10-MehrdimKalmTeil2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Der mehrmensionale Kalman-Filter, Teil 2 Simulationen\n",
    "22.4.2024, S. Mack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# display plots inside this notebook\n",
    "%matplotlib inline \n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Was ist was beim mehrdimensionalen Kalman-Filter?\n",
    "\n",
    "Nachfolgend sind alle Parameter und Startwerte eines mehrdimensionalen Kalman-Filters in einer Tabelle zusammengefasst. Viele dieser Werte müssen für einen Kalman-Filter initialisiert werden. Wie man das genau macht, wurde im vorangegangenen Jupyter-Notebook dargestellt.  \n",
    "\n",
    "\n",
    "\n",
    "|Parameter bzw. Variable|Bedeutung|Typ|Bemerkung|\n",
    "| :-------------------- | :---------------------------: | :---------------------------: | ------------------------:|\n",
    "| Prior, Vorhersagewert Zustandsvektor $\\mathbf{\\bar x}$ |Vorhersagewerte Zustandsgrößen|Vektor, 1D-Array|u.a. interner Rückgabewert ``predict()``, Eingangsgröße von ``update()``|\n",
    "| Kovarianzmatrix Prior $\\mathbf{\\bar P}$ | Varianzen und Korrelationen | Matrix, 2D-Array| u.a. interner Rückgabewert ``predict()``, Eingangsgröße von ``update()``|\n",
    "| Posterior, Korrekturwert Zustandsvektor $\\mathbf{\\hat x}$ |Erwartungswerte Zustandsgrößen, Filter Output|Vektor, 1D-Array|wird als Startwert $\\mathbf{\\hat x_0}$ vorgegeben, u.a. Rückgabewert ``update()``, Eingangsgröße von ``predict()``|\n",
    "| Kovarianzmatrix Posterior $\\mathbf{\\hat P}$ | Varianzen und Korrelationen, Filter Output | Matrix, 2D-Array| wird als Startwert $\\mathbf{\\hat P_0}$ vorgegeben mit Kovarianzen = 0, u.a. Rückgabewert ``update()``, Eingangsgröße von ``predict()``|\n",
    "| Übergangsmatrix $\\mathbf F$ | beinhaltet physikalisches Modell | Matrix, 2D-Array| Funktion für Vorhersage, kommt aus Differentialgleichung des Prozesses, Parameter von ``predict()``|\n",
    "| Kovarianzmatrix Prozessrauschen $\\mathbf Q$ | Unsicherheiten des Modells | Matrix, 2D-Array| Näherungsweise berechnet über reale Schwankungen des Prozesses, Parameter von ``predict()``|\n",
    "| Steuer-/Störgröße $\\mathbf u$ | externe Steuer-/Störgröße auf Prozess | Vektor, 1D-Array| Parameter von ``predict()``, wird hier nicht verwendet|\n",
    "| Steuer-/Störmatrix $\\mathbf B$ | Wirkung externer Steuer-/Störgrößen auf Prozess | Matrix, 2D-Array| Parameter von ``predict()``, wird hier nicht verwendet|\n",
    "| Beobachtungsmatrix $\\mathbf H$ | Transformiert Zustandsgröße in Messgröße | Matrix, 2D-Array| Parameter von ``update()``, wird hier = I angenommen, da Größe Zustand und Messung identisch|\n",
    "| Messwertvektor $\\mathbf z$ |Enthält verrauschte Messwerte|Vektor|Eingangsgröße von ``update()``|\n",
    "| Kovarianzmatrix Messwerte $\\mathbf R$ | Messunsicherheiten in Form von Varianzen (und Korrelationen)  | Matrix, 2D-Array| Parameter von ``update()`` für Gegenüberstellung Relevanz Messwert-Vorhersagewert|\n",
    "| Residuum $\\mathbf y$ | Differenz Vorhersage- und Messwert|Vektor|wird in Einheiten des Messwertes berechnet|\n",
    "| Kalman Gain $\\mathbf K$ | Berechnung Verhältnis Relevanz Mess- und Vorhersagewert | Matrix, 2D-Array| Berechnung über Varianzen und damit Verortung des Korrekturwertes|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Und hier sind nochmals die grundlegenden Kalman-Gleichungen dargestellt. Dazu wird die selbe Notation verwendet wie in den voran gegangenen Jupyter-Notebooks:  \n",
    "\n",
    "<u>Vorhersage</u>\n",
    "\n",
    "$\\begin{array}{|l|l|l|l|}\n",
    "\\hline\n",
    "\\text{Notation} &  \\text{Notation} & \\text{Notation} & \\text{Notation mehrd.}\\\\\n",
    "\\text{eindim. Statistik} & \\text{eindim. Kalman} & \\text{mehrdim. Kalman} & \\text{Kalman mit $\\mathbf{u = 0}$}\\\\\n",
    "\\hline\n",
    "\\bar \\mu = \\mu + \\mu_{f_x} & \\bar x = \\hat x + dx & \\bar{\\mathbf x} = \\mathbf{F \\hat x} + \\mathbf{Bu} & \\bar{\\mathbf x} = \\mathbf{F \\hat x}\\\\\n",
    "\\bar\\sigma^2 = \\sigma_x^2 + \\sigma_{f_x}^2 & \\bar P = \\hat P + Q & \\bar{\\mathbf P} = \\mathbf{F{\\hat P}F}^\\mathsf T + \\mathbf Q & \\bar{\\mathbf P} = \\mathbf{F{\\hat P}F}^\\mathsf T + \\mathbf Q\\\\\n",
    "\\hline\n",
    "\\end{array}$\n",
    "\n",
    "<u>Korrektur</u>\n",
    "\n",
    "$\\begin{array}{|l|l|l|l|}\n",
    "\\hline\n",
    "\\text{Notation} &  \\text{Notation} & \\text{Notation} & \\text{Notation mehrdim.}\\\\\n",
    "\\text{eindim. Statistik} & \\text{eindim. Kalman} & \\text{mehrdim. Kalman} & \\text{Kalman mit $\\mathbf H = \\mathbf I$}\\\\\n",
    "\\hline\n",
    "& y = z - \\bar x & \\mathbf y = \\mathbf z - \\mathbf{H\\bar x} & \\mathbf y = \\mathbf z - \\mathbf{\\bar x}\\\\\n",
    "& K = \\frac{\\bar P}{\\bar P+R}&\n",
    "\\mathbf K = \\mathbf{\\bar{P}H}^\\mathsf T (\\mathbf{H\\bar{P}H}^\\mathsf T + \\mathbf R)^{-1} &\n",
    "\\mathbf K = \\mathbf{\\bar{P}} (\\mathbf{\\bar{P}} + \\mathbf R)^{-1}\\\\\n",
    "\\mu=\\frac{\\bar\\sigma^2\\, \\mu_z + \\sigma_z^2 \\, \\bar\\mu} {\\bar\\sigma^2 + \\sigma_z^2} & \\hat x = \\bar x + Ky & \\mathbf{\\hat x} = \\mathbf {\\bar x} + \\mathbf{Ky} & \\mathbf{\\hat x} = \\mathbf {\\bar x} + \\mathbf{Ky}\\\\\n",
    "\\sigma^2 = \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2} & \\hat P = (1-K)\\bar P &\n",
    "\\mathbf {\\hat P} = (\\mathbf I - \\mathbf{KH})\\mathbf{\\bar{P}} &\n",
    "\\mathbf {\\hat P} = (\\mathbf I - \\mathbf{K})\\mathbf{\\bar{P}}\\\\\n",
    "\\hline\n",
    "\\end{array}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementierung des Vorhersage- und Korrektur-Algorithmus\n",
    "Der Vorhersage-Algorithmus wurde schon im voran gegangenen Jupyter-Notebook in Python implementiert. Er wird hier nochmals unverändert dargestellt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(x, P, F, Q, B, u):\n",
    "    '''Kalman Filter predict step'''\n",
    "    x_prior = np.dot(F, x)+ np.dot(B, u)\n",
    "    P_prior = np.dot(F, P).dot(F.T) + Q # A.dot(B) is the same as np.dot(A,B)\n",
    "    return x_prior,P_prior "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Somit bleibt noch die Implementierung des Korrektur-Algorithmus übrig. Dafür wird die Berechnungsformel aus der unteren Tabelle oben in Python-Code wie folgt implementiert:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.linalg import inv\n",
    "\n",
    "def update(x, P, H, R, z):\n",
    "    '''Kalman Filter update step'''\n",
    "    S = np.dot(H, P).dot(H.T) + R\n",
    "    K = np.dot(P, H.T).dot(inv(S))\n",
    "    y = z - np.dot(H, x)\n",
    "    x_post = x + np.dot(K, y)\n",
    "    P_post = P - np.dot(K, H).dot(P)  \n",
    "    return x_post, P_post"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vorbereitung für die Simulation und das anschließende zweidimensionale Kalman-Tracking eines Roboterfahrzeugs\n",
    "\n",
    "<img src=\"RoboFahrzeug15Grad.png\" width=\"400\">\n",
    "Wie im schon bekannten Bild oben dargestellt, fährt das Roboterfahrzeug geradlinig schräg zu einer Wand. Gemessen wird der Abstand zur Wand. Die Bewegung dieses Fahrzeugs wird simuliert, um anschließend anhand der erzeugten Sensordaten die Wirkung des mehrdimensionalen Kalman-Filters zu untersuchen.  \n",
    "\n",
    "Um den neuen zweidimensionalen Kalman-Filter zu testen, wird nachfolgend der Code für die Simulation des Roboterfahrzeugs erklärt. Dieser baut auf der gleichnamigen Klasse des Jupyter-Notebooks für den eindimensionalen Kalman-Filter auf.\n",
    "\n",
    "### Simulation des Roboterfahrzeugs\n",
    "\n",
    "Die Klasse ``RoboSim`` gibt in der Methode ``move_and_sense()`` nun zusätzlich eine Steuergröße $\\mathbf u$  aus. Sie ist derzeit aber nur als Platzhalter für die Funktion ``predict()`` nötig und hat den Wert Null. Somit wird ``RoboSim`` entsprechend neu implementiert.  \n",
    "Der Konstruktor ``RoboSim(x0,velocity,process_var,measurement_var)`` erhält folgende Variablen übergeben: \n",
    "* ``x0``: Startposition des Roboters. \n",
    "* ``velocity``: Die (mittlere) Positionsänderung pro Iteration, also der Erwartungswert der Geschwindigkeit.\n",
    "* ``process_var``: Die Varianz des gaussförmigen Prozessrauschens, mit dem ``velocity`` beaufschlagt wird. Der Roboter bewegt sich realitätsnah *nicht* mit absolut konstanter Geschwindigkeit relativ zur Wand. D.h. er fährt beispielsweise leichte Schlangenlinien im Gegensatz zu einer idealen Fahrspur in Form einer Geraden.\n",
    "* ``measurement_var``: Die Varianz der Messunsicherheit des Positionssensors, also des Messrauschens.  \n",
    "  \n",
    "Die Methode `sense_position()` schlägt auf den schon durch das Prozessrauschen leicht verrauschten wahren Positionswert zusätzlich ein signifikantes Messrauschen auf.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy # needed for deepcopy() in move_and_sense()\n",
    "from collections import namedtuple\n",
    "gaussian = namedtuple('Gaussverteilung', ['mean', 'var'])\n",
    "\n",
    "class RoboSim(object):\n",
    "    def __init__(self, x0=0, velocity=1, process_var=0.0, measurement_var=0.0):\n",
    "        '''currently no control input u is implemented: u = 0 for all time steps.\n",
    "        x0: initial position. process_var: velocity variance in process (m/s)^2. \n",
    "        measurement_var: variance in position measurement m^2. dt: time step size'''\n",
    "        self.x = x0\n",
    "        self.velocity = velocity\n",
    "        self.measurement_noise = np.sqrt(measurement_var)\n",
    "        self.process_noise = np.sqrt(process_var)\n",
    "\n",
    "    def move(self, dt):\n",
    "        '''compute new position of the robot assuming `dt` seconds have passed \n",
    "        since last update with process_noise added to velocity (not position)'''\n",
    "        # computes new position based on velocity + process noise added\n",
    "        velocity = self.velocity + np.random.randn() * self.process_noise * dt\n",
    "        self.x += velocity * dt\n",
    "\n",
    "    def sense_position(self):\n",
    "        '''simulates measuring the position with measurement noise'''\n",
    "        return self.x + np.random.randn() * self.measurement_noise\n",
    "\n",
    "    def move_and_sense(self, dt):\n",
    "        '''true noisy position, measured position of robot, control value u=0'''\n",
    "        self.move(dt)\n",
    "        x = copy.deepcopy(self.x)\n",
    "        return x, self.sense_position(), 0 \n",
    "\n",
    "    def run_simulation(self, count=1, dt=1):\n",
    "        '''simulates the robot moving over a period of time and returns data: \n",
    "        (3,count) size array, column 0: true robot position, column 1: measurement\n",
    "        robot position, column 2: control value (currently allways zero)'''\n",
    "        return np.array([self.move_and_sense(dt) for i in range(count)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hilfsfunktionen\n",
    "#### Anwendung des Kalmanfilters und Erzeugung von Daten für die grafische Darstellung\n",
    "Die Funktion ``kal_filt_2dim_for_plot()`` führt auf den vorher simulierten Daten ``sim_data`` einen zweidimensionalen Kalmanfilter aus mit den Größen \"Abstand\" und \"Abstandsänderung\" des Roboterfahrzeugs als Zustandsgrößen. Die Zustandsgröße \"Abstandsänderung\" ist eine verborgene Zustandsgröße.  \n",
    "Die Rückgabewerte dieser Funktion sind für jeden Iterationsschritt des Kalman-Filters jeweils der Zustandsvektor des Priors (Vorhersage) inkl. Kovarianzmatrix sowie der Zustandsvektor des Posteriors (Korrekturwert bzw. Schätzwert) inkl. Kovarianzmatrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kal_filt_2dim_for_plot(sim_data, x_start, P_start, F, Q, H, R):\n",
    "    '''Performs 2-dim Kalman filtering for subsequent plotting on data set\n",
    "    sim_data with sim_data[1]: Measurements. sim_data[2]: control values u.\n",
    "    Returns priors, posteriors of state vectors with standard deviations \n",
    "    '''    \n",
    "    prior=[] # needed for subsequent plotting\n",
    "    prior_std=[]\n",
    "    posterior=[]\n",
    "    posterior_std=[]\n",
    "    print('d wahr \\t d vorh +/-Std     d mess +/-Std     d korr +/-Std     v korr +/-Std')\n",
    "    # perform Kalman filter on simulated measurement data simdata[1,:]\n",
    "    x = x_start\n",
    "    P = P_start\n",
    "    for val in sim_data:    \n",
    "        x_prior,P_prior = predict(x, P, F, Q, B, val[2])\n",
    "        x_post,P_post = update(x_prior, P_prior, H, R, val[1])\n",
    "        print('{:6.3f}\\t{:6.3f} +/-{:6.3f}  {:6.3f} +/-{:6.3f}  {:6.3f} +/-{:6.3f}  {:6.3f} +/-{:6.3f}'.format\n",
    "              (val[0],x_prior[0,0],np.sqrt(P_prior[0,0]),val[1],np.sqrt(sensor_var),\n",
    "               x_post[0,0],np.sqrt(P_post[0,0]),x_post[1,0],np.sqrt(P_post[1,0])))\n",
    "        prior.append(x_prior[0])\n",
    "        prior_std.append(np.sqrt(P_prior[0,0]))\n",
    "        posterior.append(x_post)\n",
    "        posterior_std.append(np.sqrt(P_post[0,0]))\n",
    "        x = x_post\n",
    "        P = P_post\n",
    "    return prior, prior_std, posterior,posterior_std "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Grafische Darstellung der Simulationsdaten inkl. der Kalman-Filterschätzwerte\n",
    "Die Funktion ``plot_kal_filt_2dim()`` erstellt aus Daten der Simulation sowie aus den Ausgabewerten des darauf angewendeten zweidimensionalen Kalman-Filters eine grafische Darstellung. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_kal_filt_2dim(val_true,val_meas, est_x0, est_x1, dt):\n",
    "    '''Plots the results of a twodimensional Kalman fiter with hidden second\n",
    "    state variable x1. Needs as input: true value of x0, measured value of x0, \n",
    "    estimate of x0 and estimate of x1, time step size dt'''\n",
    "    fig, ax1 = plt.subplots(figsize=(10,4))\n",
    "    time = np.linspace(dt,val_true.size*dt, val_true.size)\n",
    "    ax1.plot(time,val_true,color='k',mfc='None',marker = 'None',linestyle=':',linewidth = 0.5,label='wahrer Wert')\n",
    "    ax1.plot(time,val_meas,color='C2',mfc='None',marker = 'o',linestyle='None',label='Messwert')\n",
    "    ax1.plot(time,est_x0,color='C1',mfc='None',marker = '+',linestyle='-.',linewidth = 1,label='Schätzwert $d$')\n",
    "    ax1.set_xlabel('Zeit (s)')\n",
    "    ax1.tick_params('y', colors='C1')\n",
    "    ax1.set_ylabel('Abstand $d$ (m)', color='C1')\n",
    "    ax2 = ax1.twinx() # second y-axis\n",
    "    ax2.plot(time, est_x1,color='C0',mfc='None',marker = '+',linestyle='--',linewidth = 1,label='Schätzwert $\\dot d$')\n",
    "    ax2.tick_params('y',colors='C0')\n",
    "    ax2.set_ylabel('Abstandsänderung $\\dot d$ (m/s)',color='C0')\n",
    "    ax2.set_ylim(-0.01,0.1)\n",
    "    fig.legend(loc='upper left',bbox_to_anchor=(0,1),bbox_transform=ax1.transAxes) # places common legend for both axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Berechnung der Kovarianzmatrix des Prozessrauschens über die erwartete (tatsächliche) Abweichung der Fahrspur von einer geraden Linie\n",
    "Wie im vorhergehenden Jupyter-Notebook dargestellt, kann die Kovarianzmatrix $\\mathbf Q$ für das hier betrachtete Roboterfahrzeug mit der Funktion ``Q_zero_mean()`` berechnet werden:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Q_zero_mean(dim, dt=1., var=1):\n",
    "    '''generates start value of process covariance matrix based on given estimate\n",
    "    of variance for the highest order state variable (e.g. velocity for two dimensions)'''\n",
    "    if not (dim == 2 or dim == 3 or dim == 4):\n",
    "        raise ValueError(\"dim must be between 2 and 4\")\n",
    "    if dim == 2:\n",
    "        Q = np.array([[.25*dt**4, .5*dt**3],\n",
    "             [ .5*dt**3,    dt**2]])\n",
    "    elif dim == 3:\n",
    "        Q = np.array([[.25*dt**4, .5*dt**3, .5*dt**2],\n",
    "             [ .5*dt**3,    dt**2,       dt],\n",
    "             [ .5*dt**2,       dt,        1]])\n",
    "    else:\n",
    "        Q = np.array([[(dt**6)/36, (dt**5)/12, (dt**4)/6, (dt**3)/6],\n",
    "             [(dt**5)/12, (dt**4)/4,  (dt**3)/2, (dt**2)/2],\n",
    "             [(dt**4)/6,  (dt**3)/2,   dt**2,     dt],\n",
    "             [(dt**3)/6,  (dt**2)/2 ,  dt,        1.]])\n",
    "    return Q*var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Untersuchung des zweidimensionalen Kalman-Filters anhand von Simulationen eines Roboterfahrzeugs\n",
    "Eine Simulation besteht immer aus drei Schritten:\n",
    "1. Den Kalman-Filter und dessen Parameter initialisieren.\n",
    "2. Für die vorgegebene Geschwindigkeit des Roboterfahrzeugs die wahren (auch leicht verrauschten) Positionsdaten und die entsprechenden (stärker verrauschen) Sensormessdaten dazu erzeugen = simulieren.\n",
    "3. Die Kalman-Filterung durchführen\n",
    "4. Den Verlauf der Schätzwerte für Abstand und Abstandsänderung, der wahren und gemessenen Abstände grafisch darstellen.\n",
    "\n",
    "In den folgenden Abschnitten werden mit verschiedenen Parametern und Randbedingungen Simulationen der Fahrzeugbewegung und daran anschließend eine Kalman-Filterung durchgeführt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Erste Simulation mit realitätsnahen Annahmen für Roboterfahrzeug aus Projekt Automatisierungstechnik (PAT)\n",
    "#### Schritt 1: Initialisierungswerte und Parameter für den zweidimensionalen Kalman-Filter zum Tracken des simulierten Roboterfahrzeugs\n",
    "Im vorherigen Jupyter-Notebook wurden folgende Initialisierungswerte und Parameter hergeleitet, berechnet und implementiert. Nachfolgend werden jeweils solche Werte verwendet, die in etwa den realen Werten für das Roboterfahrzeug im PAT entsprechen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initializing the Kalman Filter, parameter setting\n",
    "dt=1\n",
    "x_start = np.array([[0.25],[0.01]])\n",
    "P_start = np.diag([0.25, 0.0009])\n",
    "F = np.array([[1, dt],[0, 1]])\n",
    "Q = Q_zero_mean(dim=2, dt=dt, var=4e-6) # var=4e-6\n",
    "B = 0\n",
    "sigma_z = 0.07\n",
    "R = np.array([[sigma_z**2]])\n",
    "H = np.array([[1., 0.]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Schritt 2: Durchführung der Simulation der Bewegung des Roboterfahrzeugs\n",
    "Für die Simulation der Bewegung des Roboterfahrzeugs müssen noch die Varianz der Abstandsmessung sowie die Varianz des Prozesses (also wie weit die tatsächliche Fahrspur des Fahrzeugs von einer geraden Linie abweicht) festgelegt werden. Es wird dafür jeweils das Element (0,0) aus den Matrizen $\\mathbf Q$ und $\\mathbf R$ verwendet. Damit ist sicher gestellt, dass die Annahmen im Kalman-Filter über das Prozess- und Messwertrauschen immer denen der simulierten Bewegung entsprechen.   \n",
    "Weiter müssen noch die Anzahl der Schritte, die Abtastzeit ``dt`` sowie der Startabstand und die Abstandsänderung als Eingangsdaten für diese Simulation spezifiziert werden. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set parameters for robot car movement simulation\n",
    "process_var = Q[0,0] # variance of robot distance, same as later in Kalman filter\n",
    "sensor_var = R[0,0] # variance distance sensor, same as later in Kalman filter\n",
    "n = 20 # number of data sets to be simulated\n",
    "start_pos_sim = 0 # start position\n",
    "vel_sim = 0.05 # constant velocity value\n",
    "\n",
    "robot = RoboSim(x0=start_pos_sim,velocity=vel_sim,measurement_var=sensor_var,process_var=process_var)\n",
    "# create list of measurements spaced by dt\n",
    "np.random.seed(13) # to make the simulation reproducible\n",
    "sim_data = robot.run_simulation(count=n,dt=dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Schritt 3: Kalman-Filterung\n",
    "Hier wird ein Startabstand sowie eine Startabstandsänderung ``x-start`` verwendet, welche von den entsprechenden Werten ``start_pos_sim`` bzw. ``vel_sim`` abweicht. Denn dem Filter sind diese beiden Werte ja nicht bekannt, sonder er muss sich ihnen durch die Iterationen annähern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d wahr \t d vorh +/-Std     d mess +/-Std     d korr +/-Std     v korr +/-Std\n",
      " 0.049\t 0.260 +/- 0.501   0.102 +/- 0.070   0.105 +/- 0.069   0.009 +/- 0.004\n",
      " 0.099\t 0.115 +/- 0.076   0.131 +/- 0.070   0.123 +/- 0.051   0.011 +/- 0.021\n",
      " 0.151\t 0.134 +/- 0.066   0.188 +/- 0.070   0.159 +/- 0.048   0.018 +/- 0.026\n",
      " 0.202\t 0.177 +/- 0.065   0.262 +/- 0.070   0.217 +/- 0.048   0.030 +/- 0.027\n",
      " 0.253\t 0.247 +/- 0.065   0.180 +/- 0.070   0.216 +/- 0.047   0.022 +/- 0.025\n",
      " 0.303\t 0.238 +/- 0.062   0.214 +/- 0.070   0.228 +/- 0.046   0.019 +/- 0.023\n",
      " 0.353\t 0.247 +/- 0.059   0.336 +/- 0.070   0.284 +/- 0.045   0.027 +/- 0.021\n",
      " 0.404\t 0.311 +/- 0.055   0.426 +/- 0.070   0.355 +/- 0.043   0.036 +/- 0.019\n",
      " 0.454\t 0.391 +/- 0.052   0.605 +/- 0.070   0.468 +/- 0.042   0.049 +/- 0.018\n",
      " 0.505\t 0.517 +/- 0.050   0.503 +/- 0.070   0.513 +/- 0.041   0.049 +/- 0.016\n",
      " 0.554\t 0.561 +/- 0.047   0.637 +/- 0.070   0.585 +/- 0.039   0.052 +/- 0.015\n",
      " 0.605\t 0.637 +/- 0.045   0.529 +/- 0.070   0.605 +/- 0.038   0.048 +/- 0.014\n",
      " 0.655\t 0.653 +/- 0.044   0.671 +/- 0.070   0.658 +/- 0.037   0.048 +/- 0.014\n",
      " 0.703\t 0.707 +/- 0.042   0.684 +/- 0.070   0.700 +/- 0.036   0.048 +/- 0.013\n",
      " 0.754\t 0.748 +/- 0.041   0.641 +/- 0.070   0.721 +/- 0.035   0.044 +/- 0.012\n",
      " 0.805\t 0.765 +/- 0.040   0.937 +/- 0.070   0.808 +/- 0.035   0.049 +/- 0.012\n",
      " 0.854\t 0.857 +/- 0.039   0.823 +/- 0.070   0.849 +/- 0.034   0.048 +/- 0.012\n",
      " 0.905\t 0.897 +/- 0.039   0.941 +/- 0.070   0.907 +/- 0.034   0.050 +/- 0.012\n",
      " 0.955\t 0.957 +/- 0.038   0.849 +/- 0.070   0.932 +/- 0.033   0.047 +/- 0.011\n",
      " 1.004\t 0.979 +/- 0.038   1.011 +/- 0.070   0.986 +/- 0.033   0.048 +/- 0.011\n"
     ]
    }
   ],
   "source": [
    "# perform twodimensional Kalman filtering\n",
    "priors,priors_std,posts,posts_std = kal_filt_2dim_for_plot(sim_data, x_start, P_start, F, Q, H, R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Schritt 4: Grafische Darstellung der Ergebnisse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot kalman filter output together with simulated data\n",
    "plot_kal_filt_2dim(sim_data[:,0],sim_data[:,1],\n",
    "                   [val[0,0] for val in posts],[val[1,0] for val in posts],dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die oben dargestellte Simulation basiert auf recht realistischen Annahmen für das im PAT verwendete Roboterfahrzeug. Es ist schön zu sehen, wie die zweite (verdeckte) Zustandsgröße \"Abstandsänderung\" recht schnell vom Filter bestimmt wird, obwohl im Startwert des Filters eine viel zu kleine Änderung angenommen wurde."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation mit sehr schlechten Startwerten für Abstand und Abstandsänderung und normalem Rauschen\n",
    "Der eindimensionale Kalman-Filter war nicht robust gegenüber einer falsch angenommenen Abstandsänderung im physikalischen Modell. Hier im zweidimensionalen Fall kann problemlos ein Startwert dafür angenommen werden, der erheblich von der wahren Abstandsänderung abweicht.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d wahr \t d vorh +/-Std     d mess +/-Std     d korr +/-Std     v korr +/-Std\n",
      " 0.049\t 1.200 +/- 0.501   0.102 +/- 0.070   0.123 +/- 0.069   0.396 +/- 0.004\n",
      " 0.099\t 0.519 +/- 0.076   0.131 +/- 0.070   0.310 +/- 0.051   0.363 +/- 0.021\n",
      " 0.151\t 0.672 +/- 0.066   0.188 +/- 0.070   0.445 +/- 0.048   0.297 +/- 0.026\n",
      " 0.202\t 0.742 +/- 0.065   0.262 +/- 0.070   0.518 +/- 0.048   0.228 +/- 0.027\n",
      " 0.253\t 0.746 +/- 0.065   0.180 +/- 0.070   0.486 +/- 0.047   0.154 +/- 0.025\n",
      " 0.303\t 0.639 +/- 0.062   0.214 +/- 0.070   0.452 +/- 0.046   0.107 +/- 0.023\n",
      " 0.353\t 0.559 +/- 0.059   0.336 +/- 0.070   0.467 +/- 0.045   0.087 +/- 0.021\n",
      " 0.404\t 0.554 +/- 0.055   0.426 +/- 0.070   0.505 +/- 0.043   0.077 +/- 0.019\n",
      " 0.454\t 0.582 +/- 0.052   0.605 +/- 0.070   0.590 +/- 0.042   0.079 +/- 0.018\n",
      " 0.505\t 0.669 +/- 0.050   0.503 +/- 0.070   0.613 +/- 0.041   0.070 +/- 0.016\n",
      " 0.554\t 0.683 +/- 0.047   0.637 +/- 0.070   0.668 +/- 0.039   0.067 +/- 0.015\n",
      " 0.605\t 0.736 +/- 0.045   0.529 +/- 0.070   0.675 +/- 0.038   0.059 +/- 0.014\n",
      " 0.655\t 0.733 +/- 0.044   0.671 +/- 0.070   0.716 +/- 0.037   0.057 +/- 0.014\n",
      " 0.703\t 0.773 +/- 0.042   0.684 +/- 0.070   0.749 +/- 0.036   0.053 +/- 0.013\n",
      " 0.754\t 0.802 +/- 0.041   0.641 +/- 0.070   0.761 +/- 0.035   0.048 +/- 0.012\n",
      " 0.805\t 0.809 +/- 0.040   0.937 +/- 0.070   0.841 +/- 0.035   0.052 +/- 0.012\n",
      " 0.854\t 0.893 +/- 0.039   0.823 +/- 0.070   0.876 +/- 0.034   0.050 +/- 0.012\n",
      " 0.905\t 0.926 +/- 0.039   0.941 +/- 0.070   0.930 +/- 0.034   0.051 +/- 0.012\n",
      " 0.955\t 0.980 +/- 0.038   0.849 +/- 0.070   0.950 +/- 0.033   0.047 +/- 0.011\n",
      " 1.004\t 0.997 +/- 0.038   1.011 +/- 0.070   1.001 +/- 0.033   0.047 +/- 0.011\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_start = np.array([[0.8],[0.4]])\n",
    "P_start = np.diag([0.25, 0.0009])\n",
    "\n",
    "priors,priors_std,posts,posts_std = kal_filt_2dim_for_plot(sim_data, x_start, P_start, F, Q, H, R)\n",
    "plot_kal_filt_2dim(sim_data[:,0],sim_data[:,1],\n",
    "                   [val[0,0] for val in posts],[val[1,0] for val in posts],dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ein schlechter Startwert für die Anfangsposition konnte schon der eindimensionale Kalman-Filter kompensieren. Hier im zweidimensionalen Fall konvergiert der Filter jedoch wesentlich schneller.  \n",
    "Der viel zu groß angenommene Startwert der Abstandsänderung führt zu Beginn zu einem deutlichen Überschwingens des Filters. \n",
    "Auch hier wird die zweite (verdeckte) Zustandsgröße \"Abstandsänderung\" recht schnell vom Filter bestimmt, obwohl im Startwert des Filters eine viel zu große Änderung angenommen wurde."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation mit sehr hohem Messwertrauschen und guten Startwerten\n",
    "Die eigentliche Filterwirkung auf den Zustandswert \"Abstand\" steht hier im Fokus: Selbst bei stark verrauschten Messwerten liefert der mehrdimensionale Kalman-Filter einen recht glatten Schätzwertverlauf, der nahe bei den wahren Abstandswerten liegt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d wahr \t d vorh +/-Std     d mess +/-Std     d korr +/-Std     v korr +/-Std\n",
      " 0.049\t 0.260 +/- 0.501   0.125 +/- 0.100   0.130 +/- 0.098   0.010 +/- 0.006\n",
      " 0.099\t 0.139 +/- 0.103   0.144 +/- 0.100   0.142 +/- 0.072   0.010 +/- 0.021\n",
      " 0.151\t 0.152 +/- 0.083   0.204 +/- 0.100   0.173 +/- 0.064   0.014 +/- 0.028\n",
      " 0.202\t 0.187 +/- 0.080   0.288 +/- 0.100   0.226 +/- 0.063   0.023 +/- 0.031\n",
      " 0.253\t 0.250 +/- 0.080   0.149 +/- 0.100   0.210 +/- 0.063   0.014 +/- 0.031\n",
      " 0.303\t 0.224 +/- 0.079   0.176 +/- 0.100   0.206 +/- 0.062   0.010 +/- 0.030\n",
      " 0.353\t 0.215 +/- 0.077   0.329 +/- 0.100   0.258 +/- 0.061   0.018 +/- 0.028\n",
      " 0.404\t 0.276 +/- 0.075   0.436 +/- 0.100   0.333 +/- 0.060   0.029 +/- 0.026\n",
      " 0.454\t 0.362 +/- 0.071   0.669 +/- 0.100   0.466 +/- 0.058   0.047 +/- 0.024\n",
      " 0.505\t 0.513 +/- 0.068   0.502 +/- 0.100   0.509 +/- 0.056   0.046 +/- 0.022\n",
      " 0.554\t 0.555 +/- 0.066   0.673 +/- 0.100   0.591 +/- 0.055   0.051 +/- 0.021\n",
      " 0.605\t 0.642 +/- 0.063   0.496 +/- 0.100   0.600 +/- 0.053   0.046 +/- 0.019\n",
      " 0.655\t 0.646 +/- 0.061   0.678 +/- 0.100   0.655 +/- 0.052   0.047 +/- 0.018\n",
      " 0.703\t 0.702 +/- 0.059   0.675 +/- 0.100   0.695 +/- 0.051   0.046 +/- 0.017\n",
      " 0.754\t 0.741 +/- 0.057   0.593 +/- 0.100   0.705 +/- 0.049   0.042 +/- 0.017\n",
      " 0.805\t 0.747 +/- 0.055   0.994 +/- 0.100   0.804 +/- 0.048   0.048 +/- 0.016\n",
      " 0.854\t 0.853 +/- 0.054   0.809 +/- 0.100   0.843 +/- 0.047   0.047 +/- 0.015\n",
      " 0.905\t 0.890 +/- 0.053   0.956 +/- 0.100   0.904 +/- 0.047   0.049 +/- 0.015\n",
      " 0.955\t 0.953 +/- 0.052   0.804 +/- 0.100   0.921 +/- 0.046   0.045 +/- 0.015\n",
      " 1.004\t 0.967 +/- 0.051   1.014 +/- 0.100   0.977 +/- 0.045   0.046 +/- 0.014\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_start = np.array([[0.25],[0.01]])\n",
    "P_start = np.diag([0.25, 0.0009])\n",
    "sigma_z = 0.1\n",
    "R = np.array([[sigma_z**2]])\n",
    "sensor_var = R[0,0] # variance distance sensor, same as later in Kalman filter\n",
    "robot = RoboSim(x0=start_pos_sim,velocity=vel_sim,measurement_var=sensor_var,process_var=process_var)\n",
    "np.random.seed(13) # to make the simulation reproducible\n",
    "sim_data = robot.run_simulation(count=n,dt=dt)\n",
    "priors,priors_std,posts,posts_std = kal_filt_2dim_for_plot(sim_data, x_start, P_start, F, Q, H, R)\n",
    "plot_kal_filt_2dim(sim_data[:,0],sim_data[:,1],\n",
    "                   [val[0,0] for val in posts],[val[1,0] for val in posts],dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation mit plötzlicher Richtungsänderung des Roboterfahrzeugs\n",
    "Diese Simulation verwendet die gleichen Parameter wie die erste mit den realitätsnahen Annahmen für das Roboterfahrzeug. Die erste Hälfte der Bewegungssimulation fährt das Roboterfahrzeug im gleichen Winkel wie zuvor von der Wand weg. Anschließend dreht es etwas zur Wand hin und fährt während der zweiten Hälfte parallel zur Wand.  \n",
    "Der Kalmanfilter reagiert hier zwar richtig aber nicht wirklich schnell auf den plötzlichen Richtungswechsel. Eine Matrix $\\mathbf Q$ mit etwas kleineren Werten würde hier helfen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d wahr \t d vorh +/-Std     d mess +/-Std     d korr +/-Std     v korr +/-Std\n",
      " 0.049\t 0.260 +/- 0.501   0.102 +/- 0.070   0.105 +/- 0.069   0.009 +/- 0.004\n",
      " 0.099\t 0.115 +/- 0.076   0.131 +/- 0.070   0.123 +/- 0.051   0.011 +/- 0.021\n",
      " 0.151\t 0.134 +/- 0.066   0.188 +/- 0.070   0.159 +/- 0.048   0.018 +/- 0.026\n",
      " 0.202\t 0.177 +/- 0.065   0.262 +/- 0.070   0.217 +/- 0.048   0.030 +/- 0.027\n",
      " 0.253\t 0.247 +/- 0.065   0.180 +/- 0.070   0.216 +/- 0.047   0.022 +/- 0.025\n",
      " 0.303\t 0.238 +/- 0.062   0.214 +/- 0.070   0.228 +/- 0.046   0.019 +/- 0.023\n",
      " 0.353\t 0.247 +/- 0.059   0.336 +/- 0.070   0.284 +/- 0.045   0.027 +/- 0.021\n",
      " 0.404\t 0.311 +/- 0.055   0.426 +/- 0.070   0.355 +/- 0.043   0.036 +/- 0.019\n",
      " 0.454\t 0.391 +/- 0.052   0.605 +/- 0.070   0.468 +/- 0.042   0.049 +/- 0.018\n",
      " 0.505\t 0.517 +/- 0.050   0.503 +/- 0.070   0.513 +/- 0.041   0.049 +/- 0.016\n",
      " 0.554\t 0.561 +/- 0.047   0.637 +/- 0.070   0.585 +/- 0.039   0.052 +/- 0.015\n",
      " 0.605\t 0.637 +/- 0.045   0.529 +/- 0.070   0.605 +/- 0.038   0.048 +/- 0.014\n",
      " 0.655\t 0.653 +/- 0.044   0.671 +/- 0.070   0.658 +/- 0.037   0.048 +/- 0.014\n",
      " 0.703\t 0.707 +/- 0.042   0.684 +/- 0.070   0.700 +/- 0.036   0.048 +/- 0.013\n",
      " 0.754\t 0.748 +/- 0.041   0.641 +/- 0.070   0.721 +/- 0.035   0.044 +/- 0.012\n",
      " 0.805\t 0.765 +/- 0.040   0.937 +/- 0.070   0.808 +/- 0.035   0.049 +/- 0.012\n",
      " 0.854\t 0.857 +/- 0.039   0.823 +/- 0.070   0.849 +/- 0.034   0.048 +/- 0.012\n",
      " 0.905\t 0.897 +/- 0.039   0.941 +/- 0.070   0.907 +/- 0.034   0.050 +/- 0.012\n",
      " 0.955\t 0.957 +/- 0.038   0.849 +/- 0.070   0.932 +/- 0.033   0.047 +/- 0.011\n",
      " 1.004\t 0.979 +/- 0.038   1.011 +/- 0.070   0.986 +/- 0.033   0.048 +/- 0.011\n",
      " 1.000\t 1.034 +/- 0.037   1.079 +/- 0.070   1.044 +/- 0.033   0.049 +/- 0.011\n",
      " 0.999\t 1.093 +/- 0.037   0.973 +/- 0.070   1.067 +/- 0.033   0.046 +/- 0.011\n",
      " 1.001\t 1.112 +/- 0.037   0.995 +/- 0.070   1.087 +/- 0.033   0.043 +/- 0.011\n",
      " 1.000\t 1.130 +/- 0.037   1.000 +/- 0.070   1.102 +/- 0.032   0.039 +/- 0.011\n",
      " 1.000\t 1.141 +/- 0.037   1.050 +/- 0.070   1.122 +/- 0.032   0.037 +/- 0.011\n",
      " 1.000\t 1.159 +/- 0.036   0.977 +/- 0.070   1.120 +/- 0.032   0.033 +/- 0.011\n",
      " 1.000\t 1.153 +/- 0.036   0.963 +/- 0.070   1.112 +/- 0.032   0.028 +/- 0.011\n",
      " 1.001\t 1.140 +/- 0.036   1.142 +/- 0.070   1.140 +/- 0.032   0.028 +/- 0.011\n",
      " 1.001\t 1.168 +/- 0.036   1.041 +/- 0.070   1.141 +/- 0.032   0.025 +/- 0.011\n",
      " 1.002\t 1.166 +/- 0.036   0.966 +/- 0.070   1.123 +/- 0.032   0.019 +/- 0.011\n",
      " 1.001\t 1.143 +/- 0.036   0.967 +/- 0.070   1.105 +/- 0.032   0.015 +/- 0.011\n",
      " 0.999\t 1.120 +/- 0.036   0.946 +/- 0.070   1.083 +/- 0.032   0.011 +/- 0.011\n",
      " 1.000\t 1.094 +/- 0.036   1.064 +/- 0.070   1.088 +/- 0.032   0.010 +/- 0.011\n",
      " 1.000\t 1.098 +/- 0.036   0.973 +/- 0.070   1.071 +/- 0.032   0.007 +/- 0.011\n",
      " 1.000\t 1.078 +/- 0.036   1.144 +/- 0.070   1.092 +/- 0.032   0.008 +/- 0.011\n",
      " 0.999\t 1.100 +/- 0.036   0.945 +/- 0.070   1.067 +/- 0.032   0.004 +/- 0.011\n",
      " 0.999\t 1.072 +/- 0.036   1.037 +/- 0.070   1.064 +/- 0.032   0.004 +/- 0.011\n",
      " 0.998\t 1.068 +/- 0.036   1.031 +/- 0.070   1.060 +/- 0.032   0.003 +/- 0.011\n",
      " 0.997\t 1.063 +/- 0.036   1.037 +/- 0.070   1.057 +/- 0.032   0.002 +/- 0.011\n",
      " 0.997\t 1.059 +/- 0.036   0.967 +/- 0.070   1.039 +/- 0.032  -0.000 +/- 0.011\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt=1\n",
    "x_start = np.array([[0.25],[0.01]])\n",
    "P_start = np.diag([0.25, 0.0009])\n",
    "F = np.array([[1, dt],[0, 1]])\n",
    "Q = Q_zero_mean(dim=2, dt=dt, var=4e-6) # var=4e-6\n",
    "B = 0\n",
    "sigma_z = 0.07\n",
    "R = np.array([[sigma_z**2]])\n",
    "H = np.array([[1., 0.]])\n",
    "process_var = Q[0,0] # variance of robot distance, same as later in Kalman filter\n",
    "sensor_var = R[0,0] # variance distance sensor, same as later in Kalman filter\n",
    "n = 20 # number of data sets to be simulated\n",
    "start_pos_sim = 0 # start position\n",
    "vel_sim = 0.05 # constant velocity value\n",
    "# first half of simulation with non zero vel_sim\n",
    "robot = RoboSim(x0=start_pos_sim,velocity=vel_sim,measurement_var=sensor_var,process_var=process_var)\n",
    "np.random.seed(13) # to make the simulation reproducible\n",
    "sim_data_0 = robot.run_simulation(count=n,dt=dt)\n",
    "# second half of simulation with zero vel_sim\n",
    "robot = RoboSim(x0=n*vel_sim,velocity=0,measurement_var=sensor_var,process_var=process_var)\n",
    "sim_data_1 = robot.run_simulation(count=n,dt=dt)\n",
    "# join two simulation data sets\n",
    "sim_data = np.concatenate((sim_data_0, sim_data_1))\n",
    "# perform twodimensional Kalman filtering\n",
    "priors,priors_std,posts,posts_std = kal_filt_2dim_for_plot(sim_data, x_start, P_start, F, Q, H, R)\n",
    "# plot kalman filter output together with simulated data\n",
    "plot_kal_filt_2dim(sim_data[:,0],sim_data[:,1],\n",
    "                   [val[0,0] for val in posts],[val[1,0] for val in posts],dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Übersicht Einfluss der Startwerte, der Kovarianzmatrizen des Prozessrauschens und der Messwerte auf die Filterfunktion\n",
    "\n",
    "Die Robotersimulation wurde im Vergleich zum vorangegangenen Beispiel um einen Messwertsprung erweitert. Ansonsten wurden für die Simulation die Prozessvarianz, das Messrauschen und die Geschwindigkeit unverändert übernommen.   \n",
    "Diese Simulationsdaten wurden mit unterschiedlichen Werten für die Parameter $\\mathbf{x_{start}}$, $\\mathbf Q$ und  $\\mathbf R$ mit dem zweidimensionalen Kalman-Filter getrackt.  \n",
    "die Ergebnisse zeigen den Einfluss der verschiedenen Parameter. Die jeweils verwendeten Parameter sind im Titel des Plots wiedergegeben.\n",
    "\n",
    "##### Ausgangssituation:\n",
    "<img src=\"ZweiDimKalmann_Ausgangskonfi.png\">\n",
    "  \n",
    "##### Schlechte Startwerte:\n",
    "<img src=\"ZweiDimKalmann_schlStartwerte.png\">\n",
    "  \n",
    "##### Hohes Prozessrauschen, Modell wird wenig vertraut:\n",
    "<img src=\"ZweiDimKalmann_hohesProzRausch.png\">\n",
    "  \n",
    "##### Niedriges Prozessrauschen, Modell wird stark vertraut:\n",
    "<img src=\"ZweiDimKalmann_niedrProzRausch.png\">\n",
    "  \n",
    "##### Niedriges angenommenes Rauschen Messwerte, Sensoren wird stark vertraut:\n",
    "<img src=\"ZweiDimKalmann_hohesSensVertrauen.png\">  \n",
    "  \n",
    "##### Hohes angenommenes Rauschen Messwerte, Sensoren wird wenig vertraut:\n",
    "<img src=\"ZweiDimKalmann_niedrSensVertrauen.png\">\n",
    "\n",
    "##### Kompromiss-Parameter für ausgeglichenes Filterverhalten:\n",
    "<img src=\"ZweiDimKalmann_Kompromiss.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Korrespondenz der Bezeichnungen zum Buch \"Kalman-Filter\" von R. Marchthaler  und S. Dingler\n",
    "Dieses aktuelle Buch bietet die Möglichkeit, sich tiefer in den Thematik des Kalman-Filters einzuarbeiten. Hier sind auch die nötigen theoretischen Grundlagen erklärt.  \n",
    "Damit der Umstieg von diesem Jupyter-Notebook auf das Fachbuch gelingt, sind in der Tabelle die Begrifflichkeiten verglichen.\n",
    "\n",
    "|Parameter/Variable in diesem Notebook|entsprechender Parameter/Variable Marchthaler|Bemerkung|\n",
    "| :--------------------------- | :----------------------------------: | -------------------------------:|\n",
    "| Prior, Vorhersagewert Zustandsvektor $\\mathbf{\\bar x}$ |prädizierter Zustandsvektor $\\hat {\\underline x}(k)$|-|\n",
    "| Kovarianzmatrix Prior $\\mathbf{\\bar P}$ | prädizierte Kovarianz des Schätzfehlers $\\hat{\\underline P}(k)$ |-|\n",
    "| Posterior, Korrekturwert Zustandsvektor $\\mathbf{\\hat x}$ | Korrigierter Zustandsvektor $\\tilde {\\underline x}(k)$ |-|\n",
    "| Kovarianzmatrix Posterior $\\mathbf{\\hat P}$ | korrigierte Kovarianz des Schätzfehlers $\\tilde{\\underline P}(k)$ |-|\n",
    "| Übergangsmatrix $\\mathbf F$ | Systemmatrix ${\\underline A}_d$|-|\n",
    "| Kovarianzmatrix Prozessrauschen $\\mathbf Q$ | Systemrauschen ${\\underline Q}(k)$ |wird vor Addition zu $\\hat{\\underline P}(k)$ mit zusätzlicher Matrix ${\\underline G}_d$ transformiert|\n",
    "| Steuer-/Störgröße $\\mathbf u$ | $\\underline u(k)$ |-|\n",
    "| Steuer-/Störmatrix $\\mathbf B$ | ${\\underline B}_d$ |zusätzliche Durchgangsmatrix ${\\underline D}$ bei Korrekturschritt, |\n",
    "| Beobachtungsmatrix $\\mathbf H$ | $\\underline C$ |-|\n",
    "| Messwertvektor $\\mathbf z$ | Ausgangsvektor ${\\underline y}(k)$ |-|\n",
    "| Kovarianzmatrix Messwerte $\\mathbf R$ | Varianz Messrauschen ${\\underline R}(k)$ |${\\underline R}(k) = Var(\\underline v(k))$ mit Messrauschen $\\underline v(k)$|\n",
    "| Residuum $\\mathbf y$ | $\\Delta \\underline y(k)$|-|\n",
    "| Kalman Gain $\\mathbf K$ | Kalmanverstärkung $\\underline K$ |-|\n",
    "\n",
    "\n",
    "In der Einleitung dieses Buchs ist am Beispiel der Mondlandefähre der Kalman-Filter erklärt. Hier handelt es sich um einen dreidimensionalen Kalman-Filter, bei dem der Zustandsvektor aus der Ortskoordinate h, der Geschwindigkeit v und der Beschleunigung a besteht. Messwerte existieren nur für h und a. v ist also ein verdeckter Zustand.  \n",
    "\n",
    "Leider ist diese Lehrbuch recht ungeeignet für eine intuitive Einführung in die Thematik. Die vorliegende Reihe von Jupyter-Notebooks ist letztendlich ein Ergebnis der erfolglosen Auseinandersetzung des Autors mit dem Lehrbuch von Marchthaler/Dingler.  \n",
    "\n",
    "Mit Filteralgorithmen muss man spielen, um sie zuerst intuitiv zu verstehen. Danach ist es erst möglich, die zugrunde liegende Theorie zu verstehen."
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    "## Schlussbemerkung\n",
    "\n",
    "**Das Ziel dieser Reihe von Jupyter-Notbooks ist eine leicht verständliche Einführung in den Kalman-Filter ohne allzu viel Theorie in Form von Wahrscheinlichkeitsrechnung.**  \n",
    "Der Kalman-Filter gehört zu den Bayes-Filtern, die Bayes-Filter verwenden den Vorhersage-/Korrektur-Algorithmus des g-h-Filters. Aus diesem Grund wurde nicht der direkte Weg zum Kalmanfilter sondern der Umweg zuerst über den g-h-Filter und anschließend über den Bayes-Filter eingeschlagen.    \n",
    "Der Kalman-Filter basiert auf der Gaußschen Wahrscheinlichkeitsrechnung, weshalb hierzu sowohl für den eindimensionalen als auch für den mehrdimensionalen Fall die Grundlagen behandelt wurden.  \n",
    "\n",
    "Das erste Etappenziel war der eindimensionale Kalmanfilter. Jedoch ist dessen Nützlichkeit recht beschränkt: Er wirkt nicht wesentlich besser als ein Mittelwert- oder Medianfilter. Die Vorteile des Kalman-Filters treten erst im mehrdimensionalen Fall zutage, wenn mehrere Zustandsgrößen getrackt werden. Sind diese miteinander korreliert, dann ist es sogar möglich deren Werte mit einem Kalman-Filter zu schätzen, auch wenn es dafür keine Sensoren (also Messwerte) gibt. Auch die eigentliche Filterwirkung auf eine gemessene Zustandsgröße ist dann erheblich besser.\n",
    "\n",
    ">**Am Ende dieser Jupyter-Notebook-Reihe ist es wichtig zu erkennen, dass der hier am Beispiel eines Roboterfahrzeugs entwickelte Kalman-Filter *generisch* ist.** D.h. die hier entwickelten Algorithmen und Codebeispiele können 1:1 auf ganz andere \"Prozesse\" sprich Anwendungen übertragen werden. Selbst in der Finanzindustrie verwendet man Kalman-Filter. Dort sind beispielsweise die beiden Zustandsgrößen der Börsenwert und der Minutenumsatz einer Aktie. \n",
    "\n",
    "Die Begrifflichkeiten in fast allen Lehrbüchern zum Kalman-Filter sind zwar mathematisch korrekt und in sich konsistent, jedoch nicht immer hilfreich für das Verstehen. Matrizenrechnung ist nicht jedermanns Steckenpferd! Und einige Lehrbücher enthalten viele Notationsfehler.   \n",
    "Daher wurde hier der Kalman-Filter mit ganz einfacher Mathematik entwickelt. Erst spät wurde dann die Brücke zur üblichen Notation in den Lehrbüchern geschlagen.  \n",
    "\n",
    "Python wie auch MATLAB eignen sich ideal, sich dem Thema Kalman-Filter experimentell quasi spielerisch zu nähern. Dies in Kombination mit einem guten weiterführenden Lehrbuch ist vermutlich das Erfolgsrezept, um später einmal einen Kalman-Filter in einem autonom fahrenenden Auto oder in einem Batteriemanagementsystem erfolgreich einzusetzen."
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