The Kalman filter method is used to combine multiple data streams, and to drive control systems. The algorithm was described in:
The estimate of the value is the sum
is states, like discrete time intervals is estimate , value
The gain () is unknown, and the filter process finds the best averaging factor to minimize error. Fixing this at 0.5 results in simple averaging.
is linear combination of the previous value, control signal (=0), and process noise (as independent Gaussian functions).
any measured value is a linear combination of signal and measurement noise.
noise terms are independent Gaussian functions
A,B,H are matrices, but may reduce to single values, and may be constants, maybe 1
The prediction step updates values:
The correction step accounts for error:
determine R and Q