdf
[3]: http://i.stack.imgur.com/Y3sTK.jpg