(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 11.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     37851,        905]
NotebookOptionsPosition[     36839,        865]
NotebookOutlinePosition[     37187,        880]
CellTagsIndexPosition[     37144,        877]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Gauss-Newton method", "Section",
 CellChangeTimes->{{3.7610552791490326`*^9, 3.7610552867578526`*^9}, {
  3.762319154003744*^9, 3.762319163093913*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"GaussNewton", "[", 
   RowBox[{"r_", ",", "p0_", ",", "tol_", ",", "stop_"}], "]"}], ":=", 
  RowBox[{"(", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"iter", "=", "0"}], ";", "\[IndentingNewLine]", 
    RowBox[{"temp", "=", 
     RowBox[{"If", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"Length", "[", "p0", "]"}], "\[Equal]", "1"}], ",", 
       RowBox[{"{", "}"}], ",", 
       RowBox[{"Table", "[", 
        RowBox[{"0", ",", 
         RowBox[{
          RowBox[{"Length", "[", "p0", "]"}], "-", "1"}]}], "]"}]}], "]"}]}], 
    ";", "\[IndentingNewLine]", 
    RowBox[{"\[Epsilon]", "=", 
     SuperscriptBox["10", 
      RowBox[{"-", "7"}]]}], ";", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"Jacobi", "[", "p_", "]"}], ":=", 
     RowBox[{
      RowBox[{"Table", "[", 
       RowBox[{
        FractionBox[
         RowBox[{
          RowBox[{
           RowBox[{"r", "[", 
            RowBox[{"p", "+", 
             RowBox[{"Insert", "[", 
              RowBox[{"temp", ",", "\[Epsilon]", ",", "j"}], "]"}]}], "]"}], 
           "[", 
           RowBox[{"[", "i", "]"}], "]"}], "-", 
          RowBox[{
           RowBox[{"r", "[", "p", "]"}], "[", 
           RowBox[{"[", "i", "]"}], "]"}]}], "\[Epsilon]"], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", 
          RowBox[{"Length", "[", 
           RowBox[{"r", "[", "p", "]"}], "]"}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"j", ",", "1", ",", 
          RowBox[{"Length", "[", "p", "]"}]}], "}"}]}], "]"}], "//", 
      "Simplify"}]}], ";", "\[IndentingNewLine]", 
    RowBox[{"pOld", "=", "p0"}], ";", "\[IndentingNewLine]", 
    RowBox[{"pNew", "=", 
     RowBox[{"p0", "+", 
      RowBox[{"Table", "[", 
       RowBox[{"1", ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", 
          RowBox[{"Length", "[", "p0", "]"}]}], "}"}]}], "]"}]}]}], ";", 
    "\[IndentingNewLine]", "\[IndentingNewLine]", 
    RowBox[{"While", "[", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"Norm", "[", 
         RowBox[{"pOld", "-", "pNew"}], "]"}], ">", "tol"}], " ", "&&", " ", 
       RowBox[{"iter", "\[LessEqual]", "stop"}]}], " ", ",", 
      "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"pOld", "=", "pNew"}], ";", "\[IndentingNewLine]", 
       RowBox[{"\[CapitalDelta]p", "=", 
        RowBox[{"LeastSquares", "[", 
         RowBox[{
          RowBox[{"Jacobi", "[", "pOld", "]"}], ",", 
          RowBox[{"-", 
           RowBox[{"r", "[", "pOld", "]"}]}]}], "]"}]}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"\[Alpha]", "=", "1"}], ";", "\[IndentingNewLine]", 
       RowBox[{"pNew", "=", 
        RowBox[{"pOld", "+", 
         RowBox[{"\[Alpha]", " ", "\[CapitalDelta]p"}]}]}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"While", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"Norm", "[", 
           RowBox[{
            RowBox[{"r", "[", "pNew", "]"}], ",", "2"}], "]"}], ">", 
          RowBox[{"Norm", "[", 
           RowBox[{
            RowBox[{"r", "[", "pOld", "]"}], ",", "2"}], "]"}]}], ",", 
         "\[IndentingNewLine]", 
         RowBox[{
          RowBox[{"\[Alpha]", "/=", "2"}], ";", "\[IndentingNewLine]", 
          RowBox[{"pNew", "=", 
           RowBox[{"pOld", "+", 
            RowBox[{"\[Alpha]", " ", "\[CapitalDelta]p"}]}]}], ";"}]}], 
        "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", 
       RowBox[{"iter", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", 
    "\[IndentingNewLine]", "pNew"}], "\[IndentingNewLine]", ")"}]}]], "Input",
 CellChangeTimes->{{3.7610576717422743`*^9, 3.7610577389901543`*^9}, {
   3.7610577719367166`*^9, 3.76105791394031*^9}, 3.7610579596109533`*^9, {
   3.7610580172217107`*^9, 3.7610580286073866`*^9}, 3.761058351714018*^9, {
   3.7610584660734725`*^9, 3.761058525433069*^9}, {3.7610586231827865`*^9, 
   3.7610586302727346`*^9}, {3.761058692331476*^9, 3.761058699202594*^9}, {
   3.761058837930872*^9, 3.7610589105019445`*^9}, {3.761058985201689*^9, 
   3.7610590798812227`*^9}, {3.7610611973775387`*^9, 
   3.7610611985817337`*^9}, {3.76106124294853*^9, 3.761061257194768*^9}, {
   3.7610614000470076`*^9, 3.7610614100955*^9}, {3.761061689421361*^9, 
   3.7610616927861032`*^9}, {3.7610617286238546`*^9, 3.761062005592495*^9}, {
   3.761062099584234*^9, 3.761062171393074*^9}, 3.761062285573127*^9, {
   3.7610627048276267`*^9, 3.7610627159967437`*^9}, {3.7610634096910944`*^9, 
   3.7610634155884085`*^9}, 3.7610634673355894`*^9, {3.7610637035265803`*^9, 
   3.7610637229736223`*^9}, {3.761063937791129*^9, 3.7610639436815915`*^9}, {
   3.7610641776552134`*^9, 3.7610642045893335`*^9}, {3.7610642558215294`*^9, 
   3.7610642597872205`*^9}, {3.761064308614791*^9, 3.7610643200509663`*^9}, {
   3.761073814062935*^9, 3.7610738148026133`*^9}, 3.761076171751892*^9, {
   3.761076282124202*^9, 3.7610762827491693`*^9}, {3.7615554129334183`*^9, 
   3.76155541327699*^9}, {3.7615556531157827`*^9, 3.7615556591419992`*^9}, {
   3.761556096400277*^9, 3.7615560966972866`*^9}, {3.762319007014336*^9, 
   3.7623190272260776`*^9}, {3.7623191149737825`*^9, 
   3.7623191265137477`*^9}, {3.7623195658770323`*^9, 3.7623195661410275`*^9}, 
   3.762319914917793*^9, {3.7623200748677626`*^9, 3.7623200877377825`*^9}, 
   3.762320117957896*^9, {3.7623201724496827`*^9, 3.762320196379904*^9}, {
   3.7623202393897576`*^9, 3.762320243219425*^9}, 3.762320320767141*^9, 
   3.7623206382024727`*^9, 3.7623206690525756`*^9, 3.762321049039482*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell["Logistic function ", "Section",
 CellChangeTimes->{{3.762319053994063*^9, 3.7623190633040333`*^9}, 
   3.7623214220132313`*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
   "Logistic", " ", "function", " ", "parameters", " ", "estimation"}], 
   "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"y", "=", 
     RowBox[{"{", 
      RowBox[{
      "0.04", ",", "0.35", ",", "1.05", ",", "1.9", ",", "1.98", ",", "1.97", 
       ",", "1.99", ",", "1.999"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"f", "[", 
      RowBox[{"t_", ",", "p_"}], "]"}], ":=", 
     FractionBox[
      RowBox[{"p", "[", 
       RowBox[{"[", "1", "]"}], "]"}], 
      RowBox[{
       RowBox[{
        RowBox[{"(", 
         RowBox[{"1", "-", 
          FractionBox[
           RowBox[{"p", "[", 
            RowBox[{"[", "1", "]"}], "]"}], 
           RowBox[{"p", "[", 
            RowBox[{"[", "3", "]"}], "]"}]]}], ")"}], 
        RowBox[{"E", "^", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", 
            RowBox[{"p", "[", 
             RowBox[{"[", "2", "]"}], "]"}]}], " ", "t"}], ")"}]}]}], "+", 
       FractionBox[
        RowBox[{"p", "[", 
         RowBox[{"[", "1", "]"}], "]"}], 
        RowBox[{"p", "[", 
         RowBox[{"[", "3", "]"}], "]"}]]}]]}], ";"}], "\n", 
   RowBox[{
    RowBox[{
     RowBox[{"error", "[", "p_", "]"}], ":=", 
     RowBox[{
      RowBox[{"f", "[", 
       RowBox[{
        RowBox[{"Range", "[", 
         RowBox[{"0", ",", "7", ",", "1"}], "]"}], ",", "p"}], "]"}], "-", 
      "y"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tol", "=", 
     SuperscriptBox["10", 
      RowBox[{"-", "6"}]]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"stop", "=", "100"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"result", "=", 
    RowBox[{"GaussNewton", "[", 
     RowBox[{"error", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "1.2", ",", "1"}], "}"}], ",", "tol", ",", "stop"}], 
     "]"}]}]}]}]], "Input",
 CellChangeTimes->{{3.761063880119059*^9, 3.761063896721076*^9}, {
  3.761064022255937*^9, 3.7610640229583125`*^9}, {3.761064072738594*^9, 
  3.7610640987447543`*^9}, {3.7610643238790197`*^9, 3.761064325221117*^9}, {
  3.761064388561472*^9, 3.761064389495679*^9}, {3.7610738814117928`*^9, 
  3.7610739029022017`*^9}, {3.762319119883607*^9, 3.7623191201541724`*^9}, {
  3.763096290071791*^9, 3.763096297366949*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0.04378364037865879`", ",", "2.0105916114422717`", ",", 
   "2.0065642733248015`"}], "}"}]], "Output",
 CellChangeTimes->{{3.7610738993391542`*^9, 3.761073903704344*^9}, 
   3.7610761849228125`*^9, 3.7610970394113073`*^9, 3.761107213678788*^9, 
   3.7611236940342035`*^9, 3.761554968650385*^9, {3.7623190311428695`*^9, 
   3.7623191282937965`*^9}, 3.7623191682536635`*^9, 3.7623195677805696`*^9, 
   3.7623200891280007`*^9, {3.7623201739999385`*^9, 3.7623201991998634`*^9}, 
   3.76232032495504*^9, 3.762320672355884*^9, 3.76232127755497*^9, {
   3.763096285260207*^9, 3.7630962978511686`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{"{", 
     RowBox[{
     "0.04", ",", "0.35", ",", "1.05", ",", "1.9", ",", "1.98", ",", "1.97", 
      ",", "1.99", ",", "1.999"}], "}"}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"f", "[", 
      RowBox[{"t", ",", "result"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"t", ",", "0", ",", "8"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", " ", "Red"}]}], "]"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.761064337993613*^9, 3.7610644168204308`*^9}}],

Cell[BoxData[
 GraphicsBox[{{{}, {{}, 
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.012833333333333334`], AbsoluteThickness[1.6], 
      PointBox[{{1., 0.04}, {2., 0.35}, {3., 1.05}, {4., 1.9}, {5., 1.98}, {
       6., 1.97}, {7., 1.99}, {8., 
       1.999}}]}, {}}, {}, {}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 0, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJwV13k41E8YAHC5LZbdda5lQ6dcP5V0mbdLhHKkJFdIklJCuSNn6aZDEnLl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        "]]},
      Annotation[#, "Charting`Private`Tag$737#1"]& ]}, {}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0., 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
         Part[#, 1]], 
        (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
         Part[#, 1]], 
        (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0., 8.}, {0, 1.999}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.7610644094307055`*^9, 3.7610644170678253`*^9}, 
   3.761073829142984*^9, 3.761073906543152*^9, 3.7610761865008345`*^9, 
   3.761097042364236*^9, 3.761107213850638*^9, 3.7611236969870777`*^9, 
   3.7615549693560953`*^9, {3.7623191432637625`*^9, 3.7623191719335175`*^9}, 
   3.7623195687268806`*^9, 3.7623202011198807`*^9, 3.7623206742061954`*^9, 
   3.762321279104641*^9, 3.763096299335026*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["MEMS accelerometers problem", "Section",
 CellChangeTimes->{{3.761064431051032*^9, 3.761064434678895*^9}, 
   3.76107048653691*^9, {3.7623214152636943`*^9, 3.762321417093231*^9}, 
   3.763096850018113*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"rawData", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "11718.`"}], ",", "966306.`", ",", "31738.`"}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "14648.`"}], ",", "938278.4`", ",", "209862.4`"}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "17577.8`"}], ",", "891403.8`", ",", "365428.2`"}], "}"}],
      ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "21386.4`"}], ",", "815134.2`", ",", "519431.4`"}], "}"}],
      ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "26171.4`"}], ",", "710251.8`", ",", "662986.2`"}], "}"}],
      ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "31151.4`"}], ",", "583006.`", ",", "778122.8`"}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "37109.`"}], ",", "440330.4`", ",", "874997.`"}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "42675.2`"}], ",", "277831.`", ",", "941500.8`"}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "47851.`"}], ",", "112108.8`", ",", "983199.8`"}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "53124.4`"}], ",", 
       RowBox[{"-", "58593.`"}], ",", "993258.6`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
      "271343.5714285714`", ",", "488907.4285714286`", ",", 
       "780340.7142857143`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"494627.`", ",", "249413.`", ",", "780759.`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"566795.2`", ",", 
       RowBox[{"-", "59472.2`"}], ",", "779294.`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"474412.4`", ",", 
       RowBox[{"-", "366600.4`"}], ",", "775680.8`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"239842.6`", ",", 
       RowBox[{"-", "586619.2`"}], ",", "771286.8`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "80956.4`"}], ",", 
       RowBox[{"-", "656833.6`"}], ",", "766696.6`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "378986.3333333333`"}], ",", 
       RowBox[{"-", "561766.`"}], ",", "763750.5`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "597068.4`"}], ",", 
       RowBox[{"-", "326463.8`"}], ",", "763278.6`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "668943.`"}], ",", 
       RowBox[{"-", "8984.2`"}], ",", "765623.`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "573533.4`"}], ",", "296189.8`", ",", "769626.6`"}], 
      "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "337498.6`"}], ",", "513182.`", ",", "774020.8`"}], "}"}],
      ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "503904.`"}], ",", "852243.2`", ",", "22851.`"}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "884177.2`"}], ",", "491209.`", ",", "13671.`"}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "1.028903`*^6"}], ",", "4979.8`", ",", "7324.`"}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "917673.2`"}], ",", 
       RowBox[{"-", "493357.6`"}], ",", "4296.4`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "562888.4`"}], ",", 
       RowBox[{"-", "874118.4`"}], ",", "5371.`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "69432.8`"}], ",", 
       RowBox[{"-", "1.0236296`*^6"}], ",", "9277.`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"413377.6`", ",", 
       RowBox[{"-", "911911.4`"}], ",", "16698.6`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"787302.2`", ",", 
       RowBox[{"-", "571872.8`"}], ",", "24804.4`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"943681.8333333334`", ",", 
       RowBox[{"-", "52815.333333333336`"}], ",", "31167.666666666668`"}], 
      "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
      "830889.3333333334`", ",", "433998.8333333333`", ",", 
       "34504.333333333336`"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"483494.6`", ",", "812399.4`", ",", "33788.6`"}], "}"}]}], 
    "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"g", "=", "9.81"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"axhat", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1.028903`*^6"}], ",", "4979.8`", ",", "7324.`"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ayhat", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "69432.8`"}], ",", 
     RowBox[{"-", "1.0236296`*^6"}], ",", "9277.`"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"azhat", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "53124.4`"}], ",", 
     RowBox[{"-", "58593.`"}], ",", "993258.6`"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"initial", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"9.`", "*", 
      RowBox[{"10", "^", 
       RowBox[{"-", "6"}]}]}], ",", "0", ",", "0.", ",", 
     RowBox[{"-", "2.828363943901612`*^-7"}], ",", 
     RowBox[{"-", "7.00345578266001`*^-6"}], ",", "0", ",", 
     RowBox[{"-", "2.743501000251762`*^-7"}], ",", "2.1338341113069259`*^-7", 
     ",", 
     RowBox[{"-", "1.000957963396124`*^-6"}], ",", "0.7", ",", "0.7", ",", 
     "0.2"}], "}"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.7610677159840794`*^9, 3.761067733403265*^9}, {
  3.761073920017359*^9, 3.761073956710882*^9}, {3.7611015878470235`*^9, 
  3.761101614906954*^9}, {3.762319187636684*^9, 3.7623191878136015`*^9}, {
  3.7623199264387407`*^9, 3.7623200541882463`*^9}, {3.7623201369577613`*^9, 
  3.7623201547499604`*^9}, {3.7623202121698704`*^9, 3.7623202256298747`*^9}, {
  3.762320530156453*^9, 3.76232054228302*^9}, {3.7623207552115107`*^9, 
  3.76232079146047*^9}, {3.7623209732099743`*^9, 3.7623210210595617`*^9}, {
  3.762321063212882*^9, 3.762321063671146*^9}, {3.7623212447949934`*^9, 
  3.7623212489142485`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"M", "[", "p_", "]"}], ":=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"p", "[", 
        RowBox[{"[", "1", "]"}], "]"}], ",", 
       RowBox[{"p", "[", 
        RowBox[{"[", "2", "]"}], "]"}], ",", 
       RowBox[{"p", "[", 
        RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"p", "[", 
        RowBox[{"[", "4", "]"}], "]"}], ",", 
       RowBox[{"p", "[", 
        RowBox[{"[", "5", "]"}], "]"}], ",", 
       RowBox[{"p", "[", 
        RowBox[{"[", "6", "]"}], "]"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"p", "[", 
        RowBox[{"[", "7", "]"}], "]"}], ",", 
       RowBox[{"p", "[", 
        RowBox[{"[", "8", "]"}], "]"}], ",", 
       RowBox[{"p", "[", 
        RowBox[{"[", "9", "]"}], "]"}]}], "}"}]}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"b", "[", "p_", "]"}], ":=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"p", "[", 
      RowBox[{"[", "10", "]"}], "]"}], ",", 
     RowBox[{"p", "[", 
      RowBox[{"[", "11", "]"}], "]"}], ",", 
     RowBox[{"p", "[", 
      RowBox[{"[", "12", "]"}], "]"}]}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"error", "[", "p_", "]"}], ":=", " ", 
   RowBox[{"Join", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"M", "[", "p", "]"}], ".", "axhat"}], "+", 
        RowBox[{"b", "[", "p", "]"}], "-", 
        RowBox[{"{", 
         RowBox[{"g", ",", "0", ",", "0"}], "}"}]}], ")"}], "/", "g"}], ",", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"M", "[", "p", "]"}], ".", "ayhat"}], "+", 
        RowBox[{"b", "[", "p", "]"}], "-", 
        RowBox[{"{", 
         RowBox[{"0", ",", "g", ",", "0"}], "}"}]}], ")"}], "/", "g"}], ",", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"M", "[", "p", "]"}], ".", "azhat"}], "+", 
        RowBox[{"b", "[", "p", "]"}], "-", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "g"}], "}"}]}], ")"}], "/", "g"}], ",", 
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"Norm", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"M", "[", "p", "]"}], ".", 
           RowBox[{"rawData", "[", 
            RowBox[{"[", "i", "]"}], "]"}]}], "+", 
          RowBox[{"b", "[", "p", "]"}]}], "]"}], "-", "g"}], ",", 
       RowBox[{"{", 
        RowBox[{"i", ",", "1", ",", 
         RowBox[{
          RowBox[{"Dimensions", "[", "rawData", "]"}], "[", 
          RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"stop", "=", "50"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"tol", "=", 
   SuperscriptBox["10", 
    RowBox[{"-", "9"}]]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"GaussNewton", "[", 
  RowBox[{"error", ",", "initial", ",", "tol", ",", "stop"}], "]"}]}], "Input",
 CellChangeTimes->{{3.7610762323466215`*^9, 3.761076255766797*^9}, {
   3.761106154864439*^9, 3.7611061602669525`*^9}, {3.7611068975792303`*^9, 
   3.7611069521419535`*^9}, {3.7611071566829324`*^9, 
   3.7611072083198404`*^9}, {3.761555511354714*^9, 3.7615555115734158`*^9}, {
   3.7623191802436523`*^9, 3.762319318353568*^9}, {3.7623194350282183`*^9, 
   3.7623195427977753`*^9}, 3.7623199029684916`*^9, 3.762320689702626*^9, {
   3.762321154455121*^9, 3.7623211546287327`*^9}, {3.7623212155650225`*^9, 
   3.7623212169452157`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "9.921603665559579`*^-6"}], ",", "2.963714824420863`*^-7", 
   ",", "4.4774301542032325`*^-8", ",", 
   RowBox[{"-", "3.1497552948372316`*^-7"}], ",", 
   RowBox[{"-", "9.85063646270977`*^-6"}], ",", 
   RowBox[{"-", "5.269516128814831`*^-8"}], ",", "4.8872374301088366`*^-8", 
   ",", 
   RowBox[{"-", "3.4302920610580114`*^-8"}], ",", "9.758368626549387`*^-6", 
   ",", 
   RowBox[{"-", "0.4108139853989754`"}], ",", 
   RowBox[{"-", "0.2994697186489293`"}], ",", "0.12227288604262025`"}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.7611069321096587`*^9, 3.7611069582044907`*^9}, {
   3.7611072105540023`*^9, 3.7611072217875605`*^9}, 3.761295708093446*^9, 
   3.7615549749244633`*^9, {3.7615554046621885`*^9, 3.7615554297057743`*^9}, {
   3.7615555004703293`*^9, 3.761555515103632*^9}, 3.761555568319888*^9, 
   3.761555676023161*^9, 3.7615560468044205`*^9, 3.7615561062000904`*^9, {
   3.7623195165679903`*^9, 3.762319579457591*^9}, 3.7623196258783283`*^9, {
   3.7623199034686236`*^9, 3.762319939361967*^9}, {3.762320024497982*^9, 
   3.7623200914381514`*^9}, 3.7623201215279827`*^9, {3.762320157929948*^9, 
   3.762320228549864*^9}, 3.7623202634934587`*^9, 3.762320327289118*^9, 
   3.7623205446930733`*^9, 3.762320642043838*^9, {3.7623206767524567`*^9, 
   3.7623206904965086`*^9}, 3.762320793510685*^9, {3.76232102385986*^9, 
   3.762321078032098*^9}, 3.762321167998808*^9, 3.762321230066761*^9, 
   3.762321263374915*^9, 3.762321402324934*^9, 3.76309631398783*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{
  "Check", " ", "whether", " ", "the", " ", "parameters", " ", "satisfy", " ",
    "the", " ", "condition", " ", "for", " ", "the", " ", "vectors", " ", 
   "and", " ", "the", " ", "gravitational", " ", "acceleration"}], 
  "*)"}]], "Input",
 CellChangeTimes->{{3.7623212852466545`*^9, 3.762321310138857*^9}, {
  3.7623213792434826`*^9, 3.762321384523332*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Join", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"Norm", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"M", "[", "pNew", "]"}], ".", "axhat"}], "+", 
      RowBox[{"b", "[", "pNew", "]"}]}], "]"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"Norm", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"M", "[", "pNew", "]"}], ".", "ayhat"}], "+", 
      RowBox[{"b", "[", "pNew", "]"}]}], "]"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"Norm", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"M", "[", "pNew", "]"}], ".", "azhat"}], "+", 
      RowBox[{"b", "[", "pNew", "]"}]}], "]"}], "}"}], ",", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"Norm", "[", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{
         RowBox[{"M", "[", "pNew", "]"}], ".", 
         RowBox[{"rawData", "[", 
          RowBox[{"[", "i", "]"}], "]"}]}], "+", 
        RowBox[{"b", "[", "pNew", "]"}]}], "}"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", 
       RowBox[{
        RowBox[{"Dimensions", "[", "rawData", "]"}], "[", 
        RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.76110705496353*^9, 3.761107056483997*^9}, {
  3.761295717230008*^9, 3.761295744862239*^9}, {3.7615555683667517`*^9, 
  3.761555570489665*^9}, {3.7615557722796726`*^9, 3.7615558037773466`*^9}, {
  3.7623195908441734`*^9, 3.7623196030044594`*^9}, {3.7623196633940315`*^9, 
  3.7623198123635798`*^9}, {3.7623198687786646`*^9, 3.762319892828539*^9}, {
  3.762321190715068*^9, 3.7623211910248337`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "9.800436571562528`", ",", "9.808394120144994`", ",", "9.818302566302481`", 
   ",", "9.824258616384213`", ",", "9.784853632463426`", ",", 
   "9.801869302413232`", ",", "9.816759241032663`", ",", "9.835880046748484`",
    ",", "9.80292617828165`", ",", "9.82625641612432`", ",", 
   "9.793605089725638`", ",", "9.81780106853076`", ",", "9.818302566302483`", 
   ",", "9.789444772948194`", ",", "9.799407357875948`", ",", 
   "9.817085829600533`", ",", "9.818854583865946`", ",", "9.81510326408307`", 
   ",", "9.800601498603063`", ",", "9.796792809970126`", ",", 
   "9.805091818927606`", ",", "9.814893155894666`", ",", "9.814388495813718`",
    ",", "9.804457563041217`", ",", "9.819114546708605`", ",", 
   "9.800263508942887`", ",", "9.80043657156253`", ",", "9.828586680110051`", 
   ",", "9.810134281004622`", ",", "9.808394120144994`", ",", 
   "9.804120837447394`", ",", "9.8199516932132`", ",", "9.799707107130912`", 
   ",", "9.813670315195841`", ",", "9.816543950763712`"}], "}"}]], "Output",
 CellChangeTimes->{
  3.7623207462721043`*^9, 3.762320796000518*^9, {3.762321181699454*^9, 
   3.7623211912851543`*^9}, 3.762321234804807*^9, 3.762321266544769*^9, {
   3.762321387263421*^9, 3.7623214054036093`*^9}, 3.7630963290780687`*^9}]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1536, 781},
WindowMargins->{{-8, Automatic}, {Automatic, -8}},
FrontEndVersion->"11.0 for Microsoft Windows (64-bit) (September 21, 2016)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 157, 2, 70, "Section"],
Cell[740, 26, 5521, 120, 468, "Input"]
}, Closed]],
Cell[CellGroupData[{
Cell[6298, 151, 133, 2, 56, "Section"],
Cell[CellGroupData[{
Cell[6456, 157, 2327, 66, 184, "Input"],
Cell[8786, 225, 637, 11, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9460, 241, 572, 15, 30, "Input"],
Cell[10035, 258, 12094, 211, 243, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[22178, 475, 211, 3, 70, "Section"],
Cell[22392, 480, 5983, 168, 297, "Input"],
Cell[CellGroupData[{
Cell[28400, 652, 3587, 103, 145, "Input"],
Cell[31990, 757, 1528, 26, 34, "Output"]
}, Open  ]],
Cell[33533, 786, 401, 8, 30, "Input"],
Cell[CellGroupData[{
Cell[33959, 798, 1562, 41, 50, "Input"],
Cell[35524, 841, 1287, 20, 50, "Output"]
}, Open  ]]
}, Open  ]]
}
]
*)