From be9a77561bc4a1e77ed93cfeddf332bf471e39f1 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sun, 31 Aug 2014 19:03:15 -0700 Subject: [PATCH] Expanded Jacobian coverage. Added explicit computation of Jacobian, and, more interestingly, added the use of sympy to compute the Jacobian automatically. --- Designing_Nonlinear_Kalman_Filters.ipynb | 246 ++++++++++++++++++++--- 1 file changed, 217 insertions(+), 29 deletions(-) diff --git a/Designing_Nonlinear_Kalman_Filters.ipynb b/Designing_Nonlinear_Kalman_Filters.ipynb index c2c5e98..119e717 100644 --- a/Designing_Nonlinear_Kalman_Filters.ipynb +++ b/Designing_Nonlinear_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:6e6749d931110e1edad026d2237ed80b25dbe6f60372d36194549b6f735220f0" + "signature": "sha256:ff55ea156e51d203e3d4a98256614289bbe209beec4a681fe1334120c13e55b2" }, "nbformat": 3, "nbformat_minor": 0, @@ -44,7 +44,7 @@ " background: transparent;\n", " color: #000000;\n", " font-weight: 600;\n", - " font-size: 13pt;\n", + " font-size: 11pt;\n", " font-style: bold;\n", " font-family: 'Source Code Pro', Consolas, monocco, monospace;\n", " }\n", @@ -248,13 +248,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 4, + "prompt_number": 1, "text": [ - "" + "" ] } ], - "prompt_number": 4 + "prompt_number": 1 }, { "cell_type": "heading", @@ -395,11 +395,11 @@ "output_type": "display_data", "png": 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Nl4hsomvX2Adas5u6Llrkw/z58UWsqGlsgFMg8OabUDZtius56oQJiNxyi0Uj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\nc0Az2wAAAABJRU5ErkJggg==\n", "text": [ - "" + "" ] } ], - "prompt_number": 5 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -442,14 +442,38 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Instead of computing $\\mathbf{H}$ we will compute the partial derivative of $\\mathbf{H}$ with respect to the robot's position $\\mathbf{x}$. You are probably familiar with the concept of partial derivative, but if not, it just means how $\\mathbf{H}$ changes with respect to the robot's position.\n", + "Instead of computing $\\mathbf{H}$ we will compute the partial derivative of $\\mathbf{H}$ with respect to the robot's position $\\mathbf{x}$. You are probably familiar with the concept of partial derivative, but if not, it just means how $\\mathbf{H}$ changes with respect to the robot's position. It is computed as the partial derivative of $\\mathbf{H}$ as follows:\n", + "\n", + "$$\\frac{\\partial \\mathbf{h}}{\\partial \\mathbf{x}} = \n", + "\\begin{bmatrix}\n", + "\\frac{\\partial h_1}{\\partial x_1} & \\frac{\\partial h_1}{\\partial x_2} &\\dots \\\\\n", + "\\frac{\\partial h_2}{\\partial x_1} & \\frac{\\partial h_2}{\\partial x_2} &\\dots \\\\\n", + "\\vdots & \\vdots\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Let's work the first partial derivative. We want to find\n", + "\n", + "$$\\frac{\\partial }{\\partial x} \\sqrt{(x-x_A)^2 + (y-y_A)^2}\n", + "$$\n", + "\n", + "Which we compute as\n", + "$$\n", + "\\begin{aligned}\n", + "\\frac{\\partial h_1}{\\partial x} &= ((x-x_A)^2 + (y-y_A)^2))^\\frac{1}{2} \\\\\n", + "&= \\frac{1}{2}\\times 2(x-x_a)\\times ((x-x_A)^2 + (y-y_A)^2))^{-\\frac{1}{2}} \\\\\n", + "&= \\frac{x_r - x_A}{\\sqrt{(x_r-x_A)^2 + (y_r-y_A)^2}} \n", + "\\end{aligned}\n", + "$$\n", + "\n", + "We continue this computation for the partial derivatives of the two distance equations with respect to $x$, $y$, $dx$ and $dy$, yielding\n", "\n", "$$\\frac{\\partial\\mathbf{h}}{\\partial\\mathbf{x}}=\n", "\\small\\begin{bmatrix}\n", - "\\frac{(x_r - x_A)}{\\sqrt{(x_r-x_A)^2 + (y_r-y_A)^2}} & 0 & \n", - "\\frac{(y_r - y_A)}{\\sqrt{(x_r-x_A)^2 + (y_r-y_A)^2}} & 0 \\\\\n", - "\\frac{(x_r - x_B)}{\\sqrt{(x_r-x_B)^2 + (y_r-y_B)^2}} & 0 &\n", - "\\frac{(y_r - y_B)}{\\sqrt{(x_r-x_B)^2 + (y_r-y_B)^2}} & 0 \\\\\n", + "\\frac{x_r - x_A}{\\sqrt{(x_r-x_A)^2 + (y_r-y_A)^2}} & 0 & \n", + "\\frac{y_r - y_A}{\\sqrt{(x_r-x_A)^2 + (y_r-y_A)^2}} & 0 \\\\\n", + "\\frac{x_r - x_B}{\\sqrt{(x_r-x_B)^2 + (y_r-y_B)^2}} & 0 &\n", + "\\frac{y_r - y_B}{\\sqrt{(x_r-x_B)^2 + (y_r-y_B)^2}} & 0 \\\\\n", "\\end{bmatrix}\n", "$$" ] @@ -458,7 +482,158 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In a nutshell, the entry (0,0) contains the difference between the x coordinate of the robot and transmitter A's x coordinate divided by the distance between the robot and A. (2,0) contains the same, except for the y coordintates of the robot and transmitters. The bottom row contains the same computations, except for transmitter B. The 0 entries account for the velocity components of the state variables; naturally the range does notvide us with velocity.\n", + "That is pretty painful, and these are very simple equations. Computing the Jacobian can be extremely difficult or even impossible for more complicated systems. However, there is an easy way to get Python to do the work for you by using the `sympy` module [1]. `sympy` is a Python library for symbolic mathematics. The full scope of its abilities are beyond this book, but it can perform algebra, integrate and differentiate equations, find solutions to differential equations, and much more. We will use it to compute our Jabobian!\n", + "\n", + "First, a simple example. We will import sympy, initialize its pretty print functionality (which will print equations using $\\LaTeX$). We will then declare a symbol for numpy to use." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import sympy\n", + "from sympy import init_printing\n", + "#from sympy.interactive import printing\n", + "init_printing(use_latex='mathjax')\n", + "\n", + "phi, x = sympy.symbols('\\phi, x')\n", + "phi" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "latex": [ + "$$\\phi$$" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 15, + "text": [ + "\\phi" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice how we use a latex expression for the symbol `phi`. This is not necessary, but if you do it will render as LaTeX when output. Now let's do some math. What is the derivative of $\\sqrt{\\phi}$?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sympy.diff('sqrt(phi)')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "latex": [ + "$$\\frac{1}{2 \\sqrt{\\phi}}$$" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 17, + "text": [ + " 1 \n", + "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n", + " ___\n", + "2\u22c5\u2572\u2571 \u03c6 " + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can factor equations." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sympy.factor('phi**3 -phi**2 + phi - 1')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "latex": [ + "$$\\left(\\phi - 1\\right) \\left(\\phi^{2} + 1\\right)$$" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 26, + "text": [ + " \u239b 2 \u239e\n", + "(\u03c6 - 1)\u22c5\u239d\u03c6 + 1\u23a0" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`sympy` has a remarkable list of features, and as much as I enjoy exercising its features we cannot cover them all here. Instead, let's compute our Jacobian." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "phi = sympy.symbols('\\phi')\n", + "phi\n", + "\n", + "x, y, xa, xb, ya, yb, dx, dy = sympy.symbols('x, y, x_a, x_b, y_a, y_b, dx, dy')\n", + "\n", + "H = sympy.Matrix([[sympy.sqrt((x-xa)**2 + (y-ya)**2)], \n", + " [sympy.sqrt((x-xb)**2 + (y-yb)**2)]])\n", + "\n", + "state = sympy.Matrix([x, dx, y, dy])\n", + "H.jacobian(state)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "latex": [ + "$$\\left[\\begin{matrix}\\frac{x - x_{a}}{\\sqrt{\\left(x - x_{a}\\right)^{2} + \\left(y - y_{a}\\right)^{2}}} & 0 & \\frac{y - y_{a}}{\\sqrt{\\left(x - x_{a}\\right)^{2} + \\left(y - y_{a}\\right)^{2}}} & 0\\\\\\frac{x - x_{b}}{\\sqrt{\\left(x - x_{b}\\right)^{2} + \\left(y - y_{b}\\right)^{2}}} & 0 & \\frac{y - y_{b}}{\\sqrt{\\left(x - x_{b}\\right)^{2} + \\left(y - y_{b}\\right)^{2}}} & 0\\end{matrix}\\right]$$" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 28, + "text": [ + "\u23a1 x - x\u2090 y - y\u2090 \u23a4\n", + "\u23a2 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 0 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 0\u23a5\n", + "\u23a2 _______________________ _______________________ \u23a5\n", + "\u23a2 \u2571 2 2 \u2571 2 2 \u23a5\n", + "\u23a2 \u2572\u2571 (x - x\u2090) + (y - y\u2090) \u2572\u2571 (x - x\u2090) + (y - y\u2090) \u23a5\n", + "\u23a2 \u23a5\n", + "\u23a2 x - x_b y - y_b \u23a5\n", + "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 0 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 0\u23a5\n", + "\u23a2 _________________________ _________________________ \u23a5\n", + "\u23a2 \u2571 2 2 \u2571 2 2 \u23a5\n", + "\u23a3\u2572\u2571 (x - x_b) + (y - y_b) \u2572\u2571 (x - x_b) + (y - y_b) \u23a6" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In a nutshell, the entry (0,0) contains the difference between the x coordinate of the robot and transmitter A's x coordinate divided by the distance between the robot and A. (2,0) contains the same, except for the y coordintates of the robot and transmitters. The bottom row contains the same computations, except for transmitter B. The 0 entries account for the velocity components of the state variables; naturally the range does not provide us with velocity.\n", "\n", "The values in this matrix change as the robot's position changes, so this is no longer a constant; we will have to recompute it for every time step of the filter.\n", "\n", @@ -516,13 +691,13 @@ " theta_a = atan2(pos_a[1]-pos[1], pos_a[0] - pos[0])\n", " theta_b = atan2(pos_b[1]-pos[1], pos_b[0] - pos[0])\n", "\n", - " return np.mat([[0, -cos(theta_a), 0, -sin(theta_a)],\n", - " [0, -cos(theta_b), 0, -sin(theta_b)]])" + " return np.array([[0, -cos(theta_a), 0, -sin(theta_a)],\n", + " [0, -cos(theta_b), 0, -sin(theta_b)]])" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 6 + "prompt_number": 35 }, { "cell_type": "markdown", @@ -557,7 +732,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 10 + "prompt_number": 36 }, { "cell_type": "markdown", @@ -572,7 +747,7 @@ "collapsed": false, "input": [ "import math\n", - "from KalmanFilter import KalmanFilter\n", + "from filterpy.kalman import KalmanFilter\n", "import numpy as np\n", "\n", "pos_a = (100,-20)\n", @@ -580,17 +755,15 @@ "\n", "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", "\n", - "f1.F = np.mat ([[0, 1, 0, 0],\n", - " [0, 0, 0, 0],\n", - " [0, 0, 0, 1],\n", - " [0, 0, 0, 0]])\n", - "\n", - "f1.B = 0.\n", + "f1.F = np.array ([[0, 1, 0, 0],\n", + " [0, 0, 0, 0],\n", + " [0, 0, 0, 1],\n", + " [0, 0, 0, 0]], dtype=float)\n", "\n", "f1.R *= 1.\n", "f1.Q *= .1\n", "\n", - "f1.x = np.mat([1,0,1,0]).T\n", + "f1.x = np.array([[1,0,1,0]], dtype=float).T\n", "f1.P = np.eye(4) * 5.\n", "\n", "# initialize storage and other variables for the run\n", @@ -613,7 +786,7 @@ " # ranges\n", " ra,rb = d.range_of(pos)\n", " rx,ry = d.range_of((pos[0]+f1.x[0,0], pos[1]+f1.x[2,0]))\n", - " z = np.mat([[ra-rx],[rb-ry]])\n", + " z = np.array([[ra-rx],[rb-ry]])\n", "\n", " # compute linearized H for this time step\n", " f1.H = H_of (pos, pos_a, pos_b)\n", @@ -640,13 +813,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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jco6WVXoMMZ1eAIFA5xcA0GRsR47I9frrcr36qmwHDsh9+eX67tUlWvTxXnZv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\nAMCP6PwCISCnwK3Fm37U2kO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0JUXe006r9ZfR6QUQDHR+AQB+YTt8WM6FCxXzxhuSx6OCF19USS0Wv+z0Aghn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\nKex2u0aOHKnWrVvr2LFjevHFFzVt2jT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"text": [ - "" + "" ] } ], - "prompt_number": 14 + "prompt_number": 37 }, { "cell_type": "heading", @@ -664,6 +837,21 @@ "\n", "We start by assuming some function $\\mathbf f$" ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "References" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[1] http://sympy.org\n" + ] } ], "metadata": {}