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"## Part 8. Data Assimilation\n",
"$$ \\def\\pr{\\hbox{Pr}}\n",
"\\def\\var{\\hbox{var}}\n",
"\\def\\cov{\\hbox{cov}}\n",
"\\def\\tr{\\hbox{tr}}\n",
"\\def\\corr{\\hbox{corr}}\n",
"\\def\\dmX{\\un{\\mathcal{X}}}\n",
"\\def\\dmG{\\un{\\mathcal{G}}}\n",
"\\def\\dmK{\\un{\\mathcal{K}}}\n",
"\\def\\dmS{\\un{\\mathcal{S}}}\n",
"\\def\\dmC{\\un{\\mathcal{C}}}\n",
"\\def\\dmZ{\\un{\\mathcal{Z}}}\n",
"\\def\\bma{{\\mbox{\\boldmath $\\alpha$}}}\n",
"\\def\\bmb{{\\mbox{\\boldmath $\\beta$}}}\n",
"\\def\\bmu{{\\mbox{\\boldmath $\\mu$}}}\n",
"\\def\\bme{{\\mbox{\\boldmath $\\epsilon$}}}\n",
"\\def\\bmS{{\\mbox{\\boldmath $\\Sigma$}}}\n",
"\\def\\bmL{{\\mbox{\\boldmath $\\Lambda$}}}\n",
"\\def\\bmd{{\\mbox{\\boldmath $\\delta$}}}\n",
"\\def\\bmD{{\\mbox{\\boldmath $\\Delta$}}}\n",
"\\def\\bmG{{\\mbox{\\boldmath $\\Gamma$}}}\n",
"\\def\\bmphi{{\\mbox{\\boldmath $\\phi$}}}\n",
"\\def\\bmPhi{{\\mbox{\\boldmath $\\Phi$}}}\n",
"\\def\\bmpsi{{\\mbox{\\boldmath $\\psi$}}}\n",
"\\def\\bmtheta{{\\mbox{\\boldmath $\\theta$}}}\n",
"\\def\\eq{\\begin{equation}}\n",
"\\def\\eeq{\\end{equation}}\n",
"\\def\\i{{\\bf i}}\n",
"\\def\\un#1{{\\bf #1}}$$\n",
"\n",
"\n",
"Arulampalam, M. S., Maskell, S., Gordon, N., and Clapp, T. (2002).\n",
" A tutotial on particle filters for online nonlinear/non-Gaussian\n",
" Bayesian tracking.\n",
"IEEE Transactions on Signal Processing, (50)(2), 174--188.\n",
"\n",
"Bishop, C. M. (2006).\n",
"Pattern Recognition and Machine Learning, Springer.\n",
"\n",
"\n",
"Miller, R. N., Carter, E. F., and Blue, S. T. (1999).\n",
"Data assimilation into nonlinear stochastic models.\n",
"Tellus, 51A, 167--194."
]
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"Nonlinear system model (first-order Markov process):\n",
"\n",
"$$\n",
"z_n = f(z_{n-1},w_n),\\quad w_n=\\hbox{system noise}.\\tag 1\n",
"$$\n",
"\n",
"Nonlinear measurement model:\n",
"\n",
"$$\n",
"x_n = h(z_n, v_n),\\quad v_n=\\hbox{measurement noise}.\\tag 2\n",
"$$\n",
"\n",
"Given observations $X_n = (x_1,x_2\\dots x_n)$ we want to estimate the posterior probability\n",
"density function\n",
"$p(z_n\\mid X_n)$ for observing $z_n$. Then the state $z_n$ can be estimated:\n",
"\n",
"$$\n",
"\\hat z_n = \\int z_np(z_n\\mid X_n)dz_n, \\quad \\var(z_n) = \\int (z_n-\\hat z_n)^2 p(z_n\\mid X_n)dz_n.\\tag 3\n",
"$$"
]
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"source": [
"If the data $x_n$ arrive sequentially, we can write (3) as\n",
"\n",
"$$\n",
"\\hat z_n = \\int z_np(z_n\\mid x_n,X_{n-1})dz_n\\tag 4\n",
"$$\n",
"\n",
"and say that $x_n$ is being \"assimilated\" to get a better estimate of the state variable $z_n$."
]
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"we make use of\n",
"\n",
"$$\\eqalign{\n",
"p(a\\mid b,c) &\\propto p(b,c\\mid a)p(a)\\quad\\quad\\quad\\quad\\hbox{(Bayes)}\\cr\n",
"&= p(b\\mid c,a)p(c\\mid a)p(a)\\quad\\hbox{(Product rule)}\\cr\n",
"&\\propto p(b\\mid c,a)p(a\\mid c)\\quad\\quad\\quad\\hbox{(Bayes again)},\n",
"}\n",
"$$\n",
"\n",
"so that\n",
"\n",
"$$\n",
"p(a\\mid b,c) ={p(b\\mid c,a)p(a\\mid c)\\over \\int p(b\\mid c,a)p(a\\mid c)da}.\\tag 5\n",
"$$"
]
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"source": [
"Rewriting (4) with the help of (5) and $a = z_n,\\ b=x_n,\\ c=X_{n-1}$,\n",
"\n",
"$$\n",
"\\hat z_n = {\\int z_n p(x_n\\mid X_{n-1},z_n)p(z_n\\mid X_{n-1})dz_n\\over\n",
"\\int p(x_n\\mid X_{n-1},z_n)p(z_n\\mid X_{n-1})dz_n}.\\tag 6\n",
"$$\n",
"\n",
"But $x_n$ is conditionally independent of $X_{n-1}$ so we get\n",
"\n",
"$$\n",
"\\hat z_n = {\\int z_n p(x_n\\mid z_n)p(z_n\\mid X_{n-1})dz_n\\over\n",
"\\int p(x_n\\mid z_n)p(z_n\\mid X_{n-1})dz_n}.\\tag 7\n",
"$$"
]
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"Now suppose that we have a set $\\{z_n^i\\}_1^N$ of $N$ samples drawn from the\n",
"posterior PDF $p(z_n\\mid X_{n-1})$ at time $n$, i.e.,\n",
"\n",
"$$\n",
"p(z_n\\mid X_{n-1}) \\approx \\sum_{i=1}^N\\delta(z_n-z_n^i).\\tag 8\n",
"$$\n",
"\n",
"We measure $x_n$. Then we can assimilate $x_n$ to get a better current estimate\n",
"of $z_n$ by substituting (8) into (7). This gives\n",
"\n",
"$$\n",
"\\hat z_n =\\int z_np(z_n\\mid X_n)dz_n \\approx \\sum_{i=1}^N z_n^i {p(x_n\\mid z_n^i)\\over\\sum_{j=1}^Np(x_n\\mid z_n^j)} = \\sum_{i=1}^N z_n^i w_n^i,\\tag 9\n",
"$$\n",
"\n",
"where the weights $w_i$ are given by the likelihoods $p(x_n\\mid z_n^i)$ for observing $x_n$\n",
"given the model states $z_n^i$,\n",
"\n",
"$$\n",
"w_n^i = {p(x_n\\mid z_n^i)\\over\\sum_{j=1}^Np(x_n\\mid z_n^j)}.\\tag{10}\n",
"$$\n",
"\n",
"The *effective number of particles* involved in (9) is \n",
"\n",
"$$\n",
"N_{eff} = {1 \\over \\sum_i^N (w_n^i)^2}.\n",
"$$\n",
"\n",
"For example, if all of the weights are equal then $w_n^i = 1/N$ and we get\n",
"\n",
"$$\n",
"N_{eff} = {1 \\over N\\cdot(1/N^2)} = N.\n",
"$$\n",
"\n",
"Next we observe $x_{n+1}$. Now we must sample from $p(z_{n+1}\\mid X_n)$.\n",
"Using Bayes Rule as above, we get\n",
"\n",
"$$\\eqalign{\n",
"p(z_{n+1}\\mid X_n)\n",
"={\\int p(z_{n+1}\\mid z_n) p(x_n\\mid z_n)p(z_n\\mid X_{n-1})dz_n\\over\n",
"\\int p(x_n\\mid z_n)p(z_n\\mid X_{n-1})dz_n}.}\\tag{11}\n",
"$$\n",
"\n",
"**Exercise 1:** Show this.\n"
]
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"Now substitute (8) into (10) to get\n",
"\n",
"$$\n",
"p(z_{n+1}\\mid X_n) = \\sum_{i=1}^N w_n^i p(z_{n+1}\\mid z_n^i).\n",
"$$\n",
"\n",
"So to go to the next step: for $i=1\\dots N$,\n",
"choose PDF $p(z_{n+1}\\mid z_n^i)$ with probability $w_n^i$\n",
"and use the model Equation (1) to sample from that PDF. Combine the weighted samples to get $\\{z_{n+1}^i\\}_i^N$.\n",
"Then use (9) and (10) with $n\\to n+1$ to assimilate $x_{n+1}$, etc."
]
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"**Algorithm (Nonlinear Bayesian Tracking or Particle Filter):**\n",
"\n",
"1) Initialize $n=1$ , $\\{z_n^i\\}_1^N$.\n",
"\n",
"2) Measure $x_n$ and calculate weights $w_n^i = p(x_n\\mid z_n^i)$, $i=1\\dots N$ from measurement model (1). Set $w_n^i = w_n^i / \\sum_i w_n^i$.\n",
"\n",
"3) Calcultate $N_{eff} = \\sum_i 1/(w_n^i)^2$ and re-sample the $z_n^i$ if too small.\n",
"\n",
"4) Calculate $\\hat z_n = \\sum_1^N z_n^i w_n^i,\\quad \\var(z_n) = \\sum_1^N (z_n^i-\\hat z_n)^2 w_n^i$.\n",
"\n",
"5) Sample $p(z_{n+1}\\mid z_n^i)$ from system model (2) with weights $w_n^i$ to get $\\{z_{n+1}^i\\}_1^N$.\n",
"\n",
"6) Set n = n+1 and go to 2)."
]
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"### SImulation\n",
"\n",
"Following Miller et al.(1999) we use as system model, Equation (1), the stochastic Lorenz equations for the state vector $\\un Z=(Z_0,Z_1.Z_2)^\\top$\n",
"\n",
"$$\\eqalign{\n",
"{dZ_0\\over dt} &= \\sigma(Z_1-Z_0) + w_0\\cr\n",
"{dZ_1\\over dt} &= \\rho Z_0 - Z_1 -Z_0Z_2 + w_1\\cr\n",
"{dZ_2\\over dt} &= Z_0Z_1-\\beta Z_2 + w_2,\n",
"}\n",
"$$\n",
"\n",
"with $\\sigma=10,\\ \\rho=28,\\ \\beta=8/3$ and $w_i \\sim N\\left(0,0.5\\right)$, $i=0\\dots 2$. This\n",
"model is highly nonlinear and, for the choice of parameters, chaotic.\n"
]
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QCwoKqhxEqy7USveCIaScm5tLZmZmlcYysg8cDkelc1t9Ph+qqsZdAn75pcQt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PG0iE7F2MJVFA0xlURCp3LeZR070iYLxubjdDrNSslYkG7ovAOBAK+88gpr1qzhgw8+4IILLij3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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"%run /home/mort/stats2016/lorenz"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We run the model over the time interval $[0,45]$, simulating\n",
"measurements $\\un X=(X_0,X_1,X_2)^\\top$ of all three state variables every 0.48 time units with uncorrelated Gaussian error noise. The measurement variance-covariance\n",
"matrix is\n",
"\n",
"$$\n",
"{\\bf\\Sigma}_v = \\pmatrix{2 & 0 & 0\\cr\n",
" 0 & 2 & 0\\cr\n",
" 0 & 0 & 2}.\n",
"$$\n",
"\n",
"Then we restart the model and simulate the assimilation of the measurements using the particle filter described above.\n",
"The number of particles (samples) is $N=4000$, and resampling is done when $N_{eff} < 3000$.\n",
"\n",
"**show simulation in IDL**"
]
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