{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Demonstration: Trilateration With Noise!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In lecture, we learned how the GPS receiver determines its location once it knows the distance of the various signaling beacons from itself.\n", "This method is called *trilateration*.\n", "\n", "In this demonstration, we're going to further explore the connection between trilateration and least squares through a toy problem with four beacons and one GPS receiver.\n", "\n", "\n", "We are given *three* possible sets of measurements for the distances of each of the beacons from the receiver:\n", "\n", "1. First, the ideal set of measurements. $d_1 = d_2 = d_3 = d_4 = 5$.\n", "2. Next, a set of imperfect measurements. $d_1 = 5, d_2 = 4.8, d_3 = 5, d_4 = 5.2$.\n", "3. Finally, a set of mostly perfect measurements, but $d_1$ is a very bad measurement. We have $d_1 = 6.5$ and $d_2 = d_3 = d_4 = 5$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we set up some notation for the positions of the beacons, as well as their respective distances from the receivers." ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import mpld3\n", "mpld3.enable_notebook()\n", "import plotly.plotly as py\n", "from plotly.graph_objs import *\n", "\n", "\n", "axis = dict(\n", " showbackground=True, # (!) show axis background\n", " backgroundcolor=\"rgb(204, 204, 204)\", # set background color to grey\n", " gridcolor=\"rgb(255, 255, 255)\", # set grid line color\n", " zerolinecolor=\"rgb(255, 255, 255)\", # set zero grid line color\n", " range=[-10, 10]\n", ")\n", "\n", "axisZ = dict(\n", " showbackground=True, # (!) show axis background\n", " backgroundcolor=\"rgb(204, 204, 204)\", # set background color to grey\n", " gridcolor=\"rgb(255, 255, 255)\", # set grid line color\n", " zerolinecolor=\"rgb(255, 255, 255)\", # set zero grid line color\n", " range=[0, 600]\n", ")\n", "# Make a layout object\n", "layout = Layout(\n", " title='Cost Map', # set plot title\n", " scene=Scene( # (!) axes are part of a 'scene' in 3d plots\n", " xaxis=XAxis(axis), # set x-axis style\n", " yaxis=YAxis(axis), # set y-axis style\n", " zaxis=ZAxis(axisZ), # set z-axis style\n", " ),\n", " showlegend=False,\n", ")\n", "\n", "\n", "%matplotlib inline\n", "py.sign_in('ee16a', '2eqa3edyhn')\n", "\n", "\n", "################ LOOK HERE ######################\n", "distances = np.array([7.5, 5, 5, 5]) # Right now, it contains the ideal set of measurements. Change the data for the second and third sets.\n", "positions = [(0,-5),(-5/2.0,5*np.sqrt(3)/2),(0,5),(5/2.0,5*np.sqrt(3)/2)]\n", "xpositions = np.array([positions[0][0], positions[1][0], positions[2][0], positions[3][0]])\n", "ypositions = np.array([positions[0][1], positions[1][1], positions[2][1], positions[3][1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's plot the circles for each of the beacons corresponding to the respective distances of the receiver from each of them. The rough intersection of the circles will tell us, intuitively, where the receiver is located! (Note that the circles do not necessarily intersect at one point! Why?)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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xHrONwsnE3hVLiwdbsHHoRuqK1To2nsypRY2maR00TVt3zKVU07T7T7hNf03T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\nb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "circle1 = plt.Circle(positions[0],distances[0],color='b',fill=False)\n", "circle2 = plt.Circle(positions[1],distances[1],color='g',fill=False)\n", "circle3 = plt.Circle(positions[2],distances[2],color='r',fill=False)\n", "circle4 = plt.Circle(positions[3],distances[3],color='m',fill=False)\n", "\n", "fig = plt.figure(figsize=(9,9))\n", "ax=fig.add_subplot(111,xlim=[-10,10],ylim=[-10,10])\n", "ax.plot(positions[0][0], positions[0][1], 'bo')\n", "ax.text(positions[0][0] + 0.25, positions[0][1] + 0.25, \"B1\", color='b')\n", "ax.plot(positions[1][0], positions[1][1],'go')\n", "ax.text(positions[1][0] + 0.25, positions[1][1] + 0.25, \"B2\", color='g')\n", "ax.plot(positions[2][0], positions[2][1],'ro')\n", "ax.text(positions[2][0] + 0.25, positions[2][1] + 0.25, \"B3\", color='r')\n", "ax.plot(positions[3][0], positions[3][1],'mo')\n", "ax.text(positions[3][0] + 0.25, positions[3][1] + 0.25, \"B4\", color='m')\n", "fig.gca().add_patch(circle1)\n", "fig.gca().add_patch(circle2)\n", "fig.gca().add_patch(circle3)\n", "fig.gca().add_patch(circle4)\n", "ax.grid(b=True, which='both', color='0.65',linestyle='-')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's solve for the location of the receiver, $\\begin{bmatrix}x_1 \\\\ x_2\\end{bmatrix}$, using least squares.\n", "\n", "Recall that we made the system of equations linear by subtracting each of the equations for the beacon from the equation for the first beacon.\n", "\n", "This will result in the system of equations:\n", "\\begin{equation}\n", "(data\\_matrix)\\begin{bmatrix}x_1\\\\x_2\\end{bmatrix} = values\n", "\\end{equation}\n", "\n", "We have defined $data\\_matrix$ and $values$ in the code blocks below." ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 5. -18.66025404]\n", " [ 0. -20. ]\n", " [ -5. -18.66025404]]\n" ] } ], "source": [ "data_matrix = np.zeros((3,2))\n", "data_matrix[0][0] = 2*(xpositions[0] - xpositions[1])\n", "data_matrix[0][1] = 2*(ypositions[0] - ypositions[1])\n", "data_matrix[1][0] = 2*(xpositions[0] - xpositions[2])\n", "data_matrix[1][1] = 2*(ypositions[0] - ypositions[2])\n", "data_matrix[2][0] = 2*(xpositions[0] - xpositions[3])\n", "data_matrix[2][1] = 2*(ypositions[0] - ypositions[3])\n", "print(data_matrix)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-31.25 -31.25 -31.25]\n" ] } ], "source": [ "values = np.zeros(3)\n", "values[0] = xpositions[0]*xpositions[0] - xpositions[1]*xpositions[1] + ypositions[0]*ypositions[0] - ypositions[1]*ypositions[1] - distances[0]*distances[0]+distances[1]*distances[1]\n", "values[1] = xpositions[0]*xpositions[0] - xpositions[2]*xpositions[2] + ypositions[0]*ypositions[0] - ypositions[2]*ypositions[2] - distances[0]*distances[0]+distances[2]*distances[2]\n", "values[2] = xpositions[0]*xpositions[0] - xpositions[3]*xpositions[3] + ypositions[0]*ypositions[0] - ypositions[3]*ypositions[3] - distances[0]*distances[0]+distances[3]*distances[3]\n", "print(values)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we calculate the linear least squares estimate. Let's see what this gives us for the position of the receiver!" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -1.16085294e-16 1.63375527e+00]\n" ] } ], "source": [ "U1 = np.dot(data_matrix.T,data_matrix)\n", "U2 = np.dot(data_matrix.T,values)\n", "least_squares_sol = np.dot(np.linalg.inv(U1),U2)\n", "print(least_squares_sol)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's plot the estimated position of the receiver! We can see how well we've done visually -- how close is the estimated receiver position to the \"rough\" intersection of all the circles?" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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bheOJuy2OFve1YOPQjdSXqHVsvJlLixpN0xI1TVt3xFGmado9x9ymv6ZppUfc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\nHKhvYqlQV1BH0fwiYsfFyo6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UYNSGeGdSRY0XMeyMiAaBgbBpk+wUbvH8wOcJtgQfdV2w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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "circle1 = plt.Circle(positions[0],distances[0],color='b',fill=False)\n", "circle2 = plt.Circle(positions[1],distances[1],color='g',fill=False)\n", "circle3 = plt.Circle(positions[2],distances[2],color='r',fill=False)\n", "circle4 = plt.Circle(positions[3],distances[3],color='m',fill=False)\n", "\n", "fig = plt.figure(figsize=(9,9))\n", "plt.xlim(-10,10)\n", "plt.ylim(-10,10)\n", "plt.plot(positions[0][0], positions[0][1], 'bo')\n", "plt.figtext((positions[0][0] + 10)/20, (positions[0][1] + 10)/20, \"B1\", color='b')\n", "plt.plot(positions[1][0], positions[1][1],'go')\n", "plt.figtext((positions[1][0] + 10)/20, (positions[1][1] + 10)/20, \"B2\", color='g')\n", "plt.plot(positions[2][0], positions[2][1],'ro')\n", "plt.figtext((positions[2][0] + 10)/20,(positions[2][1] + 10)/20, \"B3\", color='r')\n", "plt.plot(positions[3][0], positions[3][1],'mo')\n", "plt.figtext((positions[3][0] + 10)/20,(positions[3][1] + 10)/20, \"B4\", color='m')\n", "fig.gca().add_artist(circle1)\n", "fig.gca().add_artist(circle2)\n", "fig.gca().add_artist(circle3)\n", "fig.gca().add_artist(circle4)\n", "plt.grid(b=True, which='both', color='0.65',linestyle='-')\n", "\n", "plt.plot(least_squares_sol[0],least_squares_sol[1],'ko')\n", "plt.figtext((least_squares_sol[0] + 10)/20 + 0.03, (least_squares_sol[1] + 10)/20 + 0.03, \"R\", color='k')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have seen that linearizing and solving least squares does not always do well, let's try something else.\n", "For any candidate location of the receiver, we can define its distances from each of the beacons:\n", "\n", "$$\\vec{\\hat{d}} = \\begin{bmatrix}\\hat{d}_1\\\\\\hat{d}_2\\\\\\hat{d}_3\\\\\\hat{d}_4\\end{bmatrix}$$\n", "\n", "So we might want to minimize the following:\n", "\n", "$$\\sum_{i=1}^4(d_i-\\hat{d}_i)^2$$\n", "\n", "Let's see some plots that help us visualize this. $(x,y)$ in the plot correspond to candidate positions of the receivers and $z$ corresponds to the cost.\n", "You can move your cursor over the interactive surface plot and determine where this cost is minimized.\n", "It will generally be minimized at $(0,0)$! (And most importantly, it is less at $(0,0)$ than it was at the least-squares-minimizing position.)" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": true, "scrolled": true }, "outputs": [], "source": [ "def squared_distance_between_points(pt1, pt2):\n", " return (pt1[0] - pt2[0])*(pt1[0] - pt2[0]) + (pt1[1] - pt2[1])*(pt1[1] - pt2[1])\n", "\n", "def cost_function(measured_distances, actual_distances):\n", " error = measured_distances - actual_distances\n", " cost = 0\n", " for i in range(len(error)):\n", " cost = cost + error[i]*error[i]\n", " return cost\n", "\n", "xvals = np.linspace(-10,10,200)\n", "yvals = np.linspace(-10,10,200)\n", "\n", "x, y = np.meshgrid(xvals,yvals)" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zvals = np.zeros([200,200])\n", "\n", "for i in range(200):\n", " for k in range(200):\n", " pt = [xvals[i],yvals[k]]\n", " actual_distances = np.zeros(4)\n", " for j in range(4):\n", " actual_distances[j] = np.sqrt(squared_distance_between_points(pt,[positions[j][0],positions[j][1]]))\n", " zvals[i][k] = cost_function(distances,actual_distances)\n", " \n", "\n", "blue=[[0, 'rgb(0,0,255)'], [1, 'rgb(0,0,255)']]\n", "green=[[0, 'rgb(0,255,0)'], [1, 'rgb(0,255,0)']]\n", "red=[[0, 'rgb(255,0,0)'], [1, 'rgb(255,0,0)']]\n", "\n", "trace1 = Surface(z=zvals, x=xvals,y=yvals, colorscale=blue,name='Cost')\n", "data = Data([trace1])\n", "fig = Figure(data=data,layout=layout)\n", "py.iplot(fig, filename='triangulation')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "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": "3.6.0" } }, "nbformat": 4, "nbformat_minor": 1 }