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Kalman Filter

We need to measure output value to use feedback control. But there is the value we cannot measure.

"State identification" is to identify the un-measured value.

State Space Model

State Space Model is used when the value what we want to know is not measured but other values are observed. State Space Model has two functions.

x(n) = F(n) * x(n-1) + G(n) * v(n)
y(n) = H(n) * x(n) + w(n)

The first function expresses the system. The second function expresses the relationship between the value of system and observed value. x is the system value we want to know. y is the observed value. v is the outside disorder. w is the measuring error. F, G, H are matrixes.

Kalman Filter

Kalman filter calculates the step of State Space Model one by one. The it predicts the future.

Kalman filter is also an algorithm to solve AR Model in Time Series Analysis .

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