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Part 2 - The Solution to the MH370 Pinger Locator Problem
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Locating a Black Box Pinger\n",
"## Part 2 - The Solution\n",
"\n",
"![](http://rack.2.mshcdn.com/media/ZgkyMDE0LzAzLzI4LzkwL0ZsaWdodDM3MHNlLjY3YTMwLmpwZwpwCXRodW1iCTk1MHg1MzQjCmUJanBn/3b461b70/e97/Flight-370-search.jpg)\n",
"\n",
"In part one of this post we setup the problem of locating a black box pinger locator with a series of surface based sonar buoys. To illustrate the inversion theory used, we made some simplifying assumptions about the velocity of sound in the ocean, the ocean bottom, and the uncertainty in the data. This time we are going to solve the problem in a few ways and look at some interesting properties of our solution. \n",
"\n",
"As I am writing this post, there have been 4 recordings of what appear to be pingers in the search area for flight MH370. Why the authorities are continuing to tow a listening device and not deploying a small network or underwater vehicle is unknown. The idea that 4 recordings made within 17 miles of each other of 32kHz pings at 1Hz could be coincidence is unreasonable. The recorded pings are also very close to the satellite constrained arc that the plane must have been on."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Brute Force\n",
"\n",
"By far the simplest approach is grid search or Monte Carlo. In a grid search we define a grid of points (say every 100 km for the initial test), assume that the pinger is at each one of those points, run the forward model, and compute a residual vector. We can turn the residuals into some error metric and make a map of the error metric. Where the error is minimized is the most likely location of the source. While some problems are nasty and have several areas of good fit, difficult error surfaces, etc, we will see that this problems turns out to be very well behaved. \n",
"\n",
"Monte Carlo searches are similar to grid searches, but instead of looking on an evenly spaced grid we look at randomly generated points. This allows us to sample a lot of the solution space without exhaustively enumerating the entire domain. Monte Carlo methods may miss the ideal solution entirely, but can have significant time savings when compared to grid searches. Since we do a grid search below, we won't do a Monte Carlo sampling."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Setup \n",
"\n",
"These just setup the notebook for our calculations."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Import some modules we'll need\n",
"\n",
"from sympy import *\n",
"import matplotlib.path as mpath\n",
"import matplotlib.lines as mlines\n",
"import matplotlib.patches as mpatches\n",
"from matplotlib.collections import PatchCollection\n",
"init_printing(use_unicode=True) # This will make our matrices look nice"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def GridSearch(data,s0):\n",
" error = np.zeros([11,11])\n",
" i = 0\n",
" j = 0\n",
" for y in np.arange(0,10001,1000):\n",
" i = 0\n",
" for x in np.arange(0,10001,1000):\n",
" error[j,i] = np.sum((data - ComputeModel([x,y],s0))**2)\n",
" i +=1\n",
" j += 1\n",
" \n",
" fig = plt.figure(figsize(10,10))\n",
" ax = plt.subplot(111)\n",
" cax = ax.imshow(error,cmap='hot')\n",
" ax.scatter(source_x/1000.,source_y/1000.,marker='*',color='#ffff00',s=400,zorder=50)\n",
" \n",
" ax.tick_params(axis='both', which='major', labelsize=16)\n",
" ax.set_xlabel('X [km]',fontsize=18)\n",
" ax.set_ylabel('Y [km]',fontsize=18)\n",
" cbar = fig.colorbar(cax,shrink=0.8)\n",
" cbar.set_label('RMSE',size=18)\n",
" cbar.ax.tick_params(labelsize=16)\n",
" ax.set_xlim(0,10)\n",
" ax.set_ylim(0,10)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def GetDistance(rec_x,rec_y,source_x,source_y,depth):\n",
" return sqrt((rec_x-source_x)**2 + (rec_y-source_y)**2 + depth**2)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def ComputeModel(model,s0):\n",
" rel_arrivals = []\n",
" for i in range(nRx):\n",
" d = GetDistance(rec_x[i],rec_y[i],model[0],model[1],depth)\n",
" rel_arrivals.append(d/c_sound)\n",
" rel_arrivals = np.array(rel_arrivals)\n",
" rel_arrivals = rel_arrivals - rel_arrivals[s0]\n",
" return rel_arrivals\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Number of buoy receivers\n",
"nRx = 12\n",
"depth = 5000.\n",
"c_sound = 1510\n",
"\n",
"# Set the real source location\n",
"source_x = 5000 # 5km in\n",
"source_y = 5000 # 5km up\n",
"\n",
"# Set the 12 receiver locations\n",
"rec_x = [ 8500, 7550, 5700, 6750, 3150, 4850, 8600, 3800, 2850, 8250, 700, 6050]\n",
"rec_y = [ 5200, 5400, 9300, 4200, 300, 9700, 7150, 6100, 5450, 2600, 5500, 9400]\n",
"\n",
"# Make receiver location matrix\n",
"i = 0\n",
"receivers = zeros(nRx,2)\n",
"for rec in zip(rec_x,rec_y):\n",
" receivers[i,0] = rec[0]\n",
" receivers[i,1] = rec[1]\n",
" i += 1"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Calcualate Buoy Distances from Known Receiver to Generate data\n",
"\n",
"distances = []\n",
"i = 1\n",
"for receiver in zip(rec_x,rec_y):\n",
" d = GetDistance(receiver[0],receiver[1],source_x,source_y,depth)\n",
" print \"Receiver %d, %.2f m\" %(i,d)\n",
" distances.append(d)\n",
" i += 1"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Receiver 1, 6106.55 m\n",
"Receiver 2, 5626.94 m\n",
"Receiver 3, 6631.74 m\n",
"Receiver 4, 5357.47 m\n",
"Receiver 5, 7107.21 m\n",
"Receiver 6, 6863.85 m\n",
"Receiver 7, 6525.53 m\n",
"Receiver 8, 5258.33 m\n",
"Receiver 9, 5461.23 m\n",
"Receiver 10, 6428.26 m\n",
"Receiver 11, 6613.62 m\n",
"Receiver 12, 6742.59 m\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Calculate our observed relative arrivals\n",
"\n",
"rel_arrivals = []\n",
"for d in distances:\n",
" rel_arrivals.append(d/c_sound)\n",
"rel_arrivals = np.array(rel_arrivals)\n",
"\n",
"s0 = np.argmin(rel_arrivals)\n",
"\n",
"print \"Station s0: \", s0\n",
"rel_arrivals = rel_arrivals - min(rel_arrivals)\n",
"for i in range(nRx):\n",
" print \"Receiver %d, %.2f sec\" %(i+1,rel_arrivals[i])\n",
"travel_times_obs = rel_arrivals"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Station s0: 7\n",
"Receiver 1, 0.56 sec\n",
"Receiver 2, 0.24 sec\n",
"Receiver 3, 0.91 sec\n",
"Receiver 4, 0.07 sec\n",
"Receiver 5, 1.22 sec\n",
"Receiver 6, 1.06 sec\n",
"Receiver 7, 0.84 sec\n",
"Receiver 8, 0.00 sec\n",
"Receiver 9, 0.13 sec\n",
"Receiver 10, 0.77 sec\n",
"Receiver 11, 0.90 sec\n",
"Receiver 12, 0.98 sec\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Do a Grid Search\n",
"\n",
"We will search in a 1 km grid and make a map of the misfit. Low misfit (dark colors) is what we want. Turns out that we can resolve a nice \"bull's eye\" shape since we have a transmitter surrounded by a pretty dense network."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"GridSearch(travel_times_obs,s0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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1iCNXDbpPN/C1JkS4ui3BtkwQQCoMslZHDK6iSFa4AHkGK1fPAapSgKWBKGI+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0vxK8Gu2bSYWh6hn6bTrosSkhVfuGex/YzdfKy23DgcxtTBCSVPc3wFS5OHH34YN9xwA+644w7s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777yzld1111348pe/jOOPP36GPauoqKioqKiYFFb6+j/3n2n4xS9+gec973lYvXo13v3udwMA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\nioqKioqKioqBUQlWRUVFRUVFRcXA+P+Zm0aq0Ld3PwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10adef2d0>"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Do Iterative Inversion\n",
"\n",
"We will do an iteratitive inversion with options for damping and options for controlling the step size. These parameters were defined in the first notebook.\n",
"\n",
"#### 1) Setup an initial model"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Setup the initial model, where we will start\n",
"model = Matrix([3800,6100])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 2) Run the current model through the forward problem"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# This is a generator to calculate the partials\n",
"def MakePartials(i,j):\n",
" return (model[j]-receivers[i,j])/(c_sound*sqrt((receivers[i,0]-model[0])**2+(receivers[i,1]-model[1])**2+depth**2))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Does one iteration of the model\n",
"def IterationLS(data,model):\n",
" predicted_arrivals = ComputeModel(model,s0)\n",
" residual = Matrix(data - predicted_arrivals.T)\n",
" \n",
" G = Matrix(nRx,2,MakePartials)\n",
" epsilon = 0.0 ### Tweak damping here\n",
" I = eye(2)\n",
" x_ls = ((G.T * G)+(epsilon**2*I))**-1 * G.T * residual.T\n",
" xi = 0.7 ### Tweak step fraction here\n",
" model = model + xi*x_ls\n",
" return G,x_ls,model"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Do the iterations and keeep a history\n",
"\n",
"Niter = 10 ### Number of iterations to do\n",
"\n",
"model_hist = []\n",
"misfit = []\n",
"model_hist.append(list(model))\n",
"for i in range(Niter):\n",
" G,x_ls,model = IterationLS(rel_arrivals,model)\n",
" model_hist.append(list(model))\n",
" rmse = np.sum((travel_times_obs[:] - ComputeModel(model,7))**2)\n",
" misfit.append(rmse)\n",
"model_hist = np.array(model_hist)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Final Model\"\n",
"print \"X: %.2f\"%model[0]\n",
"print \"Y: %.2f\"%model[1]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Final Model\n",
"X: 5000.02\n",
"Y: 5000.04\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that we converged to the correct solution in just a few iterations. This isn't too surprising considering that there is a strong error signal that we can follow. Below is a plot of the convergence. After about 4 iterations the error has stopped changing and we can safely stop the inversion."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize(10,10))\n",
"ax = plt.subplot(111)\n",
"\n",
"ax.tick_params(axis='both', which='major', labelsize=16)\n",
"ax.set_xlabel('Iteration',fontsize=18)\n",
"ax.set_ylabel('RMSE',fontsize=18)\n",
"ax.scatter(range(1,len(misfit)+1),misfit,color='k',s=30)\n",
"ax.plot(range(1,len(misfit)+1),misfit,color='k',linewidth=2)\n",
"ax.set_xlim(0,Niter*1.1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$\\begin{pmatrix}0, & 11.0\\end{pmatrix}$$"
],
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAAAaBAMAAADBK4ZgAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nqX8Dhhdn8e5Ck8kAAAAASUVORK5CYII=\n",
"prompt_number": 14,
"text": [
"(0, 11.0)"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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UolHYgQwAQHQhFKJR2GwCAEB0IRSiUQiFAABEF0IhGoVQCABAdKElTYBisSWNJFVWVio1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\n6gn+4pRIAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10af1c490>"
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize(10,10))\n",
"ax = plt.subplot(111, axisbg='#6666ff')\n",
"\n",
"ax.grid()\n",
"ax.scatter(source_x,source_y,marker='*',color='#ffff00',s=400,zorder=50)\n",
"ax.tick_params(axis='both', which='major', labelsize=16)\n",
"ax.set_xlabel('X [m]',fontsize=18)\n",
"ax.set_ylabel('Y [m]',fontsize=18)\n",
"ax.set_xlim(0,10000)\n",
"ax.set_ylim(0,10000)\n",
"\n",
"i = 1\n",
"for receiver in zip(rec_x,rec_y):\n",
" ax.text(receiver[0]-200,receiver[1]+150,'Rx %d'%i,color='w')\n",
" i += 1\n",
"\n",
"ax.scatter(rec_x,rec_y,marker='v',color='r',s=80,zorder=50)\n",
"ax.scatter(model_hist[:,0],model_hist[:,1],color='k',s=30,zorder=50)\n",
"ax.plot(model_hist[:,0],model_hist[:,1],color='k',linewidth=2,zorder=50)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 15,
"text": [
"[<matplotlib.lines.Line2D at 0x10b3d80d0>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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h59ND6PkEAACmoOcTAAAAAYHiExC9SyYjO7ORn7nIDu6i+AQAAIDX0PPpIfR8AgAAU9Dz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\nAQAA4DcUnwAAAPCb/wMEHTWS6forxQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10af11cd0>"
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looking at the path our source location takes over time we can clearly see the convergence. With an appropriately small step fraction this path looks like what we would expect from a gradient decent algorithm."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sparse and Out of Network Conditions\n",
"\n",
"In the initial problem we didn't put any noise on the data, we also had many receivers located at many azimuths to the source. This is an ideal setup, but we can think about a couple of practical considerations. \n",
"\n",
"1. Sonar buoys are expensive and we want to deploy as few as possible\n",
"2. There is no guarantee that the pinger will lie within the confines of our network.\n",
"3. Real data is noisy.\n",
"\n",
"We will start with the last point: noise. Picking an arrival out of noise can be challenging, but probably won't have as large of an impact on the results as the first two points. The fewer stations that are deployed, the more dependent we are on each of them to contribute relevant information. The positions of those stations can also greatly effect the position resolution of the network. Below I show an example of two stations with an out of network transmitter. The problem ultimately results in an arc of uncertainty (much like that in the satellite data used to constrain the flight path). We can still locate the transmitter, but any noise will greatly impact where on the curve the solution will fall. Initial model dependence shows up in problems like this and means that we must run the inversion for many initial models. If you are going to use that much computational power, it is probably easier to Monte Carlo or grid search!"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Make a grid of sound velocity in the water\n",
"c_sound = 1510 #m/s\n",
"velocity = c_sound * np.ones([200,200])\n",
"\n",
"nRx = 2\n",
"\n",
"# Set the real source location\n",
"source_x = 7000 \n",
"source_y = 1000 \n",
"\n",
"nRx=2\n",
"rec_x = [ 1000, 9000]\n",
"rec_y = [ 9000, 9000]\n",
"\n",
"# Make a plot to visualize the problem\n",
"fig = plt.figure(figsize(10,10))\n",
"ax = plt.subplot(111, axisbg='#6666ff')\n",
"\n",
"ax.grid()\n",
"\n",
"i = 1\n",
"for receiver in zip(rec_x,rec_y):\n",
" ax.plot([source_x,receiver[0]],[source_y,receiver[1]],color='k')\n",
" ax.text(receiver[0]-200,receiver[1]+150,'Rx %d'%i,color='w')\n",
" i += 1\n",
"\n",
"ax.scatter(rec_x,rec_y,marker='v',color='r',s=80,zorder=50)\n",
"ax.scatter(source_x,source_y,marker='*',color='#ffff00',s=400,zorder=50)\n",
"\n",
"ax.tick_params(axis='both', which='major', labelsize=16)\n",
"ax.set_xlabel('X [m]',fontsize=18)\n",
"ax.set_ylabel('Y [m]',fontsize=18)\n",
"ax.set_xlim(0,10000)\n",
"ax.set_ylim(0,10000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$\\begin{pmatrix}0, & 10000\\end{pmatrix}$$"
],
"metadata": {},
"output_type": "pyout",
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"prompt_number": 16,
"text": [
"(0, 10000)"
]
},
{
"metadata": {},
"output_type": "display_data",
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otS4cDquwsFCZmZlq166dsrKytGSJ3X+ggbrQ/wTgBvqewWZi+Hz++ed17bXX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\nRC7D5pOIiIiIXIbNJxERERG5zP8Aawer/LgQWe4AAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x10af18890>"
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"distances = []\n",
"i = 1\n",
"for receiver in zip(rec_x,rec_y):\n",
" d = GetDistance(receiver[0],receiver[1],source_x,source_y,depth)\n",
" print \"Receiver %d, %.2f m\" %(i,d)\n",
" distances.append(d)\n",
" i += 1"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Receiver 1, 11180.34 m\n",
"Receiver 2, 9643.65 m\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"rel_arrivals = []\n",
"for d in distances:\n",
" rel_arrivals.append(d/c_sound)\n",
"rel_arrivals = np.array(rel_arrivals)\n",
"s0 = np.argmin(rel_arrivals)\n",
"print \"Station s0: \", s0\n",
"rel_arrivals = rel_arrivals - min(rel_arrivals)\n",
"for i in range(nRx):\n",
" print \"Receiver %d, %.2f sec\" %(i+1,rel_arrivals[i])\n",
"travel_times_obs = rel_arrivals"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Station s0: 1\n",
"Receiver 1, 1.02 sec\n",
"Receiver 2, 0.00 sec\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"GridSearch(rel_arrivals,s0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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L8Vd/9Ve4/PLL8d3vfhfvfve7axWtrUhFemC1NSDYhJOogWhbYyRZ4siYpVcj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\nmDx5Mh577DFcfvnleOihh/DTn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"text": [
"<matplotlib.figure.Figure at 0x10a135d50>"
]
}
],
"prompt_number": 19
}
],
"metadata": {}
}
]
}
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