Kalman_Filter.ipynb

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   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# Kalman filter tutorial"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c417489-a7f8-4fa9-8278-878e808f3dca",
   "metadata": {},
   "source": [
    "This python notebook will go over implementing a Kalman filter for data assimilation in a numerically simple physical system. The system we'll consider is a three-mass-spring-oscillator:\n",
    "\n",
    "<p align=\"center\">\n",
    "<img src=\"./images/mass_spring_sketch.jpg\" width=\"500\" />\n",
    "</p>\n",
    "\n",
    "This will give a ton of options for experimenting with data assimilation as there are many coupled variables/tunable parameters/etc. to consider. The equations of motion are given by:\n",
    "$$\n",
    "\\begin{align*}\n",
    "    &m \\frac{d^2 \\xi_1}{dt^2} + k \\xi_1 + k(\\xi_1 - \\xi_2) + r \\frac{d\\xi_1 }{dt} = q_1(t)  \\\\\n",
    "    &m \\frac{d^2 \\xi_2}{dt^2} + k\\xi_2 + k(\\xi_2 - \\xi_1) + k (\\xi_2 - \\xi_3) + r \\frac{d\\xi_2}{dt} = q_2(t) \\\\ \n",
    "    &m \\frac{d^2 \\xi_3}{dt^2} + k \\xi_3 + k(\\xi_3 - \\xi_2) + r \\frac{d \\xi_3}{dt} = q_3(t)\n",
    "\\end{align*}\n",
    "$$\n",
    "The position of each mass is denoted with $\\xi_k(t)$, and the various parameters are defined as:\n",
    "$$\n",
    "\\begin{align*}\n",
    "    &m: \\; \\; \\; \\text{Mass of the oscillators (here we assume they all have the same mass)}\\\\\n",
    "    &k: \\; \\; \\; \\text{Spring coefficient (again assuming all springs have the same coefficient)} \\\\ \n",
    "    &r: \\; \\; \\; \\text{Rayleigh friction coefficient} \\\\\n",
    "    &\\mathbf{q}(t): \\; \\; \\; \\text{Forcing vector}\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c52dca3-a5f4-4cd8-9cc1-cb6cd327e453",
   "metadata": {},
   "source": [
    "# Kalman filter setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9178681d",
   "metadata": {},
   "source": [
    "## Reducing to a first order system\n",
    "\n",
    "In order to write the time-evolution of the above system as $\\mathbf{x}(t + \\Delta t) = \\mathbf{A} \\mathbf{x}(t) + \\mathbf{B} \\mathbf{q}(t) + \\mathbf{\\Gamma} \\mathbf{u}(t)$ we begin by introducing the state vector \n",
    "$$ \\mathbf{x} = \n",
    "\\begin{pmatrix}\n",
    "    \\xi_1 \\\\ \n",
    "    \\xi_2 \\\\ \n",
    "    \\xi_3 \\\\ \n",
    "    d\\xi_1/dt \\\\ \n",
    "    d\\xi_2/dt \\\\\n",
    "    d\\xi_3/dt \n",
    "\\end{pmatrix}\n",
    "$$\n",
    "With the above definition of $\\mathbf{x}$ we want to determine $\\mathbf{A}$ such that $d\\mathbf{x}(t)/dt = \\mathbf{A} \\mathbf{x}(t) + \\mathbf{B} \\mathbf{q}(t)$. The first three elements of $d\\mathbf{x}(t)/dt$ are straightforward, as they're just themselves:\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\frac{dx_1}{dt} &= \\frac{d \\xi_1}{dt} \\\\ \n",
    "\\frac{dx_2}{dt} &= \\frac{d\\xi_2}{dt} \\\\\n",
    "\\frac{dx_3}{dt} &= \\frac{d\\xi_3}{dt} \n",
    "\\end{align*}\n",
    "$$\n",
    "The final three elements of $d\\mathbf{x}(t) / dt$ can be determined from the equations of motion. For simplicity we'll drop the $(t)$ in the following:\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\frac{dx_3}{dt} = \\frac{d^2\\xi_1}{dt^2} &= \\frac{1}{m}q_1 - \\frac{k}{m} \\xi_1 - \\frac{k}{m}(\\xi_1 - \\xi_2) - r \\frac{d\\xi_1}{dt} \\\\\n",
    "&= \\frac{1}{m} q_1 - \\frac{2 k}{m} \\xi_1 + \\frac{k}{m}\\xi_2 - r \\frac{d \\xi_1}{dt} \\\\\n",
    "&= \\frac{1}{m} q_1 - \\frac{2k}{m}x_1 + \\frac{k}{m} x_2 - r x_4 \\\\\n",
    "\\frac{dx_4(t)}{dt} = \\frac{d^2\\xi_2(t)}{dt^2} &= \\frac{1}{m} q_2 - \\frac{k}{m} \\xi_2 - \\frac{k}{m}(\\xi_2 - \\xi_1) - \\frac{k}{m} (\\xi_2 - \\xi_3) - \\frac{r}{m} \\frac{d \\xi_2}{dt} \\\\ \n",
    "&= \\frac{1}{m} q_2 - \\frac{3k}{m} \\xi_2 + \\frac{k}{m} \\xi_1 + \\frac{k}{m} \\xi_3 - \\frac{r}{m} \\frac{d \\xi_2}{dt} \\\\\n",
    "&= \\frac{1}{m} q_2 + \\frac{k}{m}x_1 - \\frac{3k}{m} x_2 - \\frac{k}{m} x_3 - \\frac{r}{m} x_5 \\\\\n",
    "\\frac{dx_5}{dt} = \\frac{d^2 \\xi_3}{dt} &= \\frac{1}{m} q_3 - \\frac{k}{m} \\xi_3 - \\frac{k}{m} (\\xi_3 - \\xi_2) - \\frac{r}{m} \\frac{d \\xi_3}{dt} \\\\\n",
    "&= \\frac{1}{m} q_3 + \\frac{k}{m} x_2 - \\frac{2 k}{m} x_3 - \\frac{r}{m} x_6\n",
    "\\end{align*}\n",
    "$$\n",
    "**In the code below we've made the simplification that $m = 1$ for all of the masses**, however, feel free to do something different in the code that you write! Letting $m=1$ we then have the **continuous** state transition matrix $\\mathbf{A}_c$:\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\mathbf{A}_c = \\begin{pmatrix} \n",
    " 0 & 0 & 0 & 1 & 0 & 0 \\\\0 & 0 & 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 1 \\\\ -2k & k & 0 & -r & 0 & 0 \\\\ k & -3k & k & 0 & -r & 0 \\\\ 0 & k & -2k & 0 & 0 & -r\n",
    "\\end{pmatrix}\n",
    "\\end{equation}\n",
    "$$\n",
    "The deterministic forcing, $\\mathbf{q}(t)$, will be written separately as $\\mathbf{B} \\mathbf{q}(t)$. "
   ]
  },
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   "cell_type": "markdown",
   "id": "eae59e85",
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   "source": [
    "## Side note: computing the energy in the system\n",
    "Let \n",
    "$$\n",
    "\\mathbf{A}_c = \\begin{pmatrix}\n",
    "    \\mathbf{0}_3 & \\mathbf{I}_3 \\\\ \\mathbf{K}_c & \\mathbf{R}_c \n",
    "\\end{pmatrix}\n",
    "$$\n",
    "where $\\mathbf{K}_c$ and $\\mathbf{R}_c$ are the corresponding three by three submatrices from Eq. (1). We recall from mechanics that the potential and kinetic energy in a simple oscillator is given by \n",
    "$$\n",
    "U = \\frac{1}{2} k x^2 , \\; \\; \\; K = \\frac{1}{2} m v^2 \n",
    "$$\n",
    "where $x$ is position, $v$ is velocity, and $k$ is the spring coefficient. We've assumed that $m = 1$, giving the total energy in the system as \n",
    "$$\n",
    "\\mathcal{E} = U + K = \\frac{1}{2} (kx^2 + v^2)\n",
    "$$\n",
    "Using the definition we have for $\\mathbf{x}$ we know that $x_1, x_2,$ and $x_3$ correspond to the positions of the masses, and $x_4, x_5,$ and $x_6$ correspond to the velocities, this will make it straightforward to compute energy in the code. That is (without dissipation, $r = 0$, or forcing),\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mathcal{E} &= \\frac{1}{2} \\left(-\\begin{pmatrix}x_1 \\\\ x_2 \\\\ x_3 \\end{pmatrix}^T \\mathbf{K}_c \\begin{pmatrix}x_1 \\\\ x_2 \\\\ x_3 \\end{pmatrix} +  \\begin{pmatrix}x_4 \\\\ x_5 \\\\ x_6 \\end{pmatrix}^T \\begin{pmatrix}x_4 \\\\ x_5 \\\\ x_6 \\end{pmatrix} \\right)\n",
    "\\end{align*}\n",
    "$$\n",
    "where the minus sign makes up for the negative entries in $\\mathbf{K}_c$. The off-diagonal terms then distribute the potential energy amongst the masses."
   ]
  },
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   "cell_type": "markdown",
   "id": "8eeb3d78",
   "metadata": {},
   "source": [
    "## Time discretization, i.e. introducing Euler's method \n",
    "\n",
    "The final step is just to discretize the system in time. Eulers method is an explicit scheme that tells us \n",
    "$$\n",
    "\\mathbf{x}(t + \\Delta t) = \\mathbf{x}(t) + \\Delta t \\frac{d \\mathbf{x}(t)}{dt}.\n",
    "$$\n",
    "Using what we found previously, we can write this out as\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\begin{pmatrix}\n",
    "x_1(t + \\Delta t) \\\\ x_2(t + \\Delta t) \\\\ x_3(t + \\Delta t) \\\\ x_4(t + \\Delta t) \\\\ x_5(t + \\Delta t) \\\\ x_6(t + \\Delta t) \n",
    "\\end{pmatrix}\n",
    "&= \n",
    "\\begin{pmatrix}\n",
    "x_1(t) \\\\ x_2(t) \\\\ x_3(t) \\\\ x_4(t) \\\\ x_5(t) \\\\ x_6(t) \n",
    "\\end{pmatrix}\n",
    "+ \\Delta t \\left[\n",
    "\\begin{pmatrix} \n",
    "0 & 0 & 0 & 1 & 0 & 0 \\\\0 & 0 & 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 1 \\\\ -2k & k & 0 & -r & 0 & 0 \\\\ k & -3k & k & 0 & -r & 0 \\\\ 0 & k & -2k & 0 & 0 & -r\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}\n",
    "x_1(t) \\\\ x_2(t) \\\\ x_3(t) \\\\ x_4(t) \\\\ x_5(t) \\\\ x_6(t) \n",
    "\\end{pmatrix}\n",
    "\\right]\n",
    "+ \\mathbf{B} \\mathbf{q}(t) \\\\\n",
    "&=  \\left[ \\mathbf{I_6} + \\begin{pmatrix} \n",
    "0 & 0 & 0 & \\Delta t & 0 & 0 \\\\0 & 0 & 0 & 0 & \\Delta t & 0 \\\\ 0 & 0 & 0 & 0 & 0 & \\Delta \\\\ -2k\\Delta t & k\\Delta t & 0 & -r\\Delta t & 0 & 0 \\\\ k\\Delta t & -3k\\Delta t & k \\Delta t & 0 & -r\\Delta t & 0 \\\\ 0 & k \\Delta t & -2k \\Delta t & 0 & 0 & -r\\Delta t\n",
    "\\end{pmatrix} \\right] \\begin{pmatrix}\n",
    "x_1(t) \\\\ x_2(t) \\\\ x_3(t) \\\\ x_4(t) \\\\ x_5(t) \\\\ x_6(t) \n",
    "\\end{pmatrix} + \\mathbf{B}\\mathbf{q}(t) \\\\\n",
    "&= \\begin{pmatrix}\n",
    "        1 & 0 & 0 & \\Delta t & 0 & 0 \\\\ 0 & 1 & 0 & 0 & \\Delta t & 0 \\\\ 0 & 0 & 1 & 0 & 0 & \\Delta t \\\\ -2k\\Delta t & k\\Delta t & 0 & 1-r\\Delta t & 0 & 0 \\\\ k\\Delta t & -3k\\Delta t & k\\Delta t & 0 & 1-r\\Delta t & 0 \\\\ 0 & k\\Delta t & -2k\\Delta  & 0 & 0 & 1-r\\Delta t\n",
    "    \\end{pmatrix} \\begin{pmatrix}\n",
    "x_1(t) \\\\ x_2(t) \\\\ x_3(t) \\\\ x_4(t) \\\\ x_5(t) \\\\ x_6(t) \n",
    "\\end{pmatrix} + \\mathbf{B}\\mathbf{q}(t) \\\\\n",
    "&= \\mathbf{A} \\mathbf{x} + \\mathbf{B}\\mathbf{q}(t)\n",
    "\\end{align*}\n",
    "$$\n",
    "The remainder of the terms, $\\mathbf{B}, \\mathbf{q}, \\mathbf{\\Gamma},$ and $\\mathbf{u}$ will be defined in the code. In general though these represent:\n",
    "$$\n",
    "\\begin{align*}\n",
    "&\\mathbf{B}: \\; \\; \\; \\text{Known forcing distribution matrix} \\\\\n",
    "&\\mathbf{\\Gamma}: \\; \\; \\; \\text{Unknown forcing distribution matrix} \\\\\n",
    "&\\mathbf{u}: \\; \\; \\; \\text{Unknown forcing}.\n",
    "\\end{align*}\n",
    "$$\n",
    "and one should feel free to define them however they want! Play around with forcing, which masses are forced, how much forcing to apply, what sort of unknown forcing to apply, etc."
   ]
  },
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   "cell_type": "markdown",
   "id": "8065ba36",
   "metadata": {},
   "source": [
    "# Full Kalman filter equations\n",
    "Now that we've derived the important bits, we recall the full set of Kalman filter equations: \n",
    "$$\n",
    "\\begin{align}\n",
    "&\\tilde{\\mathbf{x}}(t, -) = \\mathbf{A} \\tilde{\\mathbf{x}}(t-\\Delta t) + \\mathbf{B} \\mathbf{q}(t-\\Delta t)\\\\\n",
    "&\\mathbf{P}(t, -) = \\mathbf{A} \\mathbf{P} \\mathbf{A}^T + \\mathbf{\\Gamma} \\mathbf{Q} \\mathbf{\\Gamma}^T\\\\\n",
    "&\\mathbf{K}(t) = \\mathbf{P}(t, -) \\mathbf{E}^T \\left(\\mathbf{E} \\mathbf{P}(t, -) \\mathbf{E}^T + \\mathbf{R} \\right)^{-1}\\\\\n",
    "&\\tilde{\\mathbf{x}}(t) = \\tilde{\\mathbf{x}}(t, -) + \\mathbf{K}(t) \\left(\\mathbf{y}(t) - \\mathbf{E}\\tilde{\\mathbf{x}}(t, -) \\right)\\\\\n",
    "&\\mathbf{P}(t) = \\mathbf{P}(t, -) - \\mathbf{K}(t) \\mathbf{E} \\mathbf{P}(t, -)\n",
    "\\end{align}\n",
    "$$\n",
    "Letting $\\langle \\cdot \\rangle$ denote the expectation value, we have\n",
    "$$\n",
    "\\begin{align*}\n",
    "&\\langle \\mathbf{n}(t) \\rangle = \\langle \\mathbf{u}(t) \\rangle = 0 \\\\\n",
    "&\\langle \\mathbf{n}(t) \\mathbf{n}(t)^T \\rangle = \\mathbf{R}(t) \\\\ \n",
    "&\\langle \\mathbf{u}(t) \\mathbf{u}(t)^T \\rangle = \\mathbf{Q}(t) \\\\ \n",
    "&\\langle \\mathbf{n}(t) \\mathbf{n(t')}^T \\rangle = 0 \\; \\text{for } t \\neq t'\n",
    "\\end{align*}\n",
    "$$\n",
    "Now we're ready to write the code that does all of this!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68ae1f1b-b409-4b4e-9dec-30df037f8ac3",
   "metadata": {},
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "53437ec0-9038-44c4-995d-f401cac08505",
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   "source": [
    "import numpy as np\n",
    "import scipy.sparse as sp\n",
    "import scipy.sparse.linalg as la\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(70)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a6edacb-d475-4685-87c3-0ecf1fb04ea8",
   "metadata": {},
   "source": [
    "## Model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "036399e8-9870-4d53-8fd6-a4fff4c18d86",
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   "source": [
    "## Defining model parameters\n",
    "\n",
    "# number of steps to integrate \n",
    "T = 10000\n",
    "\n",
    "# timestep \n",
    "dt = 0.001 \n",
    "\n",
    "#### These are what we consider the \"true\" values\n",
    "\n",
    "# initial condition\n",
    "x0 = np.array([1, 0, 0, 0, 0, 0])\n",
    "\n",
    "# spring coefficient\n",
    "k = 30 \n",
    "\n",
    "# dissipation coefficient \n",
    "r = 0.5\n",
    "\n",
    "# state transition matrix\n",
    "A = np.array([\n",
    "    [1, 0, 0, dt, 0, 0,],\n",
    "    [0, 1, 0, 0, dt, 0],\n",
    "    [0, 0, 1, 0, 0, dt],\n",
    "    [-2*k*dt, k*dt, 0, 1-r*dt, 0, 0],\n",
    "    [k*dt, -3*k*dt, k*dt, 0, 1-r*dt, 0],\n",
    "    [0, k*dt, -2*k*dt, 0, 0, 1-r*dt]\n",
    "])\n",
    "\n",
    "# a submatrix from A is needed to compute the energy\n",
    "Kc = np.array([\n",
    "    [-2*k, k, 0],\n",
    "    [k, -3*k, k],\n",
    "    [0, k, -2*k]\n",
    "])\n",
    "\n",
    "#### These are used by the Kalman filter\n",
    "\n",
    "# data steps,\n",
    "# which timesteps do we assume the existence of data?\n",
    "data_steps = np.arange(3000, 7000, 300)\n",
    "\n",
    "# construct of E, data distribution matrix,\n",
    "# determines which elements of x we have data\n",
    "E = np.eye(6)\n",
    "\n",
    "# initial condition the Kalman filter sees\n",
    "x0_kf = x0\n",
    "\n",
    "# initial uncertainty in the prediction, \n",
    "# i.e. did we select the correct initial condition?\n",
    "P0 = np.zeros((6,6))\n",
    "\n",
    "# standard deviation (sqrt(variance)) of random \n",
    "# forcing and the noise in the data\n",
    "sigma_data = 0.01\n",
    "sigma_forcing = 0.01\n",
    "\n",
    "# variance of the noise in the data\n",
    "R = sigma_data**2 * np.eye(6)\n",
    "\n",
    "# variance of the unknown forcing,\n",
    "# note that this is a white noise function (defined\n",
    "# as u)\n",
    "Q = sigma_forcing**2 * np.eye(6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8001e1a-dffa-467d-97c5-dde36020242b",
   "metadata": {},
   "source": [
    "## Forcing terms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "18226a7f-02cf-4f05-910c-cf5e136c52eb",
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   "source": [
    "# known (deterministic) forcing function\n",
    "def q(t):\n",
    "    q1 = 0.1 * np.cos(2 * np.pi * t / (2.5 / r))\n",
    "    q2 = 0\n",
    "    q3 = 0\n",
    "    q4 = 0\n",
    "    q5 = 0\n",
    "    q6 = 0\n",
    "    return np.array([q1, q2, q3, q4, q5, q6])\n",
    "\n",
    "# deterministic forcing seen by the Kalman filter,\n",
    "# same as q or different?\n",
    "def q_kf(t):\n",
    "    return 0.5 * q(t)\n",
    "\n",
    "# known forcing matrix\n",
    "B = np.array([\n",
    "    [1, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0]\n",
    "])\n",
    "\n",
    "# unknown forcing, chosen as a random 6x1 vector,\n",
    "# altering the coefficient alters the variance\n",
    "def u(t):\n",
    "    return sigma_forcing * np.random.randn(6)\n",
    "\n",
    "# unknown forcing distribution matrix\n",
    "Gamma = np.array([[1, 0, 0, 0, 0, 0,],\n",
    "            [0, 0, 0, 0, 0, 0],\n",
    "            [0, 0, 0, 0, 0, 0],\n",
    "            [0, 0, 0, 0, 0, 0],\n",
    "            [0, 0, 0, 0, 0, 0],\n",
    "            [0, 0, 0, 0, 0, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f41be1a-6f1c-480a-a6b2-4593405affd1",
   "metadata": {},
   "source": [
    "## Create data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3ab0ddae-02cb-411c-a361-1d46a9a85faa",
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   "source": [
    "# where data will be stored, we'll also store \n",
    "# the energy as we integrate\n",
    "all_states = np.zeros((6, T+1))\n",
    "all_states[:,0] = x0\n",
    "energy = np.zeros((T+1))\n",
    "energy[0] = 0.5 * (np.dot(x0[3:6], x0[3:6]) - np.dot(x0[0:3], Kc @ x0[0:3]))\n",
    "\n",
    "x = x0\n",
    "\n",
    "current_timestep = dt\n",
    "for j in range(1,T+1):\n",
    "    \n",
    "    x = A @ x + B @ q(current_timestep) + Gamma @ u(current_timestep)\n",
    "    energy[j] = 0.5 * (np.dot(x[3:6], x[3:6]) - np.dot(x[0:3], Kc @ x[0:3]))\n",
    "\n",
    "    # store the computed state\n",
    "    all_states[:, j] = x\n",
    "    current_timestep += dt\n",
    "\n",
    "# adding the noise to the states we just integrated\n",
    "data = all_states + sigma_data * np.random.randn(6, T+1)"
   ]
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(energy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "782deaee-5ca7-40bd-b966-3d914bd2e882",
   "metadata": {},
   "source": [
    "## Running the Kalman filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "f2e953d5-c79b-4674-82ce-231ea1931525",
   "metadata": {},
   "outputs": [],
   "source": [
    "P = P0 \n",
    "P_pred = P0\n",
    "x_kf = x0_kf\n",
    "x_pred = x0_kf\n",
    "\n",
    "all_states_kf = np.zeros((6,T+1))\n",
    "all_states_kf[:,0] = x0_kf\n",
    "\n",
    "energy_kf = np.zeros((T+1))\n",
    "energy_kf[0] = 0.5 * (np.dot(x0_kf[3:6], x0_kf[3:6]) - np.dot(x0_kf[0:3], Kc @ x0_kf[0:3]))\n",
    "\n",
    "current_timestep = dt\n",
    "for j in np.arange(1,T+1):\n",
    "    \n",
    "    x_pred = A @ x_pred + B @ q_kf(current_timestep)\n",
    "    P_pred = A @ P_pred @ A.T + Gamma @ Q @ Gamma.T\n",
    "    \n",
    "    # check if there's data at current timestep\n",
    "    if j in data_steps:\n",
    "\n",
    "        # determine Kalman gain matrix and \n",
    "        # incorporate data \n",
    "        \n",
    "        K = P_pred @ E.T @ np.linalg.inv(E @ P @ E.T + R)\n",
    "        x_kf = x_pred + K @ (data[:,j] - E @ x_kf)\n",
    "        P = P_pred - K @ E @ P_pred\n",
    "        \n",
    "        all_states_kf[:, j] = x_kf\n",
    "\n",
    "    else:\n",
    "        \n",
    "        x_kf = x_pred \n",
    "        P = P_pred\n",
    "\n",
    "    # store states and energy\n",
    "    all_states_kf[:, j] = x_kf\n",
    "    energy_kf[j] = 0.5 * (np.dot(x_kf[3:6], x_kf[3:6]) - np.dot(x_kf[0:3], Kc @ x_kf[0:3]))\n",
    "\n",
    "    # cycle states and uncertainty\n",
    "    x_pred = x_kf\n",
    "    P_pred = P\n",
    "\n",
    "    # step forward\n",
    "    current_timestep += dt \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "dfe9ab7d-6c0d-4a1a-9cfc-c37292062394",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13def2d50>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(energy)\n",
    "plt.plot(energy_kf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "87a16be6-73a6-4874-a9a4-d47c13cccb5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1,2,3,4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "6a2a5354-d37d-4077-8fac-28c80edd377c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "45efde11-3e1f-4ba9-b05e-6577886ba0f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5, 6])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[3:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1635b972-c835-4317-a957-2d1b85c504be",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}