notebooks/07/kalman-filter.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kalman filter\n",
    "\n",
    "<img src=\"media/cover.png\" style=\"width: 40%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Overview\n",
    "\n",
    "This lecture will cover the following topics:\n",
    "- Introduction to the Kalman Filter.\n",
    "- Model components and assumptions.\n",
    "- The Kalman Filter algorithm.\n",
    "- Application to static and dynamic one-dimensional data.\n",
    "- Application to higher-dimensional data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Imports\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import cv2\n",
    "np.random.seed(0) # for reproducibility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What is a Kalman Filter?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- The Kalman Filter (KF) is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies.\n",
    "- It produces estimates of unknown variables that tend to be more accurate than those based only on measurements.\n",
    "- Developed by Rudolf E. Kálmán in the late 1950s.\n",
    "- Applications:\n",
    "  - tracking objects (Apollo project, GPS, self driving cars).\n",
    "  - image processing.\n",
    "  - economic and financial modeling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Theoretical foundations\n",
    "\n",
    "- Dynamic systems are systems that change over time.\n",
    "- They are described by a set of equations that predict the future state of the system based on its current state.\n",
    "- The KF assumes the system is a *linear* dynamic system with *Gaussian* noise. \n",
    "- Gaussian distributions are used because of their nice properties when dealing with averages and variances."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### What are the ingredients?\n",
    "\n",
    "**State** \n",
    "- The true value of the variables we want to estimate. \n",
    "- The state vector represents all the information needed to describe the current state of the system.\n",
    "\n",
    "**Observation model** \n",
    "- Relates the current state to the measurements or observations.\n",
    "\n",
    "**Noisy measurements** \n",
    "- The process noise and measurement noise (assumed to be Gaussian) represent the uncertainty in our models and measurements. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Example:\n",
    "- Car moving at a constant velocity.\n",
    "- Model: Car position = velocity $\\times$ time $+$ system noise.\n",
    "- Measurements: position and velocity (which are also noisy)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### The role of noise\n",
    "\n",
    "The tradeoff between the influence of the model and the measurements is determined by noise.\n",
    "\n",
    "- If the model has relatively large errors, more importance is given to the latest measurements in computing the current estimate.\n",
    "- If the measurement have larger errors, more importance is given to the model in making the current estimate.\n",
    "- Therefore, you need to estimate not only your state but also the errors (the covariance) for both the model and the measurements.\n",
    "- These must be updated at each time step, too."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Update strategy\n",
    "\n",
    "KF is a recursive algorithm:\n",
    "\n",
    "- Uses information from previous time step to update the estimates.\n",
    "- Does not keep in memory all the data acquired so far.\n",
    "- Has predictor-corrector structure:\n",
    "    - Make a prediction based on the model.\n",
    "    - Update the prediction with the measurements.\n",
    "    - Repeat."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Fundamental assumptions\n",
    "\n",
    "The Kalman filter approach is based on three fundamental assumptions:\n",
    "\n",
    "1. The system can be described or approximated by a linear model.\n",
    "2. All noise (from both the system and the measurements) is white, i.e., the values are not correlated.\n",
    "3. All noise is Gaussian."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Assumption 1: linearity\n",
    "\n",
    "Each variable at the current time is a linear function of the variables at previous times.\n",
    "\n",
    "- Many systems can be approximated this way.\n",
    "- Linear systems are easy to analyze.\n",
    "- Nonlinear systems can often be approximated by linear models around a current estimate (extended KF)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Assumption 2: Whiteness\n",
    "\n",
    "The noise values are not correlated in time.\n",
    "\n",
    "- If you know the noise at time $t$, it doesn't help you to predict the noise at future times $t+\\tau$.\n",
    "- White noise is a reasonable approximation of the real noise.\n",
    "- The assumption makes the mathematics tractable.\n",
    "\n",
    "> **📝 Note** White noise contains a mix of all the different frequencies at the same intensity blended together. \n",
    ">\n",
    "> This is similar to how white light contains all the colors of the rainbow combined."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Assumption 3: Gaussian noise\n",
    "\n",
    "At any point in time, the probability density of the noise is a Gaussian.\n",
    "\n",
    "- System and measurement noise are often a combination of many small sources of noise. \n",
    "- The combination effect is approximately Gaussian.\n",
    "- If only mean and variance are known (typical case in engineering systems), Gaussian distribution is a good choice as these two quantities completely determine the Gaussian distribution.\n",
    "- Gaussian distribution have nice properties and are easy to treat mathematically.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Technical details"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Combining two sources\n",
    "\n",
    "Assume a car has a certain initial position $x_0=0$ and initial velocity $\\dot{x}_0=60 km/h$.\n",
    "\n",
    "If the speed is constant, we have:\n",
    "\n",
    "$$x_{t} = 1\\cdot x_{t-1} + \\delta t \\cdot \\dot{x}_{t-1}$$\n",
    "$$\\dot{x}_{t} = 0 \\cdot x_{t-1} + 1 \\cdot \\dot{x}_{t-1}$$\n",
    "\n",
    "In matrix form:\n",
    "\n",
    "$$ \\boldsymbol{x}_{t} = \n",
    "\\begin{bmatrix}\n",
    "x_{t} \\\\\n",
    "\\dot{x}_{t}\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "1 & \\delta t \\\\\n",
    "0 & 1 \n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "x_{t-1} \\\\\n",
    "\\dot{x}_{t-1}\n",
    "\\end{bmatrix} = \\mathbf{A} \\boldsymbol{x}_{t-1}\n",
    "$$\n",
    "\n",
    "<img src=\"media/system.png\" style=\"width: 50%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- The current position and speed will evolve according to this simple dynamical system \n",
    "\n",
    "$$\\boldsymbol{x}_{t} = \\mathbf{A} \\boldsymbol{x}_{t-1} + \\boldsymbol{w}_{t-1}$$ \n",
    "\n",
    "- where $\\boldsymbol{w}_t \\sim \\mathcal{N}(0,\\mathbf{Q})$ represents perturbations in the underlying dynamical systems (e.g., holes on the road).\n",
    "- $\\boldsymbol{x}_{t} \\in \\mathbb{R}^{N}$ represents the state of the system.\n",
    "- $\\mathbf{Q} \\in \\mathbb{R}^{N \\times N}$ is the *process noise covariance*, where $N$ represents the number of state variables (2 in our case, position and speed)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Where the car will be after 1 minute?\n",
    "\n",
    "If we rely only on our simple sistem $\\boldsymbol{x}_{t+1} = \\mathbf{A} \\boldsymbol{x}_{t}$ without even consider the noise, the car will keep moving at $60 km/h$ and will be at $1 km$ distance.\n",
    "\n",
    "<img src=\"media/model_pred.png\" style=\"width: 50%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let say our car has a GPS.\n",
    "- As all instruments, our GPS will be affected by errors and gives us measurements with uncertainties in it.\n",
    "- In addition, our GPS can only measure the position but not the speed.\n",
    "- Based on our GPS, after 1 minute we are at $0.8 km$ from where we started.\n",
    "\n",
    "<img src=\"media/gps.png\" style=\"width: 50%\" align=\"center\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Let the measure of our GPS be \n",
    "\n",
    "$$\\boldsymbol{z}_t = \\mathbf{H} \\boldsymbol{x}_t + \\boldsymbol{v}_t$$ \n",
    "\n",
    "- where $\\boldsymbol{v}_t \\sim \\mathcal{N}(0,\\mathbf{R})$ represents the uncertainty in the measures.\n",
    "- $\\boldsymbol{z}_{t} \\in \\mathbb{R}^{M}$ is the measurements vector.\n",
    "- In our case, since the GPS measures only the position, we have $\\mathbf{H} = \\begin{bmatrix} 1 & 0 \\end{bmatrix}$ and $\\mathbf{R} = \\begin{bmatrix} r_{xx} \\end{bmatrix}$.\n",
    "- In general, $\\mathbf{H} \\in \\mathbb{R}^{M,N}$ is a matrix that maps the $N$ state variables into the $M$ measurements and $\\mathbf{R} \\in \\mathbb{R}^{M,M}$ is the measurement noise covariance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In summary, we have two different sources of information:\n",
    "- a linear stochastic difference equation, representing our imprecise knowledge of a discrete-time controlled process;\n",
    "- a source of measurements, that are noisy.\n",
    "\n",
    "<img src=\"media/inputs.png\" style=\"width: 20%; display: block; margin: auto;\">\n",
    "\n",
    "How do we combine them to get the best possible estimate of our system variables?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The KF algorithm\n",
    "\n",
    "The KF is an interative procedure that consists of two steps: \n",
    "\n",
    "- **Predict** (Time update)\n",
    "- **Correct** (Measurement update)\n",
    "\n",
    "These two steps are used to update two quantities:\n",
    "- The **state estimate**.\n",
    "- The uncertainty about our state estimate, called **covariance estimate**.\n",
    "\n",
    "Before looking at the iterative procedure let's introduce this second quantity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Covariance estimate**\n",
    "\n",
    "There are two sources of error in the estimate of the state of our system.\n",
    "\n",
    "- The *prior* estimate error $e^{-}_t = x_t - \\hat{x}^{-}_t$.\n",
    "- The *posterior* estimate error $e_t = x_t - \\hat{x}_t$.\n",
    "\n",
    "Where:\n",
    "- $\\hat{x}^{-}_t$ is the estimate of the state based only on the knowledge of the system, e.g., the dynamics equations.\n",
    "- $\\hat{x}_t$ is the estimate based also on the measurement $z_t$, e.g., the GPS. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Each type of error is associated with a covariance matrix, which reflects the amount of uncertainty in the state estimates.\n",
    "\n",
    "- $\\mathbf{P}_t^{-} = \\mathbb{E}[e^{-}_t e^{-T}_t] \\in \\mathbb{R}^{N\\times N}$ (*prior* covariance estimate).\n",
    "- $\\mathbf{P}_t = \\mathbb{E}[e_t e^{T}_t] \\in \\mathbb{R}^{N\\times N}$ (*posterior* covariance estimate).\n",
    "- In our case, we have  $\\mathbf{P}_t = \\begin{bmatrix} p_{xx} & p_{\\dot x x} \\\\ p_{\\dot x x} & p_{\\dot x \\dot x} \\end{bmatrix}$ (for readability, the index $t$ on the matrix elements is omitted):\n",
    "  - $p_{xx}$ is the uncertainty about the position;\n",
    "  - $p_{\\dot x \\dot x}$ is the uncertainty about the velocity;\n",
    "  - $p_{x \\dot x}$ and $p_{\\dot x x}$ represent the correlation between the noise in the measurements of the position and the speed.\n",
    "- $\\mathbf{P}_t^{-}$ has the same form."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Predict\n",
    "\n",
    "- The dynamics equations are responsible for projecting forward (in time) the current state and error covariance estimates to obtain the *prior* estimate for the next time step.\n",
    "- Such time update equations can also be thought of as *predictor equations*.\n",
    "\n",
    "State estimate update: \n",
    "\n",
    "$$\\hat{\\boldsymbol{x}}_{t}^{-} = \\mathbf{A} \\hat{\\boldsymbol{x}}_{t-1}$$\n",
    "\n",
    "<img src=\"media/model_pred.png\" style=\"width: 50%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Covariance estimate update: \n",
    "\n",
    "$$\n",
    "\\begin{aligned} \n",
    "\\mathbf{P}_{t}^{-} &= \\mathbb{E}[e^{-}_t e^{-T}_t] \\\\\n",
    "  &= \\mathbb{E}[(\\boldsymbol{x}_{t} - \\hat{\\boldsymbol{x}}^{-}_{t})(\\boldsymbol{x}_{t} - \\hat{\\boldsymbol{x}}^{-}_{t})^T] \\\\\n",
    "  &= \\mathbb{E}[(\\mathbf{A} \\boldsymbol{x}_{t-1} + \\boldsymbol{w} - \\mathbf{A} \\hat{\\boldsymbol{x}}_{t-1})(\\mathbf{A} \\boldsymbol{x}_{t-1} + \\boldsymbol{w} - \\mathbf{A} \\hat{\\boldsymbol{x}}_{t-1})^T] \\\\\n",
    "  &= \\mathbb{E}[(\\mathbf{A}e_{t-1})(e_{t-1}^T \\mathbf{A}^T)] + \\mathbb{E}[\\boldsymbol{w}\\boldsymbol{w}^T]\\\\\n",
    "  &= \\mathbf{A}\\mathbb{E}[e_{t-1}e_{t-1}^T ]\\mathbf{A}^T + \\mathbf{Q} \\\\\n",
    "  &= \\mathbf{A}\\mathbf{P}_{t-1}\\mathbf{A}^T + \\mathbf{Q}\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In summary, the Predict step consists of two equations to update:\n",
    "- State estimate.\n",
    "- Covariance estimate.\n",
    "\n",
    "<img src=\"media/update.png\" style=\"width: 20%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Correct\n",
    "\n",
    "The measurement update equations are responsible for the feedback, i.e. for incorporating a new measurement into the prior estimate to obtain an improved posterior estimate.\n",
    "\n",
    "The posterior estimate $\\hat{\\boldsymbol{x}}_{t}$ is a linear combination of:\n",
    "- The prior estimate $\\hat{\\boldsymbol{x}}^{-}_{t}$.\n",
    "- A weighted difference between the actual measurement $\\boldsymbol{z}_{t}$ and a measurement prediction $\\mathbf{H} \\hat{\\boldsymbol{x}}^{-}_{t}$.\n",
    "\n",
    "$$\\hat{\\boldsymbol{x}}_{t} = \\hat{\\boldsymbol{x}}^{-}_{t} + \\mathbf{K}_t(\\boldsymbol{z}_{t} - \\mathbf{H} \\hat{\\boldsymbol{x}}^{-}_{t})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- The difference $\\Delta_t = \\boldsymbol{z}_{t} - \\mathbf{H} \\hat{\\boldsymbol{x}}^{-}_{t}$ is called measurement *innovation* or *residual*.\n",
    "- $\\Delta_t$ reflects the difference between our imprecise prediction ($\\mathbf{H} \\hat{\\boldsymbol{x}}^{-}_{t}$) and the actual noisy measurement ($\\boldsymbol{z}_{t}$).\n",
    "- A residual of zero means that the two are in complete agreement.\n",
    "\n",
    "<img src=\"media/innovation.png\" style=\"width: 50%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The matrix $\\mathbf{K} \\in \\mathbb{R}^{N \\times M}$ is chosen to be the **gain** that minimizes the posterior error covariance.\n",
    "\n",
    "Derivation (sketch):\n",
    "1. Define the posterior error  $e_t = x_t - \\hat{x}_t$.\n",
    "2. Define the posterior error covariance $P_t = \\mathbb{E}[e_t e^{T}_t]$.\n",
    "3. Substitute $\\hat{\\boldsymbol{x}}_{t} = \\hat{\\boldsymbol{x}}^{-}_{t} + \\mathbf{K}\\Delta_t$ in 1).\n",
    "4. Substitute the $e_t$ obtained from 3) in 2) and take the expectation.\n",
    "5. Take the derivative of the trace of the result with respect to $\\mathbf{K}$.\n",
    "6. Set the result equal to zero.\n",
    "7. Solve for $\\mathbf{K}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The previous derivation give us the following result:\n",
    "\n",
    "$$\\mathbf{K}_t = \\mathbf{P}^{-}_t \\mathbf{H}^T (\\mathbf{H} \\mathbf{P}^{-}_t \\mathbf{H}^T + \\mathbf{R})^{-1}= \\frac{\\mathbf{P}^{-}_t \\mathbf{H}^T}{\\mathbf{H} \\mathbf{P}^{-}_t \\mathbf{H}^T + \\mathbf{R}}$$\n",
    "\n",
    "Back to our car example, we have:\n",
    "\n",
    "$$\\mathbf{K}_t = \\frac{\\begin{bmatrix} p^{-}_{xx} & p^{-}_{\\dot x x} \\\\ p^{-}_{\\dot x x} & p^{-}_{\\dot x \\dot x} \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}}{\\begin{bmatrix} 1 & 0 \\end{bmatrix} \\begin{bmatrix} p^{-}_{xx} & p^{-}_{\\dot x x} \\\\ p^{-}_{\\dot x x} & p^{-}_{\\dot x \\dot x} \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} + \\begin{bmatrix} r_{xx} \\end{bmatrix}} = \\frac{\\begin{bmatrix} p^{-}_{xx} \\\\ p^{-}_{x \\dot x} \\end{bmatrix}}{p^{-}_{xx} + r_{xx}}$$\n",
    "\n",
    "Once again, the index $t$ has been dropped from the elements of $\\mathbf{P}^{-}_t$ for readability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The update equations for the position and speed become:\n",
    "\n",
    "- Position: $\\hat{x}_t = \\hat{x}_t^{-} + \\frac{p^{-}_{xx}}{p^{-}_{xx} + r_{xx}} \\Delta_t$\n",
    "- Speed: $\\hat{\\dot x}_t = \\hat{\\dot x}_t^{-} + \\frac{p^{-}_{x \\dot x}}{p^{-}_{xx} + r_{xx}} \\Delta_t$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- One key observation is that the speed is updated even if we do not have a direct measure for it in our measurement $\\boldsymbol{z}_t$.\n",
    "- The update is possible thanks to the term $p^{-}_{x \\dot x}$ in $\\mathbf{K}_t$ that relates the position (and its measurement) to the velocity.\n",
    "- This showcases one of the main strengths of KF: it can handle *partial observations*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's consider the two extreme cases for the values of $\\mathbf{K}_t$\n",
    "\n",
    "1. The measurement error covariance $\\mathbf{R}$ approaches zero, i.e., there is no noise in the measurements.\n",
    "   - The measurements are completely reliable.\n",
    "   - We have $\\lim \\limits_{\\mathbf{R} \\rightarrow 0} \\mathbf{K}_t = \\frac{\\mathbf{P}^{-}_t \\mathbf{H}^T}{\\mathbf{H} \\mathbf{P}^{-}_t \\mathbf{H}^T + \\mathbf{R}} = \\mathbf{H}^{-1}$\n",
    "   - $\\mathbf{K}$ weights the residuals more heavily: \n",
    "   \n",
    "   $$\n",
    "   \\begin{aligned} \n",
    "   \\hat{\\boldsymbol{x}}_{t} &= \\hat{\\boldsymbol{x}}^{-}_{t} + \\mathbf{H}^{-1}\\Delta_t = \\hat{\\boldsymbol{x}}^{-}_{t} + \\mathbf{H}^{-1}(\\boldsymbol{z}_{t} - \\mathbf{H} \\hat{\\boldsymbol{x}}^{-}_{t})\\\\ \n",
    "   &= \\hat{\\boldsymbol{x}}^{-}_{t} + \\mathbf{H}^{-1}\\boldsymbol{z}_{t} - \\mathbf{H}^{-1}\\mathbf{H} \\hat{\\boldsymbol{x}}^{-}_{t} = \\hat{\\boldsymbol{x}}^{-}_{t} + \\mathbf{H}^{-1}\\boldsymbol{z}_{t} -  \\hat{\\boldsymbol{x}}^{-}_{t}\\\\ \n",
    "   &= \\mathbf{H}^{-1}\\boldsymbol{z}_{t} \n",
    "   \\end{aligned}\n",
    "   $$\n",
    "\n",
    "<img src=\"media/extreme1.png\" style=\"width: 50%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "2. The covariance estimate $\\mathbf{P}^{-}_t$ approaches zero.\n",
    "   - The model is completely reliable and the measurements are not accounted for.\n",
    "   - We have $\\lim \\limits_{\\mathbf{P}^{-}_t \\rightarrow 0} \\mathbf{K}_t = \\frac{\\mathbf{P}^{-}_t \\mathbf{H}^T}{\\mathbf{H} \\mathbf{P}^{-}_t \\mathbf{H}^T + \\mathbf{R}} = 0$.\n",
    "   - $\\mathbf{K}$ does not give importance to the residuals: $\\hat{\\boldsymbol{x}}_{t} = \\hat{\\boldsymbol{x}}^{-}_{t} + 0\\Delta_t = \\hat{\\boldsymbol{x}}^{-}_{t}$.\n",
    "\n",
    "<img src=\"media/extreme2.png\" style=\"width: 50%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- The last thing that remains to update is the posterior covariance estimate $\\mathbf{P}_t$ to be used in the next predict step.\n",
    "- The formula is:\n",
    "\n",
    "$$\\mathbf{P}_t = (\\mathbf{I} - \\mathbf{K}_t \\mathbf{H})\\mathbf{P}^{-}_t$$\n",
    "\n",
    "- Let's look again at the two extreme cases:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- $\\mathbf{K}_t = \\mathbf{H}^{-1} \\rightarrow \\mathbf{P}_t = 0$\n",
    "  - This is the case where the measurements are completely reliable.\n",
    "  - The only source of uncertainty at the next Predict step will be the one of the model: $\\mathbf{P}_t^{-} = \\mathbf{A}\\mathbf{P}_t\\mathbf{A}^T + \\mathbf{Q} = \\mathbf{Q}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- $\\mathbf{K}_t = 0 \\rightarrow \\mathbf{P}_t = \\mathbf{P}^{-}_t$\n",
    "  - This is the case where the measurements are unreliable and not accounted for.\n",
    "  - The posterior covariance estimate is exactly the same as the prior covariance estimate $\\mathbf{P}^{-}_t$ obtained in the Predict step using the model and not modified with the new measurements in the Correct step."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Summary of the Correct step:\n",
    "\n",
    "<img src=\"media/correct.png\" style=\"width: 25%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The whole process is summarized below.\n",
    "\n",
    "<img src=\"media/kalman.png\" style=\"width: 50%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Parameters estimation\n",
    "\n",
    "In general, both the measurement noise covariance $\\mathbf{R}$ and the process noise covariance $\\mathbf{Q}$ are **unknown**.\n",
    "\n",
    "- Estimating $\\mathbf{R}$ is usually done prior to operation of the filter. \n",
    "- Measuring $\\mathbf{R}$ is usually possible because we measure the process anyway (while operating the filter).\n",
    "- We can take some offline sample measurements to determine the variance of the measurement noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Determining the process noise covariance $\\mathbf{Q}$ is generally more difficult.\n",
    "- We typically do not have the ability to directly observe the process we are estimating. \n",
    "- Sometimes a relatively simple process model can produce acceptable results if one \"injects\" enough uncertainty into the process. \n",
    "- This works well if the process measurements are reliable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "### Extensions and Variants\n",
    "  - The Extended Kalman Filter (EKF) is used for nonlinear systems by linearizing about the current estimate.\n",
    "  - The Unscented Kalman Filter (UKF) uses a deterministic sampling technique to capture the mean and variance of the state distribution.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Practical Considerations\n",
    "- Designing an accurate model and having reliable measurements are crucial for effective filtering.\n",
    "- Dealing with nonlinearities can be challenging and may require the EKF or UKF.\n",
    "- Tuning process and measurement noise covariances $\\mathbf{Q}$ and $\\mathbf{R}$ is essential for optimal performance.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Python implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Next, we will implement the Kalman Filter in Python and use it to estimate the value of a signal from noisy data. \n",
    "- Initially, we will construct the algorithm by hand so we understand all the steps involved. \n",
    "- Also, we will generate datasets from scratch so we know what our true result should be and therefore gain insight into how well the Kalman Filter works. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The algorithm \n",
    "\n",
    "This is the workflow of the algorithm we are going to implement:\n",
    "\n",
    "1. Make an initial estimate of your state vector and covariance matrix.\n",
    "2. Predict the state and covariance for the next time step.\n",
    "3. Computer the Kalman gain.\n",
    "4. Make a measurement.\n",
    "5. Update estimates of state and covariance.\n",
    "6. Repeat from step 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "For one-dimensional examples, there are a couple of simplifications: \n",
    "- the state vector is a single number (a scalar).\n",
    "- the covariance matrix reduces to the variance (also a scalar). \n",
    "\n",
    "Therefore, only normal multiplication (as opposed to matrix multiplication) is involved."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example 1: Static one-dimensional data\n",
    "\n",
    "- Let's start by considering a simple example: determine the position of a stationary car. \n",
    "- We'll assume that all we are interested in is a one-dimensional value, such as the distance along a road from a landmark.\n",
    "- We are going to try to predict the true position based on some noisy measurements of the distance. \n",
    "- Since we are going to generate the noisy measurements by hand, we will know the true position and we can see how well our algorithm performs. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- We assume the measurements to follow this distribution:\n",
    "\n",
    "$$z_t = \\mu + v_t \\;\\; \\text{with}\\;\\; v_t \\sim \\mathcal{N}(0, R)$$ \n",
    "\n",
    "- where $\\mu$ is the actual position and $R$ is the actual measurement noise covariance.\n",
    "- Note that both $\\mu$ and $R$ are unknown to the filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = 124.5 # Actual position\n",
    "R = 0.1    # Actual standard deviation of actual measurements (R)\n",
    "\n",
    "# Generate measurements\n",
    "n_measurements = 1000 # Change the number of points to see how the convergence changes\n",
    "Z = np.random.normal(mu, np.sqrt(R), size=n_measurements)\n",
    "\n",
    "plt.plot(Z,'k+',label='measurements $z_t$',alpha=0.2)\n",
    "plt.title('Noisy position measurements')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('$z_t$')\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- As discussed previously, since the actual measurement noise covariance is unknown, we have to provide an estimate.\n",
    "- This is usually feasible as we can estimate $R$ from the available measurements.\n",
    "- In addition, we need to estimate the process noise covariance $Q$, which is usually harder to guess.\n",
    "- Remember that $Q$ represents the noise of the model used to describe the actual position.\n",
    "- In our case:\n",
    "\n",
    "$$x_t = x_0 + w_t \\;\\; \\text{with}\\;\\; w_t \\sim \\mathcal{N}(0,Q)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- In summary, we have two noise parameters: one for the model ($Q$) and one for the measurement ($R$). \n",
    "- The values of $Q$ and $R$ are inputs for the algorithm.  \n",
    "- Therefore, since we usually don't $Q$ and $R$, we have to make reasonable estimates. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- In this example, we know the actual variance for the measurements (since we are generating the measurements ourselves).\n",
    "- We can see the effect of making a good or a bad estimate for this parameter. \n",
    "- Also, we choose the actual position of our car, so we can see how quickly the KF converges to the true value.\n",
    "- Finally, we need to guess initial values for the initial position of the car and the variance in this initial estimate. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Estimated covariances\n",
    "Q_est = 1e-4 \n",
    "R_est = 2e-2 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Create a function that computes the estimated position and associated error using the KF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kalman_1d(x, P, measurement, R_est, Q_est):\n",
    "    \n",
    "    # Prediction\n",
    "    x_pred = x\n",
    "    P_pred = P + Q_est\n",
    "\n",
    "    # Update\n",
    "    K = P_pred / (P_pred + R_est)\n",
    "    x_est = x_pred + K * (measurement - x_pred)\n",
    "    P_est = (1 - K) * P_pred\n",
    "\n",
    "    return x_est, P_est"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Apply the filter to the 1D static measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial guesses \n",
    "x = 123 # Use an integer (imagine the initial guess is determined with a meter stick)\n",
    "P = 0.04 # error covariance P\n",
    "\n",
    "KF_estimate=[] # To store the position estimate at each time point \n",
    "KF_error=[] # To store estimated error at each time point\n",
    "for z in Z:\n",
    "    x, P = kalman_1d(x, P, z, R_est, Q_est)\n",
    "    KF_estimate.append(x)\n",
    "    KF_error.append(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Now, plot an estimate for the value $x_t$ on top of the measurements $z_t$. \n",
    "- We also plot how the covariance estimate $P_t$ changes during the process. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "def plot_1d_comparison(measurements_made, estimate, true_value, axis):\n",
    "    axis.plot(measurements_made,'k+',label='measurements',alpha=0.3)\n",
    "    axis.plot(estimate,'-',label='KF estimate')\n",
    "    if not isinstance(true_value, (list, tuple, np.ndarray)):\n",
    "        # plot line for a constant value\n",
    "        axis.axhline(true_value,color='r',label='true value', alpha=0.5) \n",
    "    else:\n",
    "        # for a list, tuple or array, plot the points\n",
    "        axis.plot(true_value,color='r',label='true value', alpha=0.5)\n",
    "    axis.legend(loc = 'lower right')\n",
    "    axis.set_title('Estimated position vs. time step')\n",
    "    axis.set_xlabel('Time')\n",
    "    axis.set_ylabel('$x_t$')\n",
    "    \n",
    "def plot_1d_error(estimated_error, lower_limit, upper_limit, axis):\n",
    "    # lower_limit and upper_limit are the lower and upper limits of the vertical axis \n",
    "    axis.plot(estimated_error, label='KF estimate for $P$')\n",
    "    axis.legend(loc = 'upper right')\n",
    "    axis.set_title('Estimated error vs. time step')\n",
    "    axis.set_xlabel('Time')\n",
    "    axis.set_ylabel('$P_t$')\n",
    "    plt.setp(axis,'ylim',[lower_limit, upper_limit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1,2, figsize=(12, 5))\n",
    "plot_1d_comparison(Z, KF_estimate, mu, axes[0])\n",
    "plot_1d_error(KF_error, 0, 0.015, axes[1])\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- We see that for the parameters we've chosen, the filter converges to the true value quickly and the noise is filtered out. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Question:** How much the KF estimate fluctuates around the true value? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Answer:** The fluctuations around the true value are approximately the size of the standard deviation of the estimate, which is $\\sqrt{P_t}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example 2: Dynamic one-dimensional data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Let's now consider the system we saw earlier, a car that moves approximately at a constant velocity $v_0$.\n",
    "- The position changes over time according to the following formula:\n",
    "\n",
    "$$x_{t} = x_{t-1} + \\delta t \\cdot v_0 + w_t$$ \n",
    "\n",
    "- where $w_t \\sim \\mathcal{N}(0, Q)$ represents the model noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Now, assume we have measurements only for the position, but not the velocity.\n",
    "- Let the measurements be generated according to the following distribution:\n",
    "\n",
    "$$z_t = z_{t-1} + \\delta t \\cdot v_t$$\n",
    "\n",
    "- In this case, $v_t$ represent a noisy measurement for the velocity, that is not observed directly.\n",
    "- We let $v_t \\sim \\mathcal{N}(v_0, R)$, where $R$ represents the variance of the measurements error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Let's now modify our static algorithm to take into account this motion. \n",
    "- At each time point, we will generate a random value $v_t$ for the velocity measurement. \n",
    "- We will assume that the car moves at velocity $v_t$ until the next time point, which allows us to calculate the distance traveled. \n",
    "- By summing all of the distances traveled, we can calculate the measured position of the car $z_t$.\n",
    "- Then we will apply the KF and compare the KF estimate for the position with both the actual position $x_t = x_0 + v_0 \\cdot t$ and the measured positions $z_t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# initial parameters\n",
    "v0 = 0.3 \n",
    "x0 = 0.0     \n",
    "R = 4.0\n",
    "\n",
    "# generate noisy measurements\n",
    "n_measurements = 1000\n",
    "Zv = np.zeros(n_measurements) # velocity measurements\n",
    "Zx = np.zeros(n_measurements) # position measurements\n",
    "for t in range(0, n_measurements-1):\n",
    "    Zv[t] = np.random.normal(v0, np.sqrt(R)) \n",
    "    Zx[t+1] = Zx[t] + Zv[t] * 1 # delta_t = 1\n",
    "\n",
    "# generate true positions\n",
    "Xt = np.zeros(n_measurements) \n",
    "for t in range(0, n_measurements):\n",
    "    Xt[t]= x0 + v0*t\n",
    "\n",
    "plt.plot(Zx,'k+',label='measurements $z_t$',alpha=0.2)\n",
    "plt.title('Noisy position measurements')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('$z_t$')\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# initial guesses and estimates\n",
    "x = 0 \n",
    "P = 0.5\n",
    "Q_est = 4 \n",
    "R_est = 4\n",
    "KF_estimate = [] # To store the position estimate at each time point \n",
    "KF_error = [] # To store estimated error at each time point\n",
    "\n",
    "# Kalman filter\n",
    "for z in Zx:\n",
    "    x, P = kalman_1d(x, P, z, R_est, Q_est)\n",
    "    KF_estimate.append(x)\n",
    "    KF_error.append(P)\n",
    "\n",
    "fig, axes = plt.subplots(1,2, figsize=(12, 5))\n",
    "plot_1d_comparison(Zx, KF_estimate, Xt, axes[0])\n",
    "plot_1d_error(KF_error, min(KF_error)-0.1, max(KF_error)+0.1, axes[1])\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Question:** Neither the measurements nor the KF estimate are close to the true value. Why?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Answer:** The measurements are not close to the true value because the variance of the measurements error $R$ is large compared to the velocity $v_0$. \n",
    "\n",
    "- The KF estimate is tracking the measurements, so it won't be close to the true value. \n",
    "- In addition, we do not have measurements for the instant velocity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- With dynamic models, there are more parameters to tune, so it can be more challenging to reach convergence. \n",
    "- If we had a way to measure velocity, we could use that information too. \n",
    "- Nevertheless, the KF can work with incomplete observations, which is one of its main advantages. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example 3: Dynamic two-dimensional data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Now we consider an example that is closer to real-world applications: estimating the motion of a point in two dimensions, $x$ and $y$. \n",
    "- This 2D algorithm is used in mouse tracking software and also to track objects in videos. \n",
    "- As before, we will use instantaneous measurements for the position ($x, y$).\n",
    "- We are going to use the Kalman filter built into OpenCV. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Our system is defined by the following quantities:\n",
    "\n",
    "- State vector $\\boldsymbol{x} = \\begin{bmatrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\end{bmatrix}$, representing the 2D position and 2D velocity.\n",
    "- Measurement vector $\\boldsymbol{z} = \\begin{bmatrix} z_x \\\\ z_y  \\end{bmatrix}$, representing measurements for the 2D position.\n",
    "- Transition matrix $\\mathbf{A} = \\begin{bmatrix} 1 & 0 & \\delta_t & 0 \\\\ 0 & 1 & 0 & \\delta_t \\\\ 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 1 \\end{bmatrix}$ (called `transitionMatrix` in OpenCV).\n",
    "- Measurement matrix $\\mathbf{H} = \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 \\end{bmatrix}$ (called `measurementMatrix` in OpenCV)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- The covariance of the model noise $\\mathbf{Q} = \\begin{bmatrix}  q & 0 & 0 & 0 \\\\  0 & q & 0 & 0 \\\\ 0 & 0 & q & 0 \\\\ 0 & 0 & 0 & q  \\end{bmatrix}$ (called `processNoiseCov` in OpenCV).\n",
    "- The covariance of the measurements noise $\\mathbf{R} = \\begin{bmatrix}  r & 0 \\\\ 0 & r  \\end{bmatrix}$ (called `measurementNoiseCov` in OpenCV).\n",
    "\n",
    "For simplicity, we use diagonal covariances in this example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The constructor has has the following sintax:\n",
    "\n",
    "> `KalmanFilter(state_size, measurements_size, control_size)`\n",
    "\n",
    "where:\n",
    "- `state_size` is the dimension of the state vector $\\boldsymbol{x}$, which is 4 in our case.\n",
    "- `measurements_size` is the dimension of the state vector $\\boldsymbol{x}$, which is 2 in our case.\n",
    "- `control_size`, which is 0 since we do not have the optional control $\\boldsymbol{u}$ (not discussed in this lecture)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "kalman = cv2.KalmanFilter(4,2,0) # 4 states, 2 measurements, 0 control vector\n",
    "\n",
    "q = 1 # the variance in the model\n",
    "r = 20 # the variance in the measurement\n",
    "dtime = 1 # size of time step\n",
    "\n",
    "kalman.measurementMatrix = np.array([[1,0,0,0],\n",
    "                                     [0,1,0,0]],np.float32) #  H\n",
    "kalman.transitionMatrix = np.array([[1,0,dtime,0],\n",
    "                                    [0,1,0,dtime],\n",
    "                                    [0,0,1,0],\n",
    "                                    [0,0,0,1]],np.float32) # A\n",
    "kalman.processNoiseCov = np.array([[1,0,0,0],\n",
    "                                   [0,1,0,0],\n",
    "                                   [0,0,1,0],\n",
    "                                   [0,0,0,1]],np.float32) * q # Q\n",
    "kalman.measurementNoiseCov = np.array([[1,0],\n",
    "                                       [0,1]],np.float32) * r # R\n",
    "\n",
    "KF_estimate_xy = [] # To store the position estimate at each time point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Next, we will load some pre-computed data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xy_motion = pd.read_csv('https://zenodo.org/records/10951538/files/kf_ts1.csv?download=1',\n",
    "                        header = None).values.astype('float32')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Here, we use pre-computed data for simplicity/reproducibility.\n",
    "- However, you can generate your own $(z_x, z_y)$ measurements by clicking first on the grid and then on ``Generate Sample``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"900\"\n",
       "            height=\"800\"\n",
       "            src=\"https://guoguibing.github.io/librec/datagen.html\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x7f1ff4deab60>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import IFrame\n",
    "IFrame('https://guoguibing.github.io/librec/datagen.html', width=900, height=800)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- As always, take a look at the data before analyzing it. \n",
    "- Also, it is good practice to make sure the data loaded properly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "205\n",
      "[[2.35 1.45]\n",
      " [3.55 1.8 ]\n",
      " [3.   2.9 ]\n",
      " [2.65 4.2 ]\n",
      " [2.95 5.15]\n",
      " [3.7  5.4 ]\n",
      " [4.8  5.55]\n",
      " [5.3  5.25]\n",
      " [5.7  5.25]\n",
      " [5.8  5.85]]\n"
     ]
    }
   ],
   "source": [
    "print(len(xy_motion))\n",
    "print(xy_motion[0:10]) # Print first 10 items for clarity, but can look at all 205 or plot them"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- We are now ready to apply the KF. \n",
    "- In the OpenCV implementation of the KF there is no initialization options. \n",
    "- Both the state vector $\\boldsymbol{x}$ and the covariance matrix $\\mathbf{P}$ are always initialized to zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "for i in xy_motion:\n",
    "    pred = kalman.predict()  # predicts new state using the model\n",
    "    kalman.correct((i))      # updates estimated state with the measurement\n",
    "    KF_estimate_xy.append(((pred[0]),(pred[1]))) # store the estimated position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "205\n"
     ]
    }
   ],
   "source": [
    "# Quick check: estimate has same length as measurement data\n",
    "print(len(KF_estimate_xy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now plot the data and the KF estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_est, y_est = zip(*KF_estimate_xy)\n",
    "x_true, y_true = zip(*xy_motion)\n",
    "plt.scatter(x_est, y_est, marker= '.', label = 'KF estimate', alpha = 0.5)\n",
    "plt.scatter(x_true, y_true,marker= '.', label = 'true value', alpha = 0.5)\n",
    "plt.legend(loc = 'lower center')\n",
    "plt.title('2D position')\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Pretty good agreement. \n",
    "- Once again, you are encouraged to change the parameters and explore what happens.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Summary\n",
    "\n",
    "What we covered in this lecture:\n",
    "\n",
    "1. What is the Kalman Filter\n",
    "2. The recursive formulation used to update the predictions.\n",
    "3. The importance of tuning the parameters of the Kalman Filter.\n",
    "4. How to apply the Kalman Filter in various situations.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Exercise #1\n",
    "This exercise refers to [Example 1](#example-1-static-one-dimensional-data).\n",
    "1. Choose a value for the estimated model variance `Q_est` that is larger than estimated measurement variance `R_est`.\n",
    "2. Repeat the analysis of Example 1 for this new value. \n",
    "3. Does the KF estimate converge?\n",
    "4. Why the estimates changed? Do they look more noisy than before? Why?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Exercise #2\n",
    "\n",
    "This exercise refers to [Example 2](#example-2-dynamic-one-dimensional-data). \n",
    "\n",
    "In the case we examined above, the KF estimate was close to the measurements and both were different from the true value.\n",
    "Change the parameters of the algorithm until you find some combinations that achieve the following:\n",
    "\n",
    "1. Measurements, KF estimate and true value are all close.\n",
    "2. Measurements, KF estimate and true value are all noticeably different.\n",
    "3. The measurements are close to the true value, but the KF estimate is different.\n",
    "\n",
    "Discuss your findings."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Exercise #3\n",
    "\n",
    "This exercise refers to [Example 3](#example-3-dynamic-two-dimensional-data). \n",
    "\n",
    "In the original example, we used both Position and Velocity (PV model) in the state vector, i.e., $\\boldsymbol{x} = \\begin{bmatrix} x & y & \\dot x & \\dot y \\end{bmatrix}^T$. \n",
    "\n",
    "What happens if we use only the Position (P model) to describe the state? After all, our measurements only provide position. Do we really need to include the velocity?\n",
    "\n",
    "1. Rewrite the algorithm above for the P model. \n",
    "\n",
    "**💡 Hint:** what is the size of the state vector in this case? What are the dimensions of the matrices that characterize the system?"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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": "3.10.14"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}