From 8a01161ea4dd7b078975371de39762be05d93a0c Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sun, 3 Jan 2016 11:32:22 -0800 Subject: [PATCH] Streamlined description of EKF linearization --- 07-Kalman-Filter-Math.ipynb | 48 ++-- 11-Extended-Kalman-Filters.ipynb | 448 ++++++++++++++----------------- code/ekf_internal.py | 22 +- 3 files changed, 245 insertions(+), 273 deletions(-) diff --git a/07-Kalman-Filter-Math.ipynb b/07-Kalman-Filter-Math.ipynb index ca4ee14..9557192 100644 --- a/07-Kalman-Filter-Math.ipynb +++ b/07-Kalman-Filter-Math.ipynb @@ -296,7 +296,9 @@ "\n", "Modeling dynamic systems is properly the topic of several college courses. To an extent there is no substitute for a few semesters of ordinary and partial differential equations followed by a graduate course in control system theory. If you are a hobbyist, or trying to solve one very specific filtering problem at work you probably do not have the time and/or inclination to devote a year or more to that education.\n", "\n", - "Fortunately, I can present enough of the theory to allow us to create the system equations for many different Kalman filters. My goal is to get you to the stage where you can read a publication and understand it well enough to implement the algorithms. The background math is deep, but in practice we end up using a few simple techniques over and over again.\n", + "Fortunately, I can present enough of the theory to allow us to create the system equations for many different Kalman filters. My goal is to get you to the stage where you can read a publication and understand it well enough to implement the algorithms. The background math is deep, but in practice we end up using a few simple techniques over and over again. \n", + "\n", + "This is the longest section of pure math in this book. You will need to master everything in this section to understand the Extended Kalman filter (EKF), the workhorse nonlinear filter. I do cover more modern filters that do not require as much of this math. You can choose so skim now, and come back to this if you decide to learn the EKF.\n", "\n", "We need to start by understanding the underlying equations and assumptions that the Kalman filter uses. We are trying to model real world phenomena, so what do we have to consider?\n", "\n", @@ -314,10 +316,10 @@ "$$ \\mathbf v = \\frac{d \\mathbf x}{d t}, \n", "\\quad \\mathbf a = \\frac{d \\mathbf v}{d t} = \\frac{d^2 \\mathbf x}{d t^2}\n", "$$\n", - " \n", - "Perfectly modeling a system is impossible except for the most trivial problems. A typical automobile tracking problem would have you compute the distance traveled given a constant velocity or acceleration. But, of course we know this is not all that is happening. No car travels on a perfect road. There are bumps that cause the car to slow down, there is wind drag, there are hills that raise and lower the speed. The suspension is a mechanical system with friction and imperfect springs. Gusts of wind alter the car's state.\n", "\n", - "So control theory is forced to make a simplification. At any time $t$ we say that the true state (such as the position of our car) is the predicted value from the imperfect model plus some unknown *process noise*:\n", + "A typical automobile tracking problem would have you compute the distance traveled given a constant velocity or acceleration as we did in previous chapters. But, of course we know this is not all that is happening. No car travels on a perfect road. There are bumps that cause the car to slow down, there is wind drag, there are hills that raise and lower the speed. The suspension is a mechanical system with friction and imperfect springs. Gusts of wind alter the car's state.\n", + "\n", + "Acurately modeling a system with linear equations is impossible except for the most trivial problems. So control theory is forced to make a simplification. At any time $t$ we say that the true state (such as the position of our car) is the predicted value from the imperfect model plus some unknown *process noise*:\n", "\n", "$$\n", "x(t) = x_{pred}(t) + noise(t)\n", @@ -384,7 +386,7 @@ "\n", "We can do that only because $\\dot x = v$ is simplest differential equation possible. Almost all other in physical systems result in more complicated differential equation which do not yield to this approach. \n", "\n", - "*State-space* methods became popular around the time of the Apollo missions, largely due to the work of Dr. Kalman. The idea is simple. Model a system with a set of $n^{th}$-order differential equations. Convert them into an equivalent set of first-order differential equations. Put them into the vector-matrix form used in the previous section: $ \\dot{\\mathbf x} = \\mathbf{Ax} + \\mathbf{Bu}$. Once in this form we use of of several techniques to convert these linear differential equations into the recursive equation:\n", + "*State-space* methods became popular around the time of the Apollo missions, largely due to the work of Dr. Kalman. The idea is simple. Model a system with a set of $n^{th}$-order differential equations. Convert them into an equivalent set of first-order differential equations. Put them into the vector-matrix form used in the previous section: $\\dot{\\mathbf x} = \\mathbf{Ax} + \\mathbf{Bu}$. Once in this form we use of of several techniques to convert these linear differential equations into the recursive equation:\n", "\n", "$$ \\mathbf x_k = \\mathbf{Fx}_{k-1} + \\mathbf B_k\\mathbf u_k$$\n", "\n", @@ -478,16 +480,18 @@ "\n", "$$ \\dot{\\mathbf x} = \\mathbf{Ax}$$\n", "\n", - "and want to find the *fundamental matrix* $\\mathbf F$ that propagates the state $\\mathbf x$ with the equation\n", + "where $\\mathbf A$ is the system dynamics matrix, and want to find the *fundamental matrix* $\\mathbf F$ that propagates the state $\\mathbf x$ over the interval $\\Delta t$ with the equation\n", "\n", "$$\\begin{aligned}\n", "\\mathbf x(t_k) = \\mathbf F(\\Delta t)\\mathbf x(t_{k-1})\\end{aligned}$$\n", "\n", - "It is conventional to drop the $t_k$ and use the notation\n", + "In other words, $\\mathbf A$ is a set of continuous differential equations, and we need $\\mathbf F$ to be a set of discrete linear equations that computes the change in $\\mathbf A$ over a discrete time step.\n", "\n", - "$$\\mathbf x_k = \\Phi(\\Delta t)\\mathbf x_{k-1}$$\n", + "It is conventional to drop the $t_k$ and $(\\Delta t)$ and use the notation\n", "\n", - "$\\mathbf x_k$ does not mean the k$^{th}$ value of $\\mathbf x$, but the value of $\\mathbf x$ at the k$^{th}$ value of $t$.\n", + "$$\\mathbf x_k = \\mathbf {Fx}_{k-1}$$\n", + "\n", + "$\\mathbf x_k$ does not mean the k$^{th}$ value of $\\mathbf x$, but the value of $\\mathbf x$ at the k$^{th}$ value of $t$. In this book I go even further and drop the suffixes entirely in favor of an overline to denote the prediction: $\\overline{\\mathbf x} = \\mathbf{Fx}$.\n", "\n", "Broadly speaking there are three common ways to find this matrix for Kalman filters. The technique most often used with Kalman filters is to use a matrix exponential. Linear Time Invariant Theory, also known as LTI System Theory, is a second technique. Finally, there are numerical techniques. You may know of others, but these three are what you will most likely encounter in the Kalman filter literature and praxis." ] @@ -532,15 +536,15 @@ "\n", "$$\\begin{bmatrix}\\dot x \\\\ \\dot v\\end{bmatrix} =\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix} \\begin{bmatrix}x \\\\ v\\end{bmatrix}$$\n", "\n", - "This is a first order differential equation, so we can set $\\mathbf{A}=\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}$ and solve the following equation.\n", + "This is a first order differential equation, so we can set $\\mathbf{A}=\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}$ and solve the following equation. I have substituted the interval $\\Delta t$ for $t$ to emphasize that the fundamental matrix is discrete:\n", "\n", - "$$\\mathbf F e^{\\mathbf At} = \\mathbf{I} + \\mathbf At + \\frac{(\\mathbf At)^2}{2!} + \\frac{(\\mathbf At)^3}{3!} + ... $$\n", + "$$\\mathbf F = e^{\\mathbf A\\Delta t} = \\mathbf{I} + \\mathbf A\\Delta t + \\frac{(\\mathbf A\\Delta t)^2}{2!} + \\frac{(\\mathbf A\\Delta t)^3}{3!} + ... $$\n", "\n", "If you perform the multiplication you will find that $\\mathbf{A}^2=\\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}$, which means that all higher powers of $\\mathbf{A}$ are also $\\mathbf{0}$. Thus we get an exact answer without an infinite number of terms:\n", "\n", "$$\n", "\\begin{aligned}\n", - "\\mathbf F &=\\mathbf{I} + \\mathbf At + \\mathbf{0} \\\\\n", + "\\mathbf F &=\\mathbf{I} + \\mathbf A \\Delta t + \\mathbf{0} \\\\\n", "&= \\begin{bmatrix}1&0\\\\0&1\\end{bmatrix} + \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}t\\\\\n", "&= \\begin{bmatrix}1&t\\\\0&1\\end{bmatrix}\n", "\\end{aligned}$$\n", @@ -1241,7 +1245,7 @@ "data": { "image/png": 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wcL/nzZo1a7DlEI2avpEbPq80HvB5pfFkIj+vgiBAU1+J88UnkFNyAteaamz2c3dRYEbs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\nas/Ly7MZyNPT03H27FmrEW+lUonISK7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6Ok2t9T8F9YrjaGqrv2z/MHUUxidMRWbiVIyNSYNM5nZ/kBeNzWaDXq9HTEyM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\nUT91GjscRs0bDDrU9YTz5tZ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3N/r164e1a9eK29PT05GdnY24uDhxTqFQICYmps6VKIiIyDqwvhMRSaPBBjwtLQ3r1q1D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\nzLuG65rLuJ5zFdeyU6EpuP8n2WuoHNU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bPzdv3syll16K3W4nKiqKVatWkZ6ezvr16zEYDJhMJq/+JpOJPXv2AGC1WgkI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\nnHEwN5vNuN1urFYrSUlH5xh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XruT9998nOTnZ1+XIaVi/fj01NTWkp6cTFBREUFAQH374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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1558,7 +1562,7 @@ "\n", "In filtering our goal is to compute an optimal estimate for a set of states $\\mathbf x_{0:t}$ from time 0 to time $t$. If we knew $\\mathbf x_{0:t}$ then it would be trivial to compute a set of measurements $\\mathbf z_{0:t}$ corresponding to those states. However, we receive a set of measurements $\\mathbf z_{0:t}$, and want to compute the corresponding states $\\mathbf x_{0:t}$. This is called *statistical inversion* because we are trying to compute the input from the output. \n", "\n", - "Inversion is a difficult problem because there is typically no unique solution. For a given set of states $\\mathbf x_{0:t}$ there is only one possible set of measurements (plus noise), but for a given set of measurements there are many different sets of states that could have led to those measurements. This difficulty is compounded by the requirement to find the inverse function **blah - is this inversion statement true and complete revisit this whole paragraph**\n", + "Inversion is a difficult problem because there is typically no unique solution. For a given set of states $\\mathbf x_{0:t}$ there is only one possible set of measurements (plus noise), but for a given set of measurements there are many different sets of states that could have led to those measurements. \n", "\n", "Recall Bayes Theorem:\n", "\n", @@ -1592,7 +1596,11 @@ "\n", "The details of the mathematics for this computation varies based on the problem. The **Discrete Bayes** and **Univariate Kalman Filter** chapters gave two different formulations which you should have been able to reason through. The univariate Kalman filter assumes that for a scalar state both the noise and process are linear model are affected by zero-mean, uncorrelated Gaussian noise. \n", "\n", - "The Multivariate Kalman filter make the same assumption but for states and measurements that are vectors, not scalars. Dr. Kalman was able to prove that if these assumptions hold true then the Kalman filter is *optimal*. Colloquially this means there is no way to derive more information from the noise. In the remainder of the book I will present filters that relax the constraints on linearity and Gaussian noise." + "The Multivariate Kalman filter make the same assumption but for states and measurements that are vectors, not scalars. Dr. Kalman was able to prove that if these assumptions hold true then the Kalman filter is *optimal*. Colloquially this means there is no way to derive more information from the noise. In the remainder of the book I will present filters that relax the constraints on linearity and Gaussian noise.\n", + "\n", + "Before I go on, a few more words about statistical inversion. As Calvetti and Somersalo write in *Introduction to Bayesian Scientific Computing*, \"we adopt the Bayesian point of view: *randomness simply means lack of information*.\"[4] Our state parametize physical phenomena that we could in principle measure or compute: velocity, air drag, and so on. We lack enough information to compute or measure their value, so we opt to consider them as random variables. Strictly speaking they are not random, thus this is a subjective position. \n", + "\n", + "They devote a full chapter to this topic. I can spare a paragraph. Bayesian filters are possible because we ascribe statistical properties to unknown parameters. In the case of the Kalman filter we have closed-form solutions to find an optimal estimate. Other filters, such as the discrete Bayes filter or the particle filter which we cover in a later chapter, model the probability in a more ad-hoc, non-optimal manner. The power of our technique comes from treating lack of information as a random variable, describing that random variable as a probability distribution, and then using Bayes Theorem to solve the statistical inference problem." ] }, { @@ -1797,7 +1805,9 @@ "\n", " * [2] *LTI System Theory* http://en.wikipedia.org/wiki/LTI_system_theory\n", " \n", - " * [3] C.F. van Loan, \"Computing Integrals Involving the Matrix Exponential,\" IEEE Transactions Automatic Control, June 1978." + " * [3] C.F. van Loan, \"Computing Integrals Involving the Matrix Exponential,\" IEEE Transactions Automatic Control, June 1978.\n", + " \n", + " * [4] Calvetti, D and Somersalo E, \"Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing,\", Springer, 2007." ] } ], diff --git a/11-Extended-Kalman-Filters.ipynb b/11-Extended-Kalman-Filters.ipynb index 12ffd82..d056dde 100644 --- a/11-Extended-Kalman-Filters.ipynb +++ b/11-Extended-Kalman-Filters.ipynb @@ -288,16 +288,29 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Linearizing a System" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider the function $f(x)=x^2−2x$. It could be our measurement function or process model. We want a linear approximation of this function to use in the Kalman filter. There is no linear function that gives a close approximation of this function for all values of $x$. However, during each epoch (update) of the Kalman filter we know its current state, so if we linearize the function at that value we will have a close approximation in that location. For example, suppose our current state is $x=1.5$. What would be a good linearization for this function?\n", + "## Linearizing the Kalman Filter\n", "\n", - "We can use any linear function that passes through the curve at (1.5,-0.75). For example, consider using f(x)=8x−12.75 as the linearization, as in the plot below." + "The Kalman filter uses linear equations, so it does not work with nonlinear problems. Problems can be nonlinear in two ways. First, the process model might be nonlinear. An object falling through the atmosphere encounters drag which reduces its acceleration. The amount of drag varies based on the velocity the object. The resulting behavior is nonlinear - it cannot be modeled with linear equations. Second, the measurements could be nonlinear. For example, a radar gives a range and bearing to a target. We use trigonometry, which is nonlinear, to compute the position of the target.\n", + "\n", + "For the linear filter we have these equations for the process and measurement models:\n", + "\n", + "$$\\begin{aligned}\\overline{\\mathbf x} &= \\mathbf{Ax} + \\mathbf{Bu} + w_x\\\\\n", + "\\mathbf z &= \\mathbf{Hx} + w_z\n", + "\\end{aligned}$$\n", + "\n", + "For the nonlinear model these equations must be modified to read:\n", + "\n", + "$$\\begin{aligned}\\overline{\\mathbf x} &= f(\\mathbf x, \\mathbf u) + w_x\\\\\n", + "\\mathbf z &= h(\\mathbf x) + w_z\n", + "\\end{aligned}$$\n", + "\n", + "The linear expression $\\mathbf{Ax} + \\mathbf{Bu}$ is replaced by a nonlinear function $f(\\mathbf x, \\mathbf u)$, and the linear expression $\\mathbf{Hx}$ is replaced by a nonlinear function $h(\\mathbf x)$.\n", + "\n", + "You might imagine that we proceed by finding a new set of Kalman filter equations that optimally solve these equations. But if you remember the charts in the **Nonlinear Filtering** chapter you'll recall that passing a Gaussian through a nonlinear function results in a probability distribution that is no longer Gaussian. So this will not work.\n", + "\n", + "The EKF does not alter the Kalman filter's linear equations. Instead, it *linearizes* the nonlinear equations at the point of the current estimate, and uses this linearization in the linear Kalman filter. \n", + "\n", + "*Linearize* means what it sounds like. We find a line that most closely matches the curve at a defined point. The graph below linearizes the parabola $f(x)=x^2−2x$ at $x=1.5$." ] }, { @@ -309,9 +322,9 @@ "outputs": [ { "data": { - "image/png": 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lu0fLAeklQ0n6tIDF4Bk1j43Rdus/e6LugKGdiIhaRQiBRRuBZ/7ia9PHAW/N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\nEREREUW4/wc0qShQ1sGZ4QAAAABJRU5ErkJggg==\n", 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Jk2o34VpiQeBaOFuPVVBkj8yfPx/Hjh2DWCyWtAkEAhw9ehQrV66U6T969OgB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\nltnysLAww419fn5+mDx5Mo4cOYKbN2/C39+/MUMksihfX19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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -319,112 +332,68 @@ } ], "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "xs = np.arange(0, 2, 0.01)\n", - "ys = [x**2 - 2*x for x in xs]\n", - "\n", - "def y(x): \n", - " return 8*x - 12.75\n", - "\n", - "plt.plot(xs, ys)\n", - "plt.plot([1.25, 1.75], [y(1.25), y(1.75)])\n", - "plt.xlim(1, 2)\n", - "plt.ylim([-1.5, 1]);" + "import ekf_internal\n", + "ekf_internal.show_linearization()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "This is not a good linearization for $f(x)$. It is exact for $x=1.5$, but quickly diverges when $x$ varies by a small amount.\n", + "If the curve above is the process model, then the dotted lines shows the linearization of that curve for the estimate $x=1.5$.\n", "\n", - "A much better approach is to use the slope of the function at the evaluation point as the linearization. We find the slope by taking the first derivative of the function:\n", + "We linearize systems by finding the slope of the curve at the given point:\n", "\n", - "$$f(x) = x^2 -2x \\\\\n", - "\\frac{df}{dx} = 2x - 2$$ \n", - " \n", - "Let's plot that." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def y(x): \n", - " return x - 2.25\n", + "$$\\begin{aligned}\n", + "f(x) &= x^2 -2x \\\\\n", + "\\frac{df}{dx} &= 2x - 2\n", + "\\end{aligned}$$\n", "\n", - "plt.plot(xs, ys)\n", - "plt.plot([1, 2], [y(1), y(2)])\n", - "plt.xlim(1, 2)\n", - "plt.ylim([-1.5, 1]);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This linearization is much better. It is still exactly correct at $x=1.5$, but the errors are very small as x varies. Compare the tiny error at $x=1.4$ vs the very large error at $x=1.4$ in the previous plot. This does not constitute a formal proof of correctness, but this sort of geometric depiction should be fairly convincing. It is easy to see that if the line had any other slope the errors would accumulate more quickly. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Linearizing the Kalman Filter\n", + "and then finding its value at the evaluation point:\n", "\n", - "To implement the extended Kalman filter we will leave the linear equations as they are and use partial derivatives to evaluate the system matrix $\\mathbf F$ and the measurement matrix $\\mathbf H$ at the filter's state at time t ($\\mathbf x_t$). In other words we linearize the equations at time t by finding the slope (derivative) of the equations at that time. Since $\\mathbf F$ also depends on the control input vector $\\mathbf u$ we will need to include that term:\n", + "$$\\begin{aligned}m &= f'(x=1.5) \\\\&= 2(1.5) - 2 \\\\&= 1\\end{aligned}$$ \n", + "\n", + "Our math will be more complicated because we are working with systems of differential equations. We linearize $f(\\mathbf x, \\mathbf u)$, and $h(\\mathbf x)$ by taking the partial derivatives ($\\frac{\\partial}{\\partial \\mathbf x}$) of each to evaluate $\\mathbf A$ and $\\mathbf H$ at the point $\\mathbf x_t$ and $\\mathbf u_t$. This gives us the the system dynamics matrix and measurement model matrix:\n", "\n", "$$\n", "\\begin{aligned}\n", - "\\mathbf F \n", - "&\\equiv {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}} \\\\\n", - "\\mathbf H &\\equiv \\frac{\\partial{h(\\mathbf x_t)}}{\\partial{\\mathbf x}}\\biggr|_{\\mathbf x_t} \n", + "\\mathbf A \n", + "&= {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}} \\\\\n", + "\\mathbf H &= \\frac{\\partial{h(\\mathbf x_t)}}{\\partial{\\mathbf x}}\\biggr|_{\\mathbf x_t} \n", "\\end{aligned}\n", - "$$\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we find the discrete state transition matrix $\\mathbf F$ by using the approximation of the Taylor-series expansion of $e^{\\mathbf A \\Delta t}$:\n", "\n", - "This notation states that at each update step we compute $\\mathbf F$ as the partial derivative of our function $f()$ evaluated at $\\mathbf x_t$, $\\mathbf u_t$.\n", + "$$\\mathbf F = e^{\\mathbf A\\Delta t} = \\mathbf{I} + \\mathbf A\\Delta t + \\frac{(\\mathbf A\\Delta t)^2}{2!} + \\frac{(\\mathbf A\\Delta t)^3}{3!} + ... $$\n", "\n", - "This leads to these equations for the EKF:\n", + "Alternatively, you can use one of the other techniques we learned in the **Kalman Math** chapter. \n", "\n", - "Predict step:\n", + "This leads to the following equations for the EKF. I placed them beside the equations for the linear Kalman filter, and put boxes around the only changes:\n", "\n", - "$$\\begin{aligned}\n", - "\\mathbf F &= {\\frac{\\partial{f(\\mathbf x)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}} \\\\\n", - "\\mathbf{\\overline x} &= \\mathbf{Fx} + \\mathbf{Bu} \\\\\n", - "\\mathbf{\\overline P} &= \\mathbf{FPF}^\\mathsf T + \\mathbf Q \n", - "\\end{aligned}$$\n", + "$$\\begin{array}{l|l}\n", + "\\text{linear Kalman filter} & \\text{EKF} \\\\\n", + "\\hline \n", + "& \\boxed{\\mathbf A = {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}}} \\\\\n", + "& \\boxed{\\mathbf F = e^{\\mathbf A \\Delta t}} \\\\\n", + "\\mathbf{\\overline x} = \\mathbf{Fx} + \\mathbf{Bu} & \\boxed{\\mathbf{\\overline x} = f(\\mathbf x, \\mathbf u)} \\\\\n", + "\\mathbf{\\overline P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q & \\mathbf{\\overline P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q \\\\\n", + "\\hline\n", + "& \\boxed{\\mathbf H = \\frac{\\partial{h(\\mathbf x_t)}}{\\partial{\\mathbf x}}\\biggr|_{\\mathbf x_t}} \\\\\n", + "\\textbf{y} = \\mathbf z - \\mathbf{H \\bar{x}} & \\textbf{y} = \\mathbf z -\\mathbf{H \\bar{x}}\\\\\n", + "\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} & \\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} \\\\\n", + "\\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} & \\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} \\\\\n", + "\\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}} & \\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}}\n", + "\\end{array}$$\n", "\n", - "Update step:\n", + "We don't normally use $\\mathbf{Fx}$ to propagate the state for the EKF as the linearization causes inaccuracies. It is typical to compute $\\overline{\\mathbf x}$ using a numerical integration technique such as Euler or Runge Kutta. Thus I wrote $\\mathbf{\\overline x} = f(\\mathbf x, \\mathbf u)$.\n", "\n", - "\n", - "$$\\begin{aligned}\n", - "\\mathbf H &= \\frac{\\partial{h(\\mathbf x)}}{\\partial{\\mathbf x}}\\biggr|_{\\mathbf x_t} \\\\\n", - "\\mathbf K &= \\mathbf{\\overline PH}^\\mathsf T(\\mathbf{H\\overline PH}^\\mathsf T + \\mathbf R)^{-1}\\\\\n", - "\\mathbf x &= \\mathbf{\\overline x} + \\mathbf K(\\mathbf{z}-\\mathbf{H\\overline x}) \\\\\n", - "\\mathbf P &= \\mathbf{\\overline P}(\\mathbf{I} - \\mathbf{KH})\n", - "\\end{aligned}$$\n", - "\n", - "\n", - "\n", - "\n", - "I think the easiest way to understand the EKF is to start off with an example. Perhaps the reason for some of my mathematical choices will not be clear, but trust that the end result will be an EKF." + "I think the easiest way to understand the EKF is to start off with an example. After we do a few examples you may want to come back and reread this section." ] }, { @@ -447,16 +416,16 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -504,16 +473,15 @@ "source": [ "We assume a Newtonian, kinematic system for the aircraft. We've used this model in previous chapters, so by inspection you may recognize that we want\n", "\n", - "$$\\mathbf F = \\begin{bmatrix}1 & \\Delta t & 0\\\\\n", - "0 & 1 & 0 \\\\\n", - "0 & 0 & 1\\end{bmatrix}$$\n", + "$$\\mathbf F = \\left[\\begin{array}{cc|c} 1 & \\Delta t & 0\\\\\n", + "0 & 1 & 0 \\\\ \\hline\n", + "0 & 0 & 1\\end{array}\\right]$$\n", "\n", - "However, let's practice finding these matrix for a nonlinear system. Please review the section *Modeling a Dynamic System that Has Noise* in the **Kalman Filter Math** chapter if you cannot follow this presentation.\n", + "I've partioned the matrix into blocks to show the upper left block is a constant velocity model for $x$, and the lower right block is a constant position model for $y$.\n", "\n", - "We model nonlinear systems with a set of differential equations. We need an equation in the form \n", + "However, let's practice finding these matrix for a nonlinear system. We model nonlinear systems with a set of differential equations. We need an equation in the form \n", "\n", "$$\\dot{\\mathbf x} = \\mathbf{Ax} + \\mathbf{w}$$\n", - "\n", "where $\\mathbf{w}$ is the system noise. \n", "\n", "The variables $x$ and $y$ are independent so we can compute them separately. The differential equations for motion in one dimension are:\n", @@ -523,35 +491,31 @@ "\n", "Now we put the differential equations into state-space form. If this was a second or greater order differential system we would have to first reduce them to an equivalent set of first degree equations. The equations are first order, so we put them in state space matrix form as\n", "\n", - "$$\\begin{bmatrix}\\dot x \\\\ \\ddot{x}\\end{bmatrix} =\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}$$\n", + "$$\\begin{aligned}\\begin{bmatrix}\\dot x \\\\ \\ddot{x}\\end{bmatrix} &= \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix} \\begin{bmatrix}x \\\\ \n", + "\\dot x\\end{bmatrix} \\\\ \\dot{\\mathbf x} &= \\mathbf{Ax}\\end{aligned}$$\n", + "where $\\mathbf A=\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}$. \n", + "\n", + "Recall that $\\mathbf A$ is the *system dynamics matrix*. It describes a set of linear differential equations. From it we must compute the state transition matrix $\\mathbf F$. $\\mathbf F$ describes a discrete set of linear equations which compute $\\mathbf x$ for a discrete time step $\\Delta t$.\n", + "\n", + "and solve the following power series expansion of the matrix exponential to linearize the equations at $t$:\n", + "\n", + "$$\\mathbf F(\\Delta t) = e^{\\mathbf A\\Delta t} = \\mathbf{I} + \\mathbf A\\Delta t + \\frac{(\\mathbf A\\Delta t)^2}{2!} + \\frac{(\\mathbf A \\Delta t)^3}{3!} + ... $$\n", "\n", "\n", - "We let $\\mathbf F=\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}$ and solve the following Taylor series expansion to linearize the equations at $t$:\n", - "\n", - "$$\\Phi(t) = e^{\\mathbf Ft} = \\mathbf{I} + \\mathbf Ft + \\frac{(\\mathbf Ft)^2}{2!} + \\frac{(\\mathbf Ft)^3}{3!} + ... $$\n", - "\n", - "\n", - "$\\mathbf F^2 = \\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}$, so all higher powers of $\\mathbf F$ are also $\\mathbf{0}$. Thus the Taylor series expansion is:\n", + "$\\mathbf A^2 = \\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}$, so all higher powers of $\\mathbf A$ are also $\\mathbf{0}$. Thus the power series expansion is:\n", "\n", "$$\n", "\\begin{aligned}\n", - "\\Phi(t) &=\\mathbf{I} + \\mathbf Ft + \\mathbf{0} \\\\\n", - "&= \\begin{bmatrix}1&0\\\\0&1\\end{bmatrix} + \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}t\\\\\n", + "\\mathbf F(\\Delta t) &=\\mathbf{I} + \\mathbf At + \\mathbf{0} \\\\\n", + "&= \\begin{bmatrix}1&0\\\\0&1\\end{bmatrix} + \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}\\Delta t\\\\\n", "&= \\begin{bmatrix}1&t\\\\0&1\\end{bmatrix}\n", "\\end{aligned}$$\n", "\n", - "We are trying to find the state transition function for\n", - "\n", - "$$\\mathbf x(t_k) = \\Phi(t_k-t_{k-1})\\mathbf x(t_{k-1})$$ \n", - "\n", - "If we define $\\Delta t = t_k-t_{k-1}$ and substitute it for $t$ in the equation above we get\n", - "\n", + "This give us\n", "$$\n", "\\begin{aligned}\n", - "x(t_k) &= \\Phi(\\Delta t)x(t_{k-1}) \\\\\n", - "\\mathbf{\\overline x} &= \\Phi(\\Delta t)\\mathbf x \\\\\n", - "\\mathbf{\\overline x} &=\\begin{bmatrix}1&\\Delta t\\\\0&1\\end{bmatrix}\\mathbf x \\\\\n", - "\\overline{\\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}} &=\\begin{bmatrix}1&\\Delta t\\\\0&1\\end{bmatrix}\\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}\n", + "\\mathbf{\\overline x} &=\\mathbf{Fx} \\\\\n", + "\\mathbf{\\overline x} &=\\begin{bmatrix}1&\\Delta t\\\\0&1\\end{bmatrix}\\mathbf x\n", "\\end{aligned}$$\n", "\n", "This is the same result used by the kinematic equations! This exercise was unnecessary other than to illustrate linearizing differential equations. Subsequent examples will require you to use these techniques. " @@ -570,15 +534,15 @@ "source": [ "The measurement function for our filter needs to take the filter state $\\mathbf x$ and turn it into a measurement, which is the slant range distance. We use the Pythagorean theorem to derive\n", "\n", - "$$h(\\mathbf x) = \\sqrt{x_{pos}^2 + x_{alt}^2}$$\n", + "$$h(\\mathbf x) = \\sqrt{x^2 + y^2}$$\n", "\n", - "The relationship between the slant distance and the position on the ground is nonlinear due to the square root term. To use it in the EKF we must linearize it. As we discussed above, the best way to linearize an equation at a point is to find its slope, which we do by taking its derivative.\n", + "The relationship between the slant distance and the position on the ground is nonlinear due to the square root term. To use it in the EKF we must linearize it. As we discussed above, the best way to linearize an equation at a point is to find its slope, which we do by evaluatiing its partial derivative at a point:\n", "\n", "$$\n", - "\\mathbf H \\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_x \n", + "\\mathbf H = \\frac{\\partial{h(\\mathbf x)}}{\\partial{\\mathbf x}}\\biggr|_{\\mathbf x_t}\n", "$$\n", "\n", - "The derivative of a matrix is called a Jacobian, which in general takes the form \n", + "The partial derivative of a matrix is called a Jacobian, and takes the form \n", "\n", "$$\\frac{\\partial \\mathbf H}{\\partial \\mathbf x} = \n", "\\begin{bmatrix}\n", @@ -590,38 +554,40 @@ "\n", "In other words, each element in the matrix is the partial derivative of the function $h$ with respect to the variables $x$. For our problem we have\n", "\n", - "$$\\mathbf H = \\begin{bmatrix}\\frac{\\partial h}{\\partial x_{pos}} & \\frac{\\partial h}{\\partial x_{vel}} & \\frac{\\partial h}{\\partial x_{alt}}\\end{bmatrix}$$\n", + "$$\\mathbf H = \\begin{bmatrix}{\\partial h}/{\\partial x} & {\\partial h}/{\\partial \\dot{x}} & {\\partial h}/{\\partial y}\\end{bmatrix}$$\n", "\n", - "where $h(x) = \\sqrt{x_{pos}^2 + x_{alt}^2}$ as given above.\n", + "where $h(x) = \\sqrt{x^2 + y^2}$.\n", "\n", "Solving each in turn:\n", "\n", "$$\\begin{aligned}\n", - "\\frac{\\partial h}{\\partial x_{pos}} &=\\frac{\\partial}{\\partial x_{pos}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{pos}}{\\sqrt{x^2 + x_{alt}^2}}\n", + "\\frac{\\partial h}{\\partial x} &= \\frac{\\partial}{\\partial x} \\sqrt{x^2 + y^2} \\\\\n", + "&= \\frac{x}{\\sqrt{x^2 + y^2}}\n", "\\end{aligned}$$\n", "\n", "and\n", "\n", "$$\\begin{aligned}\n", - "\\frac{\\partial h}{\\partial x_{vel}} &=\n", - "\\frac{\\partial}{\\partial x_{vel}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ \n", + "\\frac{\\partial h}{\\partial \\dot{x}} &=\n", + "\\frac{\\partial}{\\partial \\dot{x}} \\sqrt{x^2 + y^2} \\\\ \n", "&= 0\n", "\\end{aligned}$$\n", "\n", "and\n", "\n", "$$\\begin{aligned}\n", - "\\frac{\\partial h}{\\partial x_{alt}} &= \\frac{\\partial}{\\partial x_{alt}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n", + "\\frac{\\partial h}{\\partial y} &= \\frac{\\partial}{\\partial y} \\sqrt{x^2 + y^2} \\\\ \n", + "&= \\frac{y}{\\sqrt{x^2 + y^2}}\n", "\\end{aligned}$$\n", "\n", "giving us \n", "\n", "$$\\mathbf H = \n", "\\begin{bmatrix}\n", - "\\frac{x_{pos}}{\\sqrt{x_{pos}^2 + x_{alt}^2}} & \n", + "\\frac{x}{\\sqrt{x^2 + y^2}} & \n", "0 &\n", "&\n", - "\\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n", + "\\frac{y}{\\sqrt{x^2 + y^2}}\n", "\\end{bmatrix}$$\n", "\n", "This may seem daunting, so step back and recognize that all of this math is doing something very simple. We have an equation for the slant range to the airplane which is nonlinear. The Kalman filter only works with linear equations, so we need to find a linear equation that approximates $\\mathbf H$. As we discussed above, finding the slope of a nonlinear equation at a given point is a good approximation. For the Kalman filter, the 'given point' is the state variable $\\mathbf x$ so we need to take the derivative of the slant range with respect to $\\mathbf x$. \n", @@ -631,7 +597,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -639,7 +605,7 @@ "source": [ "from math import sqrt\n", "def HJacobian_at(x):\n", - " \"\"\" compute Jacobian of H matrix for state x \"\"\"\n", + " \"\"\" compute Jacobian of H matrix at x \"\"\"\n", "\n", " horiz_dist = x[0]\n", " altitude = x[2]\n", @@ -656,7 +622,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -679,7 +645,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -769,21 +735,21 @@ " rk.predict()\n", "```\n", "\n", - "Putting that all together along with some boilerplate code to save the results and plot them, we get" + "Adding some boilerplate code to save and plot the results we get:" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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oUSOKiw22Hyzm0cefZsWSOXi42bFptxPPL4rmT1+V5fCHZvH0fbrsvT04+F1W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\nB+ZTGaRFinbuAAAAAElFTkSuQmCC\n", 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kZUuSM4wx0ML1dDOKVaNyjzM1LqawSENRse7+RlGgS0vdasNN6kNXf3kCIO5ftQoJPXv2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\nFy4U2TYlJaVUx87IyGDr1q0MHTqUwMDAEj+LOnXqcP36dTI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HysqKFi1a8Pnnn6f1DQgPD8fc3BxHR0eD/VxcXIiIiMjz+J7UuD7wQi31OjEJ+nwIB05J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\nqalMIpGwFStW1FpfIpGwpUuXPnDdJ9m3v78/s7KyYpmZmQ8tD2OMBQU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IIYQQxd0zk/4pU6ZgbGyMsbExiqLQv3//lP20LxsbG1avXk3fvn3zKm5RwLzR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\nkpISIpJ3EqZOnSrG6XQ6WrBggeL9M2bMEP/XarU0ffp0kSs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RERHRXcToZOCxxx7DJ598gurq6o6sDxERERER3SFGTxPy8fHBV199hREjRiAuLg59+/Zt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\nadGiRTh//jxOnTolWQwqlQrOzs5YuXIlli1bJlkcRERS4Zw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AACIjIzFkyJB2VyV64IEHurWCRERERETU88xODBYuXKj8/vTTT7dbRpIkJgZERERERP2Q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\nRAQWBkREREREBBYGREREREQEFgZERERERATg/7zbTx7D4Sc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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -814,6 +780,7 @@ "from filterpy.common import Q_discrete_white_noise\n", "from filterpy.kalman import ExtendedKalmanFilter\n", "from numpy import eye, array, asarray\n", + "import numpy as np\n", "\n", "dt = 0.05\n", "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n", @@ -822,9 +789,9 @@ "# make an imperfect starting guess\n", "rk.x = array([radar.pos-100, radar.vel+100, radar.alt+1000])\n", "\n", - "rk.F = array([[1, dt, 0],\n", - " [0, 1, 0],\n", - " [0, 0, 1]])\n", + "rk.F = eye(3) + array([[0, 1, 0],\n", + " [0, 0, 0],\n", + " [0, 0, 0]]) * dt\n", "\n", "range_std = 5. # meters\n", "rk.R = np.diag([range_std**2])\n", @@ -858,14 +825,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Depending on your experience with derivatives you may have found the computation of the Jacobian above either fairly straightforward, or quite difficult. Even if you found it easy, a slightly more difficult problem easily leads to very difficult computations.\n", + "Depending on your experience with derivatives you may have found the computation of the Jacobian difficult. Even if you found it easy, a slightly more difficult problem easily leads to very difficult computations.\n", "\n", - "As explained in Appendix A, we can use the SymPy package to compute the Jacobian for us. " + "As explained in Appendix A, we can use the SymPy package to compute the Jacobian for us." ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": { "collapsed": false, "scrolled": true @@ -873,32 +840,32 @@ "outputs": [ { "data": { - "image/png": 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"text/latex": [ - "$$\\left[\\begin{matrix}\\frac{x_{pos}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}}\\end{matrix}\\right]$$" + "$$\\left[\\begin{matrix}\\frac{x}{\\sqrt{x^{2} + y^{2}}} & 0 & \\frac{y}{\\sqrt{x^{2} + y^{2}}}\\end{matrix}\\right]$$" ], "text/plain": [ - "⎡ x_pos x_alt ⎤\n", - "⎢──────────────────── 0 ────────────────────⎥\n", - "⎢ _________________ _________________⎥\n", - "⎢ ╱ 2 2 ╱ 2 2 ⎥\n", - "⎣╲╱ x_alt + x_pos ╲╱ x_alt + x_pos ⎦" + "⎡ x y ⎤\n", + "⎢──────────── 0 ────────────⎥\n", + "⎢ _________ _________⎥\n", + "⎢ ╱ 2 2 ╱ 2 2 ⎥\n", + "⎣╲╱ x + y ╲╱ x + y ⎦" ] }, - "execution_count": 9, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy\n", - "sympy.init_printing()\n", + "sympy.init_printing(use_latex=True)\n", "\n", - "x_pos, x_vel, x_alt = sympy.symbols('x_pos, x_vel x_alt')\n", + "x, x_vel, y = sympy.symbols('x, x_vel y')\n", "\n", - "H = sympy.Matrix([sympy.sqrt(x_pos**2 + x_alt**2)])\n", + "H = sympy.Matrix([sympy.sqrt(x**2 + y**2)])\n", "\n", - "state = sympy.Matrix([x_pos, x_vel, x_alt])\n", + "state = sympy.Matrix([x, x_vel, y])\n", "H.jacobian(state)" ] }, @@ -939,16 +906,16 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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VyR/qBQUFEEIgLi7OaK67uzsOHjzYbABcq0+fPk2OHTt2TB47cuQIHnvsMTg7O8PJyQlu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\nRkZi5cqV6N27t5k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JAJg/fz4aN25s8qdJkybQ6/XIy8sDAJw+fRo3btzAxx9/bDbX19cXv//+u3Gupc/crl07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\n/bUCVRER1Z/Vh53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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -963,31 +930,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Here we see the front tire is pointing in direction $\\alpha$ relative to the wheelbase. Over a short time period the car moves forward and the rear wheel ends up further ahead and slightly turned inward, as depicted with the blue shaded tire. Over such a short time frame we can approximate this as a turn around a radius $R$. We can compute the turn angle $\\beta$ with\n", - "\n", - "$$\\beta = \\frac{d}{w} \\tan{(\\alpha)}$$\n", - "\n", - "and the turning radius R is given by \n", - "\n", - "$$R = \\frac{d}{\\beta}$$\n", - "\n", - "where the distance the rear wheel travels given a forward velocity $v$ is $d=v\\Delta t$.\n", - "\n", - "If we let $\\theta$ be our current orientation then we can compute the position $C$ before the turn starts as\n", - "\n", - "$$ C_x = x - R\\sin(\\theta) \\\\\n", - "C_y = y + R\\cos(\\theta)\n", - "$$\n", - "\n", - "After the move forward for time $\\Delta t$ the new position and orientation of the robot is\n", - "\n", - "$$\\begin{aligned} x &= C_x + R\\sin(\\theta + \\beta) \\\\\n", - "y &= C_y - R\\cos(\\theta + \\beta) \\\\\n", - "\\theta &= \\theta + \\beta\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "Once we substitute in for $C$ we get\n", + "In the **Unscented Kalman Filter** chapter we derived these equations describing for this model:\n", "\n", "$$\\begin{aligned} x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n", "y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n", @@ -995,7 +938,9 @@ "\\end{aligned}\n", "$$\n", "\n", - "You do not need to understand this math in detail if you are not interested in steering models. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter." + "where $\\theta$ is the robot's heading.\n", + "\n", + "You do not need to understand this model in detail if you are not interested in steering models. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter." ] }, { @@ -1008,7 +953,7 @@ "\n", "$$\\mathbf x = \\begin{bmatrix}x \\\\ y \\\\ \\theta\\end{bmatrix}$$\n", "\n", - "Our control input $\\mathbf u$ is the velocity and steering angle\n", + "Our control input $\\mathbf u$ is the velocity $v$ and steering angle $\\alpha$:\n", "\n", "$$\\mathbf u = \\begin{bmatrix}v \\\\ \\alpha\\end{bmatrix}$$" ] @@ -1069,7 +1014,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -1095,7 +1040,7 @@ "⎣0 0 1 ⎦" ] }, - "execution_count": 11, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -1126,7 +1071,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": { "collapsed": false }, @@ -1144,7 +1089,7 @@ "⎣0 0 1 ⎦" ] }, - "execution_count": 12, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -1179,7 +1124,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": { "collapsed": false }, @@ -1225,7 +1170,7 @@ " ⎦" ] }, - "execution_count": 13, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -1288,7 +1233,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 13, "metadata": { "collapsed": false }, @@ -1296,28 +1241,28 @@ { "data": { "text/latex": [ - "$$\\left[\\begin{matrix}\\frac{- px + x}{\\sqrt{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}}} & \\frac{- py + y}{\\sqrt{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}}} & 0\\\\- \\frac{- py + y}{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}} & - \\frac{px - x}{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}} & -1\\end{matrix}\\right]$$" + "$$\\left[\\begin{matrix}\\frac{- p_{x} + x}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & \\frac{- p_{y} + y}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & 0\\\\- \\frac{- p_{y} + y}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & - \\frac{p_{x} - x}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & -1\\end{matrix}\\right]$$" ], "text/plain": [ - "⎡ -px + x -py + y ⎤\n", - "⎢────────────────────────── ────────────────────────── 0 ⎥\n", - "⎢ _______________________ _______________________ ⎥\n", - "⎢ ╱ 2 2 ╱ 2 2 ⎥\n", - "⎢╲╱ (px - x) + (py - y) ╲╱ (px - x) + (py - y) ⎥\n", - "⎢ ⎥\n", - "⎢ -(-py + y) -(px - x) ⎥\n", - "⎢ ───────────────────── ───────────────────── -1⎥\n", - "⎢ 2 2 2 2 ⎥\n", - "⎣ (px - x) + (py - y) (px - x) + (py - y) ⎦" + "⎡ -pₓ + x -p_y + y ⎤\n", + "⎢─────────────────────────── ─────────────────────────── 0 ⎥\n", + "⎢ ________________________ ________________________ ⎥\n", + "⎢ ╱ 2 2 ╱ 2 2 ⎥\n", + "⎢╲╱ (pₓ - x) + (p_y - y) ╲╱ (pₓ - x) + (p_y - y) ⎥\n", + "⎢ ⎥\n", + "⎢ -(-p_y + y) -(pₓ - x) ⎥\n", + "⎢ ────────────────────── ────────────────────── -1⎥\n", + "⎢ 2 2 2 2 ⎥\n", + "⎣ (pₓ - x) + (p_y - y) (pₓ - x) + (p_y - y) ⎦" ] }, - "execution_count": 14, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "px, py = symbols('px, py')\n", + "px, py = symbols('p_x, p_y')\n", "z = Matrix([[sympy.sqrt((px-x)**2 + (py-y)**2)],\n", " [sympy.atan2(py-y, px-x) - theta]])\n", "z.jacobian(Matrix([x, y, theta]))" @@ -1334,7 +1279,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 14, "metadata": { "collapsed": true }, @@ -1368,7 +1313,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 15, "metadata": { "collapsed": true }, @@ -1421,7 +1366,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 16, "metadata": { "collapsed": true }, @@ -1502,7 +1447,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 17, "metadata": { "collapsed": true }, @@ -1527,7 +1472,7 @@ }, { "cell_type": "code", - "execution_count": 107, + "execution_count": 18, "metadata": { "collapsed": false, "scrolled": true @@ -1536,8 +1481,9 @@ "source": [ "from filterpy.stats import plot_covariance_ellipse\n", "from math import sqrt, tan, cos, sin, atan2\n", - "dt = 1.0\n", + "import matplotlib.pyplot as plt\n", "\n", + "dt = 1.0\n", "\n", "def z_landmark(lmark, sim_pos, std_rng, std_brg):\n", " x, y = sim_pos[0, 0], sim_pos[1, 0]\n", @@ -1603,17 +1549,17 @@ }, { "cell_type": "code", - "execution_count": 108, + "execution_count": 19, "metadata": { "collapsed": false, - "scrolled": true + "scrolled": false }, "outputs": [ { "data": { - "image/png": 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hJJkWQghxzNTWwty5QyfLS5dGmDBh+OcxDMWW2jaq97ZRW1dHj68LHUWKFsVm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\nLyhN09TRo0enbZf+mD+XX365uu2226Zt6+/vV3/913+9QC26OIXDYfW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SCTdWzEJTMXQ9Nex5NnsKX9Ehwk1OnD29pA8fILr/TQCck5xkfToL3fnuTCEK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\nutX0dszWnE5Gz2+1FCGEEAtHQrUQ4qTKdYt6vU44cOa7J5b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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1623,7 +1569,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Final P: [ 0.025 0.041 0.002]\n" + "Final P: [ 0.024 0.042 0.002]\n" ] } ], @@ -1651,16 +1597,16 @@ }, { "cell_type": "code", - "execution_count": 109, + "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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hvzdat24dV199NUVFRei6zvLlywdd95ZbbkHXdX784x+f9CCFEEKIU6mu1c83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\nswt1GiGEEEIIIS66SCQy6+t510i/7K677uInP/kJ27dvPyOJFkIIIYQ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7FUKcPZJUCyGEOG90+8Jsf6uZ+oYm3jragBEN4jXHyXcPrpuuzFLUB1z0tcxG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\n73nk97u1xrz86f9o59GdTnrHvSR7wiT7UrjDYzjcBZTSKKX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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1670,7 +1616,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Final P: [ 0.021 0.02 0.002]\n" + "Final P: [ 0.019 0.022 0.002]\n" ] } ], @@ -1693,7 +1639,7 @@ }, { "cell_type": "code", - "execution_count": 110, + "execution_count": 21, "metadata": { "collapsed": false, "scrolled": true @@ -1701,9 +1647,9 @@ "outputs": [ { "data": { - "image/png": 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qz32h4UC2hYITHrhUB2azJ/179aBvnw7N0odoOfLz17adz/xZrdZ66xqdSE+d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\nkCYiIiIiGof/D20aws3V7zlAAAAAAElFTkSuQmCC\n", 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CBx980NKmhBBCiAtC36BqKrd+iDszHQw6Am4JoN3EIIxmHSG+ZgIj0nGZisgq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\nucZv1JPqH/7wh5Bl+RO/FEXBzp07s14Ti8Xwla98BZWVldi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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1713,7 +1659,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Final P: [ 0.018 0.046 0. ]\n" + "Final P: [ 0.02 0.046 0. ]\n" ] } ], @@ -1733,7 +1679,7 @@ }, { "cell_type": "code", - "execution_count": 111, + "execution_count": 22, "metadata": { "collapsed": false, "scrolled": false @@ -1741,9 +1687,9 @@ "outputs": [ { "data": { - "image/png": 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xemc+G3cVRR37k5lnk2BOJFSXTsBjBsAc7yQmvpRqdw1/XLI56vhZEwYwql8v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\n", 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GOlcq0Y4yNDGllFQ7eezNyCkcRoOOG79Zra75zmp1XMZh/JpKducX89bKXRHH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\nk0jIT2VxhNqyAvynWLtaRETOXgrVInLW8/ssGioLadDyeCI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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1753,7 +1699,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Final P: [ 0.276 0.809 0.004]\n" + "Final P: [ 0.284 0.74 0.003]\n" ] } ], @@ -1773,7 +1719,7 @@ }, { "cell_type": "code", - "execution_count": 115, + "execution_count": 23, "metadata": { "collapsed": false, "scrolled": true @@ -1781,9 +1727,9 @@ "outputs": [ { "data": { - "image/png": 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vdBLY3QuAqdiFvnAJYf90nCSxqDSP+z51FVfMysdqll9NQojJQz6xhBBCnJdu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\nDh8+LCRJEmfPno3WNEeEo0ePCkmSxIULF4LamWn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pCqkOC7veqsf/wUsQDaMmqjhudOEoTWDI143NNx9fTyFJ1iT+4aZLuO3KuZTm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\nHD9+3KstJiZGHDhwwPP1yMiIMJlM4rPPPnvY05u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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1793,7 +1739,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Final P: [ 0.008 0.009 0.001]\n" + "Final P: [ 0.009 0.008 0.001]\n" ] } ], @@ -1837,16 +1783,16 @@ }, { "cell_type": "code", - "execution_count": 117, + "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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WjY2NpVu3btSsWRNPT08aN27M66+/ztWrVwslaJHCtnUrJCY6OwoREREp6+ya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\nSUVORK5CYII=\n", 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oOTwiHhUVRb169fD09CQ4OJjY2JyXU9u9ezcdO3akevXqeHp6Ur9+fd544w3M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\nIQ39rGuFVvGsQnpGum0qy9Wvni6ePHn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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1856,7 +1802,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "actual mean=1.30, std=1.14\n", + "actual mean=1.29, std=1.13\n", "EKF mean=1.00, std=0.95\n" ] } @@ -1877,16 +1823,16 @@ }, { "cell_type": "code", - "execution_count": 119, + "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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YRUREpGjlKflesWIF48aNY8qUKezduxd/f38CAwOJiYnJsr6zszPDhg0jIiKC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\nL81rdzCs7TDcHN1ITkvm2MVjtKvdjvk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N5izrN3p5ebFpU/Y3q7m7u/PWW28REBCAk5MTq1atom/fvixatIh+/frleK3du3fneEyy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\npb7FYiEmJqbEJOJxcfDLL9bt2zMyrA+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"text/plain": [ - "" + "" ] }, "metadata": {}, diff --git a/code/ekf_internal.py b/code/ekf_internal.py index 1f7964b..d968c5d 100644 --- a/code/ekf_internal.py +++ b/code/ekf_internal.py @@ -75,7 +75,7 @@ def plot_radar(xs, track, time): plt.ylim((900, 1600)) plt.show() - + def plot_bicycle(): plt.clf() plt.axes() @@ -227,6 +227,22 @@ def show_radar_chart(): ax.yaxis.set_ticklabels([]) ax.xaxis.set_ticks([]) ax.yaxis.set_ticks([]) - - plt.show() + + +def show_linearization(): + xs = np.arange(0, 2, 0.01) + ys = [x**2 - 2*x for x in xs] + + def y(x): + return x - 2.25 + + plt.plot(xs, ys, label='$f(x)=x^2−2x$') + plt.plot([1, 2], [y(1), y(2)], color='k', ls='--', label='linearization') + plt.axes().axvline(1.5, lw=1, c='k') + plt.xlim(0, 2) + plt.ylim([-1.5, 0.0]) + plt.title('Linearization of $f(x)$ at $x=1.5$') + plt.xlabel('$x=1.5$') + plt.legend(loc=4) + plt.show() \ No newline at end of file