There is one aspect missing. When taking the weighted average of a prediction and measurement, the weights can be time varying in a Kalman filter. Otherwise I believe it goes by a different name.
A good example is a single sensor measuring a slowly changing quantity. A fuel Guage for example. A good estimate from second to second is that there is no change, but a measurement may have noise (fuel sloshing around in the tank). A Kalman filter in this case will look like a first order low-pass filter with an exponentially decaying gain. The cutoff frequency changes so you can find the starting level quickly (in seconds) but then ignore the noise with a very low frequency cutoff (0.01hz say).
A good example is a single sensor measuring a slowly changing quantity. A fuel Guage for example. A good estimate from second to second is that there is no change, but a measurement may have noise (fuel sloshing around in the tank). A Kalman filter in this case will look like a first order low-pass filter with an exponentially decaying gain. The cutoff frequency changes so you can find the starting level quickly (in seconds) but then ignore the noise with a very low frequency cutoff (0.01hz say).