Прикладные области

Построение фильтра Калмана для стохастических систем

Выход системы до и после осуществления оптимального фильтрирования.

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antenna = \!\(\*

TagBox[

SubsuperscriptBox[

FormBox[

TagBox[

RowBox[{"(", "", GridBox[{

{"0.5", "0.07869", "0.0042", "0.0104"},

{"0",

RowBox[{"-", "0.60653"}], "0.0786", "0.00786"},

{"1", "0", "0", "0"}

AllowScriptLevelChange->False,

BaseStyle->(Deployed -> False),

GridBoxAlignment->{

"Columns" -> {{Center}}, "ColumnsIndexed" -> {},

"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},

GridBoxDividers->{

"Columns" -> {False, False, True, {False}, False},

"ColumnsIndexed" -> {},

"Rows" -> {False, False, True, {False}, False},

"RowsIndexed" -> {}},

GridBoxItemStyle->{

"ItemsIndexed" -> {{{1, 1}, {}} -> {

Deployed -> True,

ShowStringCharacters -> False}, {{}, {1, 1}} -> {

Deployed -> True, ShowStringCharacters -> False}}},

GridBoxSpacings->{"Columns" -> {

Offset[0.27999999999999997`], {

Offset[0.7]},

Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {

Offset[0.2], {

Offset[0.4]},

Offset[0.2]}, "RowsIndexed" -> {}}], "", ")"}],

Function[BoxForm`e$,

MatrixForm[BoxForm`e$]]],

StandardForm],

FormBox["0.1",

StandardForm],

FormBox[

StyleBox["\<\"\[ScriptCapitalS]\"\>",

Editable->False,

ShowStringCharacters->False,

"NodeID" -> 64],

StandardForm],

MultilineFunction->None],

{StateSpaceModel, {

SamplingPeriod -> 0.1, Control`CommonDump`noD -> True}}]\);

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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