diff --git a/07_Kalman_Filter_Math.ipynb b/07_Kalman_Filter_Math.ipynb index 6688230..0336191 100644 --- a/07_Kalman_Filter_Math.ipynb +++ b/07_Kalman_Filter_Math.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:3e8e9b87a74764e36232074e47d0a3ce000af637924cfb9109a5aa769cefbd65" + "signature": "sha256:816c4af5667b2362a00c0592827f2972df778d9fb1e9947c284f686761053b42" }, "nbformat": 3, "nbformat_minor": 0, @@ -261,7 +261,7 @@ "output_type": "pyout", "prompt_number": 1, "text": [ - "" + "" ] } ], @@ -738,7 +738,7 @@ "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAxYAAAGaCAYAAACSU9UtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAIDL/gdIbaLw6+733QAAAABJRU5ErkJggg==\n", "text": [ - "" + "" ] } ], @@ -1512,7 +1512,7 @@ "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAyIAAAGNCAYAAADtmMVMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ - "" + "" ] }, { @@ -1537,9 +1537,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The previous section took a somewhat naive approach to integrating several sensor measurements into the filter. Let's work with a real world scenerio, albeit somewhat simplified. The GPS system is designed so that at least 6 satellites are in view at any time, assuming no line of sight blockage, at any point on the globe. The GPS receiver knows the location of the satellites in the sky relative to the Earth. At each epoch (instant in time) the receiver gets a signal from each satellite from which it can derive the *pseudorange* to the satellite. In more detail, the GPS receiver gets a signal identifying the satellite along with the time stamp of when the signal was transmitted. The GPS satellite has an atomic clock onboard so this timestamp is extremely accurate. The signal travels at the speed of light, which is constant in a vacuum, so in theory the GPS should be able to produce an extremely accurate distance measurement to the measurement by measuring how long the signal took to reach the receiver. There are several problems with that. First, the signal is not travelling through a vacuum, but through the atmosphere. The atmosphere causes the signal to bend, so it is not travelling in a straight line. This causes the signal to take longer to reach the receiver than theory suggests. Second, the on board clock on the GPS *receiver* is not very accurate, so deriving an exact time duration is nontrivial. Third, in many environments the signal can bounce off of buildings, trees, and other objects, causing either a longer path or *multipaths*, in which case the receive receives both the original signal from space and the reflected signals. \n", + "A broad category of use for the Kalman filter is *sensor fusion*. For example, we might have a position sensor and a velocity sensor, and we want to combine the data from both to find an optimal estimate of state. In this section we will discuss a different case, where we have multiple sensors providing the same type of measurement. \n", "\n", - "In the figure below I have shown how three pseudoranges might intersect in a 2D space. The width of the circle is meant to illustrate the measurement error for each pseudorange." + " The Global Positioning System (GPS) is designed so that at least 6 satellites are in view at any time at any point on the globe. The GPS receiver knows the location of the satellites in the sky relative to the Earth. At each epoch (instant in time) the receiver gets a signal from each satellite from which it can derive the *pseudorange* to the satellite. In more detail, the GPS receiver gets a signal identifying the satellite along with the time stamp of when the signal was transmitted. The GPS satellite has an atomic clock onboard so this timestamp is extremely accurate. The signal travels at the speed of light, which is constant in a vacuum, so in theory the GPS should be able to produce an extremely accurate distance measurement to the measurement by measuring how long the signal took to reach the receiver. There are several problems with that. First, the signal is not travelling through a vacuum, but through the atmosphere. The atmosphere causes the signal to bend, so it is not travelling in a straight line. This causes the signal to take longer to reach the receiver than theory suggests. Second, the on board clock on the GPS *receiver* is not very accurate, so deriving an exact time duration is nontrivial. Third, in many environments the signal can bounce off of buildings, trees, and other objects, causing either a longer path or *multipaths*, in which case the receive receives both the original signal from space and the reflected signals. \n", + "\n", + "Let's look at this graphically. I will due this in 2D just to make it easier to graph and see, but of course this will generalize to three dimensions. We know the position of each satellite and the range to each (the range is called the *pseudorange*; we will discuss why later). We cannot measure the range exactly, so there is noise associated with the measurement, which I have depicted with the thickness of the lines. Here is an example of four pseudorange readings from four satellites. I positioned them in a configuration which is unlikely for the actual GPS constellation merely to make the intersections easy to visualize. Also, the amount of error shown is not to scale with the distances, again to make it easier to see." ] }, { @@ -1548,7 +1550,7 @@ "input": [ "import ukf_internal\n", "with book_format.figsize(10,6):\n", - " ukf_internal.show_three_gps()" + " ukf_internal.show_four_gps()" ], "language": "python", "metadata": {}, @@ -1556,27 +1558,29 @@ { "metadata": {}, "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAp8AAAGNCAYAAABXHhoFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n", + "png": "iVBORw0KGgoAAAANSUhEUgAAAp8AAAGNCAYAAABXHhoFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhBDiM/8/3QDBZRpvieYAAAAASUVORK5CYII=\n", "text": [ - "" + "" ] } ], - "prompt_number": 17 + "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "So we need to solve for the 3 dimensions of space, and 1 dimension of time. That is 4 unknowns, so in theory with 4 satellites we have all the information we need. However, we normally have at least 6 satellites in view, and often more than 6. This means the system is *overdetermined*. Finally, because of the noise in the measurements none of pseudoranges intersect exactly.\n", + "In 2D two measurements are typically enough to determine a unique solution. There are two intersections of the range circles, but usually the second intersection is not physically realizable (it is in space, or under ground). However, with GPS we also need to solve for time, so we would need a third measurement to get a 2D position.\n", "\n", - "Probably the most common approach used by GPS receivers to find the position is the *iterative least squares* algorithm, commonly abbreviated ILS. As you know, if the errors are Gaussian then the least squares algorithm finds the optimal solution. In other words, we want to minimize the square of the residuals for an overdetermined system.\n", + "However, since GPS is a 3D system we need to solve for the 3 dimensions of space, and 1 dimension of time. That is 4 unknowns, so in theory with 4 satellites we have all the information we need. However, we normally have at least 6 satellites in view, and often more than 6. This means the system is *overdetermined*. Finally, because of the noise in the measurements none of pseudoranges intersect exactly.\n", + "\n", + "If you are well versed in linear algebra you know that this an extremely common problem in scientific computing, and that there are various techniques for solving overdetermied systems. Probably the most common approach used by GPS receivers to find the position is the *iterative least squares* algorithm, commonly abbreviated ILS. As you know, if the errors are Gaussian then the least squares algorithm finds the optimal solution. In other words, we want to minimize the square of the residuals for an overdetermined system.\n", "\n", "Let's start with some definitions which should be familar to you. First, we define the innovation as \n", "\n", - "$$\\delta \\mathbf{z}= \\mathbf{z} - h(\\mathbf{x}^-)$$\n", + "$$\\delta \\mathbf{z}^-= \\mathbf{z} - h(\\mathbf{x}^-)$$\n", "\n", - "where $\\mathbf{z}$ is the measurement, $h(\\bullet)$ is the measurement function, and $\\delta \\mathbf{z}$ is the innovation, which we abbreviate as $y$ in FilterPy. I don't use the $\\mathbf{x}^-$ symbology often, but it is the prediction for the state variable. In other words, this is just the equation $\\mathbf{y} = \\mathbf{z} - \\mathbf{Hx}$ in the linear Kalman filter's update step.\n", + "where $\\mathbf{z}$ is the measurement, $h(\\bullet)$ is the measurement function, and $\\delta \\mathbf{z}^-$ is the innovation, which we abbreviate as $y$ in FilterPy. I don't use the $\\mathbf{x}^-$ symbology often, but it is the prediction for the state variable. In other words, this is just the equation $\\mathbf{y} = \\mathbf{z} - \\mathbf{Hx}$ in the linear Kalman filter's update step.\n", "\n", "Next, the *measurement residual* is\n", "\n", @@ -1584,6 +1588,14 @@ "\n", "I don't use the plus superscript much because I find it quickly makes the equations unreadable, but $\\mathbf{x}^+$ it is just the *a posteriori* state estimate, which is just the predicted or unknown future state. In other words, the predict step of the linear Kalman filter computes this value. Here it is stands for the value of x which the ILS algorithm will compute on each iteration.\n", "\n", + "These equations give us the following linear algebra equation:\n", + "\n", + "$$\\delta \\mathbf{z}^- = \\mathbf{H}\\delta \\mathbf{x} + \\delta \\mathbf{z}^+$$\n", + "\n", + "$\\mathbf{H}$ is our measurement function, defined as\n", + "\n", + "$$\\mathbf{H} = \\frac{d\\mathbf{h}}{d\\mathbf{x}} = \\frac{d\\mathbf{z}}{d\\mathbf{x}}$$\n", + "\n", "We find the minimum of an equation by taking the derivative and setting it to zero. In this case we want to minimize the square of the residuals, so our equation is" ] }, @@ -1591,26 +1603,26 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "$$ \\frac{\\partial}{\\partial \\mathbf{x}}({\\delta \\mathbf{z}}^\\mathsf{T}\\delta \\mathbf{z}) = 0,$$\n", + "$$ \\frac{\\partial}{\\partial \\mathbf{x}}({\\delta \\mathbf{z}^+}^\\mathsf{T}\\delta \\mathbf{z}^+) = 0,$$\n", "\n", "where\n", "\n", - "$$\\delta \\mathbf{z}=\\delta \\mathbf{z}^- - \\mathbf{H}\\delta \\mathbf{x}.$$\n", + "$$\\delta \\mathbf{z}^+=\\delta \\mathbf{z}^- - \\mathbf{H}\\delta \\mathbf{x}.$$\n", "\n", - "Here I have switched to using the matrix $\\mathbf{H}$ as the measurement function. We want to use linear algebra to peform the ILS, so for each step we will have to compute the matrix $\\mathbf{H}$ which corresponds to $h(\\mathbf{x^-})$ during each iteration.\n", + "Here I have switched to using the matrix $\\mathbf{H}$ as the measurement function. We want to use linear algebra to peform the ILS, so for each step we will have to compute the matrix $\\mathbf{H}$ which corresponds to $h(\\mathbf{x^-})$ during each iteration. $h(\\bullet)$ is usually nonlinear for these types of problems so you will have to linearize it at each step (more about this soon).\n", "\n", "For various reasons you may want to weigh some measurement more than others. For example, the geometry of the problem might favor orthogonal measurements, or some measurements may be more noisy than others. We can do that with the equation\n", "\n", - "$$ \\frac{\\partial}{\\partial \\mathbf{x}}({\\delta \\mathbf{z}}^\\mathsf{T}\\mathbf{W}\\delta \\mathbf{z}) = 0$$\n", + "$$ \\frac{\\partial}{\\partial \\mathbf{x}}({\\delta \\mathbf{z}^+}^\\mathsf{T}\\mathbf{W}\\delta \\mathbf{z}^+) = 0$$\n", "\n", "If we solve the first equation for ${\\delta \\mathbf{x}}$ (the derivation is shown in the next section) we get\n", "\n", - "$${\\delta \\mathbf{x}} = {{(\\mathbf{H}^\\mathsf{T}\\mathbf{H})^{-1}}\\mathbf{H}^\\mathsf{T} \\delta \\mathbf{z}}\n", + "$${\\delta \\mathbf{x}} = {{(\\mathbf{H}^\\mathsf{T}\\mathbf{H})^{-1}}\\mathbf{H}^\\mathsf{T} \\delta \\mathbf{z}^-}\n", "$$\n", "\n", "And the second equation yields\n", "\n", - "$${\\delta \\mathbf{x}} = {{(\\mathbf{H}^\\mathsf{T}\\mathbf{WH})^{-1}}\\mathbf{H}^\\mathsf{T}\\mathbf{W} \\delta \\mathbf{z}}\n", + "$${\\delta \\mathbf{x}} = {{(\\mathbf{H}^\\mathsf{T}\\mathbf{WH})^{-1}}\\mathbf{H}^\\mathsf{T}\\mathbf{W} \\delta \\mathbf{z}^-}\n", "$$\n", "\n", "Since the equations are overdetermined we cannot solve these equations exactly so we use an iterative approach. An initial guess for the position is made, and this guess is used to compute for $\\delta \\mathbf{x}$ via the equation above. $\\delta \\mathbf{x}$ is added to the intial guess, and this new state is fed back into the equation to produce another $\\delta \\mathbf{x}$. We iterate in this manner until the difference in the measurement residuals is suitably small." @@ -1630,7 +1642,7 @@ "source": [ "I will implement the ILS in code, but first let's derive the equation for $\\delta \\mathbf{x}$. You can skip the derivation if you want, but it is somewhat instructive and not too hard if you know basic linear algebra and partial differential equations.\n", "\n", - "Substituting $\\delta \\mathbf{z}=\\delta \\mathbf{z}^- - \\mathbf{H}\\delta \\mathbf{x}$ into the partial differential equation we get\n", + "Substituting $\\delta \\mathbf{z}^+=\\delta \\mathbf{z}^- - \\mathbf{H}\\delta \\mathbf{x}$ into the partial differential equation we get\n", "\n", "$$ \\frac{\\partial}{\\partial \\mathbf{x}}(\\delta \\mathbf{z}^- -\\mathbf{H} \\delta \\mathbf{x})^\\mathsf{T}(\\delta \\mathbf{z}^- - \\mathbf{H} \\delta \\mathbf{x})=0$$\n", "\n", @@ -1639,8 +1651,13 @@ "$$ \\frac{\\partial}{\\partial \\mathbf{x}}({\\delta \\mathbf{x}}^\\mathsf{T}\\mathbf{H}^\\mathsf{T}\\mathbf{H}\\delta \\mathbf{x} - \n", "{\\delta \\mathbf{x}}^\\mathsf{T}\\mathbf{H}^\\mathsf{T}\\delta \\mathbf{z}^- - \n", "{\\delta \\mathbf{z}^-}^\\mathsf{T}\\mathbf{H}\\delta \\mathbf{x} +\n", - "{\\delta \\mathbf{z}^-}^\\mathsf{T}\\delta \\mathbf{z}^-)=0$$\n", - "\n", + "{\\delta \\mathbf{z}^-}^\\mathsf{T}\\delta \\mathbf{z}^-)=0$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "We know that \n", "\n", "$$\\frac{\\partial \\mathbf{A}^\\mathsf{T}\\mathbf{B}}{\\partial \\mathbf{B}} = \\frac{\\partial \\mathbf{B}^\\mathsf{T}\\mathbf{A}}{\\partial \\mathbf{B}} = \\mathbf{A}^\\mathsf{T}$$\n", @@ -1721,16 +1738,40 @@ "source": [ "Our goal is to implement an iterative solution to \n", "$${\\delta \\mathbf{x}} = {{(\\mathbf{H}^\\mathsf{T}\\mathbf{H})^{-1}}\\mathbf{H}^\\mathsf{T} \\delta \\mathbf{z}^-}\n", - "$$" + "$$\n", + "\n", + "First, we have to compute $\\mathbf{H}$, where $\\mathbf{H} = d\\mathbf{z}/d\\mathbf{x}$. Just to keep the example small so the results are easier to interpret we will do this in 2D. Therefore for $n$ satellites $\\mathbf{H}$ expands to\n", + "\n", + "$$\\mathbf{H} = \\begin{bmatrix}\n", + "\\frac{\\partial p_1}{\\partial x_1} & \\frac{\\partial p_1}{\\partial y_1} \\\\\n", + "\\frac{\\partial p_2}{\\partial x_2} & \\frac{\\partial p_2}{\\partial y_2} \\\\\n", + "\\vdots & \\vdots \\\\\n", + "\\frac{\\partial p_n}{\\partial x_n} & \\frac{\\partial p_n}{\\partial y_n}\n", + "\\end{bmatrix}$$\n", + "\n", + "We will linearize $\\mathbf{H}$ by computing the partial for $x$ as\n", + "\n", + "$$ \\frac{estimated\\_x\\_position - satellite\\_x\\_position}{estimated\\_range\\_to\\_satellite}$$\n", + "\n", + "The equation for $y$ just subtitutes $y$ for $x$.\n", + "\n", + "Then the algorithm is as follows.\n", + "\n", + " def ILS:\n", + " guess position\n", + " while not converged:\n", + " compute range to satellites for current estimated position\n", + " compute H linearized at estimated position\n", + " compute new estimate delta from (H^T H)'H^T dz\n", + " new estimate = current estimate + estimate delta\n", + " check for convergence\n", + " " ] }, { "cell_type": "code", "collapsed": false, "input": [ - "# this code needs exposition. Just putting here without\n", - "# explanation for the moment.\n", - "\n", "import numpy as np\n", "from numpy.linalg import norm, inv\n", "from numpy.random import randn\n", @@ -1741,19 +1782,19 @@ "user_pos = np.array([800, 200])\n", "\n", "\n", - "transmitter_pos = np.asarray(\n", + "sat_pos = np.asarray(\n", " [[0, 1000],\n", " [0, -1000],\n", " [500, 500]], dtype=float)\n", "\n", - "def transmitter_range(pos, transmitter_pos):\n", + "def satellite_range(pos, sat_pos):\n", " \"\"\" Compute distance between position 'pos' and the list of positions\n", - " in transmitter_pos\"\"\"\n", + " in sat_pos\"\"\"\n", "\n", - " N = len(transmitter_pos)\n", + " N = len(sat_pos)\n", " rng = np.zeros(N)\n", "\n", - " diff = np.asarray(pos) - transmitter_pos\n", + " diff = np.asarray(pos) - sat_pos\n", "\n", " for i in range(N):\n", " rng[i] = norm(diff[i])\n", @@ -1761,16 +1802,27 @@ " return norm(diff, axis=1)\n", "\n", "\n", - "def hx_ils(pos, t_pos, r_est):\n", - " N = len(t_pos)\n", + "def hx_ils(pos, sat_pos, range_est):\n", + " \"\"\" compute measurement function where\n", + " pos : array_like \n", + " 2D current estimated position. e.g. (23, 45)\n", + " \n", + " sat_pos : array_like of 2D positions\n", + " position of each satellite e.g. [(0,100), (100,0)]\n", + " \n", + " range_est : array_like of floats\n", + " range to each satellite\n", + " \"\"\"\n", + " \n", + " N = len(sat_pos)\n", " H = np.zeros((N, 2))\n", " for j in range(N):\n", - " H[j,0] = -(t_pos[j,0] - pos[0]) / r_est[j]\n", - " H[j,1] = -(t_pos[j,1] - pos[1]) / r_est[j]\n", + " H[j,0] = (pos[0] - sat_pos[j,0]) / range_est[j]\n", + " H[j,1] = (pos[1] - sat_pos[j,1]) / range_est[j]\n", " return H\n", "\n", "\n", - "def lop_ils(zs, t_pos, pos_est, hx, eps=1.e-6):\n", + "def lop_ils(zs, sat_pos, pos_est, hx, eps=1.e-6):\n", " \"\"\" iteratively estimates the solution to a set of measurement, given\n", " known transmitter locations\"\"\"\n", " pos = np.array(pos_est)\n", @@ -1778,10 +1830,10 @@ " with book_format.numpy_precision(precision=4):\n", " converged = False\n", " for i in range(20):\n", - " r_est = transmitter_range(pos, t_pos)\n", + " r_est = satellite_range(pos, sat_pos)\n", " print('iteration:', i)\n", "\n", - " H=hx(pos, t_pos, r_est) \n", + " H=hx(pos, sat_pos, r_est) \n", " Hinv = inv(dot(H.T, H)).dot(H.T)\n", "\n", " #update position estimate\n", @@ -1789,12 +1841,8 @@ " print('innovation', y)\n", "\n", " Hy = np.dot(Hinv, y)\n", - "\n", " pos = pos + Hy\n", - " print('pos ', pos)\n", - "\n", - " print()\n", - " print()\n", + " print('pos {}\\n\\n'.format(pos))\n", "\n", " if max(abs(Hy)) < eps:\n", " converged = True\n", @@ -1803,10 +1851,10 @@ " return pos, converged\n", "\n", "# compute measurement of where you are with respect to each sensor\n", - "rz= transmitter_range(user_pos, transmitter_pos)\n", + "rz= satellite_range(user_pos, sat_pos)\n", "\n", - "pos, converted = lop_ils(rz, transmitter_pos, (900,90), hx=hx_ils)\n", - "print('Iterated solution: ', pos)\n" + "pos, converted = lop_ils(rz, sat_pos, (900,90), hx=hx_ils)\n", + "print('Iterated solution: ', pos)" ], "language": "python", "metadata": {}, @@ -1817,29 +1865,29 @@ "text": [ "iteration: 0\n", "innovation [-148.512 28.6789 -148.5361]\n", - "pos [ 805.4175 205.2868]\n", + "pos [ 805.4175 205.2868]\n", "\n", "\n", "iteration: 1\n", "innovation [-0.1177 -7.4049 -0.1599]\n", - "pos [ 800.04 199.9746]\n", + "pos [ 800.04 199.9746]\n", "\n", "\n", "iteration: 2\n", "innovation [-0.0463 -0.001 -0.0463]\n", - "pos [ 800. 200.]\n", + "pos [ 800. 200.]\n", "\n", "\n", "iteration: 3\n", "innovation [-0. -0. -0.]\n", - "pos [ 800. 200.]\n", + "pos [ 800. 200.]\n", "\n", "\n", "Iterated solution: [ 800. 200.]\n" ] } ], - "prompt_number": 19 + "prompt_number": 17 }, { "cell_type": "markdown", @@ -1850,14 +1898,14 @@ "$$\\mathbf{y} = \\mathbf{z} - \\mathbf{Hx}\\\\\n", "\\mathbf{x} = \\mathbf{x} + \\mathbf{Ky}$$\n", "\n", - "but for the Kalman gain equalling one. You can see that despite the very inaccurate initial guess (900, 90) the computed value for $\\mathbf{x}$ was very close to the actual value of (800,100). However, it was not perfect. But after three iterations the ILS algorithm was able to find the exact answer. So hopefully it is clear why we use ILS instead of doing the sensor fusion with the Kalman filter - it gives a better result. Of course, we started with a very inaccurate guess; what if the guess was better?" + "where the Kalman gain equals one. You can see that despite the very inaccurate initial guess (900, 90) the computed value for $\\mathbf{x}$, (805.4, 205.3), was very close to the actual value of (800, 200). However, it was not perfect. But after three iterations the ILS algorithm was able to find the exact answer. So hopefully it is clear why we use ILS instead of doing the sensor fusion with the Kalman filter - it gives a better result. Of course, we started with a very inaccurate guess; what if the guess was better?" ] }, { "cell_type": "code", "collapsed": false, "input": [ - "pos, converted = lop_ils(rz, transmitter_pos, (801, 201), hx=hx_ils)\n", + "pos, converted = lop_ils(rz, sat_pos, (801, 201), hx=hx_ils)\n", "print('Iterated solution: ', pos)" ], "language": "python", @@ -1869,24 +1917,24 @@ "text": [ "iteration: 0\n", "innovation [-0.0009 -1.3868 -0.0024]\n", - "pos [ 800.0014 199.9991]\n", + "pos [ 800.0014 199.9991]\n", "\n", "\n", "iteration: 1\n", "innovation [-0.0016 -0. -0.0016]\n", - "pos [ 800. 200.]\n", + "pos [ 800. 200.]\n", "\n", "\n", "iteration: 2\n", "innovation [-0. -0. -0.]\n", - "pos [ 800. 200.]\n", + "pos [ 800. 200.]\n", "\n", "\n", "Iterated solution: [ 800. 200.]\n" ] } ], - "prompt_number": 20 + "prompt_number": 18 }, { "cell_type": "markdown", @@ -1905,7 +1953,7 @@ "nrz = []\n", "for z in rz:\n", " nrz.append(z + randn())\n", - "pos, converted = lop_ils(nrz, transmitter_pos, (601,198.3), hx=hx_ils)\n", + "pos, converted = lop_ils(nrz, sat_pos, (601,198.3), hx=hx_ils)\n", "print('Iterated solution: ', pos)" ], "language": "python", @@ -1917,34 +1965,34 @@ "text": [ "iteration: 0\n", "innovation [ 129.8823 100.461 107.5398]\n", - "pos [ 831.4474 186.1222]\n", + "pos [ 831.4474 186.1222]\n", "\n", "\n", "iteration: 1\n", "innovation [-31.6446 -7.4837 -30.7861]\n", - "pos [ 800.3284 198.8076]\n", + "pos [ 800.3284 198.8076]\n", "\n", "\n", "iteration: 2\n", "innovation [-0.6041 -0.3813 0.3569]\n", - "pos [ 799.948 198.6026]\n", + "pos [ 799.948 198.6026]\n", "\n", "\n", "iteration: 3\n", "innovation [-0.4803 0.0004 0.4802]\n", - "pos [ 799.9476 198.6025]\n", + "pos [ 799.9476 198.6025]\n", "\n", "\n", "iteration: 4\n", "innovation [-0.4802 0.0007 0.4803]\n", - "pos [ 799.9476 198.6025]\n", + "pos [ 799.9476 198.6025]\n", "\n", "\n", "Iterated solution: [ 799.9475854 198.60245871]\n" ] } ], - "prompt_number": 21 + "prompt_number": 19 }, { "cell_type": "markdown", @@ -1952,49 +2000,9 @@ "source": [ "Here we can see that the noise means that we no longer find the exact solution but we are still able to quickly converge onto a more accurate solution than the first iteration provides.\n", "\n", - "This is far from a complete coverage of the iterated least squares algorithm, let alone methods used in GNSS to compute positions from GPS pseudoranges. You will find a number of approaches in the literature, including QR decomposition, using SVD, and other techniques to solve the overdetermined system. For a nontrivial task you will have to survey the literature and perhaps invent a technique for your specifc sensor configuration. " + "This is far from a complete coverage of the iterated least squares algorithm, let alone methods used in GNSS to compute positions from GPS pseudoranges. You will find a number of approaches in the literature, including QR decomposition, SVD, and other techniques to solve the overdetermined system. For a nontrivial task you will have to survey the literature and perhaps design your algorithm depending on your specifc sensor configuration, the amounts of noise, your accuracy requirements, and the amount of computation you can afford to do." ] }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - }, { "cell_type": "heading", "level": 2, diff --git a/code/ukf_internal.py b/code/ukf_internal.py index cf71b64..4427d49 100644 --- a/code/ukf_internal.py +++ b/code/ukf_internal.py @@ -59,6 +59,24 @@ def show_three_gps(): plt.show() + + +def show_four_gps(): + circle1=plt.Circle((-4,2),5,color='#004080',fill=False,linewidth=20, alpha=.7) + circle2=plt.Circle((5.5,1),5,color='#E24A33', fill=False, linewidth=8, alpha=.7) + circle3=plt.Circle((0,-3),6,color='#534543',fill=False, linewidth=13, alpha=.7) + circle4=plt.Circle((0,8),5,color='#214513',fill=False, linewidth=13, alpha=.7) + + fig = plt.gcf() + ax = fig.gca() + + ax.add_patch(circle1) + ax.add_patch(circle2) + ax.add_patch(circle3) + ax.add_patch(circle4) + + plt.axis('equal') + plt.show() def show_sigma_transform(): fig = plt.figure() ax=fig.gca() @@ -174,7 +192,7 @@ def show_sigmas_for_2_kappas(): if __name__ == '__main__': - show_three_gps() + show_four_gps() #show_sigma_transform() #show_sigma_selections()