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Construct a Kalman Filter for a Stochastic System

Output of a system before and after optimal filtering.

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antenna = \!\(\*

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W = {{0.01}}; V = {{0.001}};

kalmanFilter =

SystemsModelExtract[KalmanEstimator[{antenna, All, 1}, {W, V}],

All, {3}];

u = Table[Sin[(2 \[Pi] i)/20.0], {i, 100}]; processNoise =

RandomReal[NormalDistribution[0, Sqrt[W[[1, 1]]]], {100}];

measurementNoise =

RandomReal[NormalDistribution[0, Sqrt[V[[1, 1]]]], {100}];

y = Flatten[OutputResponse[antenna, {u, processNoise}]] +

measurementNoise;

ListLinePlot[y]

ListLinePlot[OutputResponse[kalmanFilter, {u, y}]]

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