I understand you want to know the difference between the usage of Weighted Least Squared(WLS) and Kalman Filters in Power System state estimation.
WLS is a static approach which uses single set of measurement for state estimation, it has limited ability in terms of predicting future operating state.
Kalman filter is a set of mathematical equations that provides and efficient computational algorithm to estimate the state of a process, in a way that minimizes the squared error. The filter supports estimation of past present and future states.
You can refer to the following links for more on Kalman filtering: