intent_inference_for_simulation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m  Activating\u001b[22m\u001b[39m project at `~/Documents/GitHub/Chengfeng_intent_inference`\n"
     ]
    }
   ],
   "source": [
    "using Pkg\n",
    "Pkg.activate(\".\")\n",
    "Pkg.instantiate()\n",
    "# IJulia.clear_output();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ReactiveMP\n",
    "using GraphPPL\n",
    "using Rocket\n",
    "using Distributions\n",
    "using Random\n",
    "using BenchmarkTools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "@model function filtering(Q::ConstVariable, R::ConstVariable)\n",
    "    A = datavar(Vector{Float64})\n",
    "    B = constvar([ .0 .0 .0 .0; .0 .0 .0 .0; .0 .0 1. .0; .0 .0 .0 1. ]) \n",
    "    prior_m1=[ 0.0, 0.0, 1/8π, 0.01 ]\n",
    "    prior_m2=[ 0.0, 0.0, -1/8π, 0.01 ]\n",
    "    prior_m3=[ 0.0, 0.0, 0.0, 0.01 ]\n",
    "    prior_w1=[1.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0; 0.0 0.0 1/16π .0; 0.0 0.0 0.0 0.05]\n",
    "    prior_w2=[1.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0; 0.0 0.0 1/16π .0; 0.0 0.0 0.0 0.05]\n",
    "    prior_w3=[1.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0; 0.0 0.0 1/16π .0; 0.0 0.0 0.0 0.05]\n",
    "\n",
    "    nmixtures=3\n",
    "\n",
    "    m = randomvar(nmixtures)\n",
    "    w = randomvar(nmixtures)\n",
    "\n",
    "    mean_mean_cov       = [ 1e-6 0.0 0.0 0.0; 0.0 1e-6 0.0 0.0; 0.0 0.0 1e-1 0.0; 0.0 0.0 0.0 1e-1 ]\n",
    "\n",
    "    m[1] ~ MvNormalMeanCovariance(prior_m1, mean_mean_cov)\n",
    "    m[2] ~ MvNormalMeanCovariance(prior_m2, mean_mean_cov)\n",
    "    m[3] ~ MvNormalMeanCovariance(prior_m3, mean_mean_cov)\n",
    "    w[1] ~ Wishart(6, prior_w1)\n",
    "    w[2] ~ Wishart(6, prior_w2)\n",
    "    w[3] ~ Wishart(6, prior_w3)\n",
    "\n",
    "    means = tuple(m...)\n",
    "    precs = tuple(w...)\n",
    "    # control ~ NormalMixture(intent, means, precs)\n",
    "\n",
    "    x_k_mean = datavar(Vector{Float64})\n",
    "    x_k_cov  = datavar(Matrix{Float64})\n",
    "    \n",
    "    #control depends on intent, and intent is a category Distributions.\n",
    "    #control is GMM Distributions\n",
    "\n",
    "    intent ~ Categorical([1/3,1/3,1/3]) where { q = MeanField() }\n",
    "    println(intent)\n",
    "    # println((m1, m2))\n",
    "    control = randomvar()\n",
    "    control ~ NormalMixture(intent, means, precs) where { q = MeanField() }\n",
    "\n",
    "    # control ~ MvNormalMeanCovariance(control_mean,  control_covariance)\n",
    "    x_k ~ MvNormalMeanCovariance(x_k_mean, x_k_cov)\n",
    "    \n",
    "    tmp1 ~ (A + x_k) \n",
    "    tmp2 ~ (B * control)\n",
    "\n",
    "    x_k_p_one ~ MvNormalMeanCovariance(tmp1 + tmp2, Q)\n",
    "\n",
    "    # own ship state\n",
    "    o_x_k_p_one=datavar(Vector{Float64})\n",
    "    \n",
    "    # relative observation between two ships\n",
    "    y_k = datavar(Vector{Float64})\n",
    "    \n",
    "    y_k ~ MvNormalMeanCovariance(x_k_p_one-o_x_k_p_one, R)\n",
    "    \n",
    "    return x_k_mean, x_k_cov, x_k_p_one, y_k, A, control, intent, m, w,o_x_k_p_one\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "own_ship_moving (generic function with 1 method)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function  own_ship_moving(X,δt,mode)\n",
    "#    This function can be change to get the state of own ship\n",
    "    if mode==\"head-on\"\n",
    "        c=[0.0 ;0.0 ;-0.0005 ;0.00001]\n",
    "        qq=diageye(4)*tiny\n",
    "        o_p=rand(rng,MvNormal(X+[X[4]*cos(X[3])*δt,X[4]*sin(X[3])*δt,0,0]+c*δt,qq))\n",
    "    end\n",
    "    \n",
    "    if mode==\"overtaking\"\n",
    "        c=[0.0 ;0.0 ;0.000005 ;0.000000]\n",
    "        qq=diageye(4)*tiny\n",
    "        o_p=rand(rng,MvNormal(X+[X[4]*cos(X[3])*δt,X[4]*sin(X[3])*δt,0,0]+c*δt,qq))\n",
    "    end\n",
    "\n",
    "    if mode==\"crossing\"\n",
    "        c=[0.0 ;0.0 ;0.0005 ;0.0000001]\n",
    "        qq=diageye(4)*tiny\n",
    "        o_p=rand(rng,MvNormal(X+[X[4]*cos(X[3])*δt,X[4]*sin(X[3])*δt,0,0]+c*δt,qq))\n",
    "    end\n",
    "    return o_p\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "slicedim(dim) = (a) -> map(e -> e[dim], a)\n",
    "rng= MersenneTwister(1234)\n",
    "# X=[0.0;800.0 ;-π/2;5.0]\n",
    "# X=[-20.0;100.0;π/2.00001;1.0]\n",
    "X=[-700.0;410.0;0.00001;5.0]\n",
    "o_w=[]\n",
    "for i = 1:500\n",
    "    X=own_ship_moving(X,1.0,\"crossing\")\n",
    "    # println(X)\n",
    "    push!(o_w,X)\n",
    "end\n",
    "o_w\n",
    "px = plot()\n",
    "# px = plot!(px, o_w |> slicedim(1), label = \"Hidden Signal (dim-1)\", color = :orange)\n",
    "p1 = scatter(map(o -> o[1], o_w), map(o -> o[2], o_w),  ms = 2, xlims=[-800, 800],ylims=[0, 800])\n",
    "\n",
    "# plot(o_w, label = \"c[3]\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Vector{Float64}:\n",
       " -694.9999991329028\n",
       "  410.00004909825617\n",
       "    0.0005095055212464958\n",
       "    4.999999197085707"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "o_w[:][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "getAFromState (generic function with 1 method)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function getAFromState(x,δt)\n",
    "    A=zeros(4)\n",
    "    A[1]=x[4]*cos(x[3])*δt\n",
    "    A[2]=x[4]*sin(x[3])*δt\n",
    "    return A\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "generateNewObservation (generic function with 1 method)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function generateNewObservation(ii, δt, observation, actual_control,mode)\n",
    "    \n",
    "    # 1.0 simulate true action\n",
    "    \n",
    "    # 2.0 update your observation\n",
    "\n",
    "    q=diageye(4)*0.00000001\n",
    "    if mode==\"head-on\"\n",
    "        if ii<100\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=0.0\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "        end\n",
    "        if ii>=100 && ii<250\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=-1/80π\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "        end\n",
    "        if ii>=250 && ii<380\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=1/100π\n",
    "            c_m[4]=0.001\n",
    "            actual_control=c_m\n",
    "        end\n",
    "\n",
    "        if ii>=380\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=1/2000π\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "        end\n",
    "    end\n",
    "    if mode ==\"overtaking\"\n",
    "        if ii<100\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=0.00\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "            \n",
    "        end\n",
    "        if ii>=100 && ii<200\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=1/80π\n",
    "            c_m[4]=0.01\n",
    "            actual_control=c_m\n",
    "        end\n",
    "        if ii>=200 && ii<300\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=-1/100π\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "        end\n",
    "        if ii>=300\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=0.0\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "        end\n",
    "    end\n",
    "    if mode ==\"crossing\"\n",
    "        if ii < 100\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=0.0\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "        end\n",
    "        if ii >= 100 && ii<200\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=1/50π\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "    \n",
    "        end\n",
    "        if ii >= 200 && ii<310\n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=-1/60π\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "    \n",
    "        end\n",
    "        if ii >= 310 \n",
    "            c_m=zeros(4)\n",
    "            c_m[3]=0.0\n",
    "            c_m[4]=0.00\n",
    "            actual_control=c_m\n",
    "    \n",
    "        end\n",
    "    end\n",
    "\n",
    "    x=observation\n",
    "    μ=actual_control\n",
    "    x_0=rand(rng,MvNormal(x+[x[4]*cos(x[3])*δt,x[4]*sin(x[3])*δt,0,0]+μ*δt,q))\n",
    "    return x_0\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "inference (generic function with 1 method)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function inference(δt, max_data_points, max_vmp_iterations,mode)\n",
    "    \n",
    "    data_stream1 = ReplaySubject(Vector{Float64}, 1)\n",
    "    data_stream2 = ReplaySubject(Vector{Float64}, 1)\n",
    "\n",
    "    saved_controls = []\n",
    "    saved_position = []\n",
    "    saved_observations = []\n",
    "    saved_intent   = []\n",
    "    saved_own_position=[]\n",
    "    ii = 0\n",
    "\n",
    "    # y_current = zeros(4)\n",
    "    # y_current = [0.0,0.0,0,1.0]\n",
    "    \n",
    "    # TODO: Depend on δt\n",
    "    Q = diageye(4)*1.0\n",
    "    R = diageye(4)*10\n",
    "    \n",
    "    model, (x_k_mean, x_k_cov, x_k_p_one, y_k, A, control, intent, m, w, o_x_k_p_one) = filtering(Q, R)\n",
    "    # ** setmarginal\n",
    "\n",
    "    setmarginal!(m[1], MvNormalMeanCovariance(ones(4), diageye(4)))\n",
    "    setmarginal!(m[2], MvNormalMeanCovariance(zeros(4), diageye(4)))\n",
    "    setmarginal!(m[3], MvNormalMeanCovariance(zeros(4), diageye(4)))\n",
    "\n",
    "    setmarginal!(w[1], Wishart(5, diageye(4)))\n",
    "    setmarginal!(w[2], Wishart(5, diageye(4)))\n",
    "    setmarginal!(w[3], Wishart(5, diageye(4)))\n",
    "\n",
    "    setmarginal!(intent, vague(Categorical, 3))\n",
    "    setmarginal!(control, vague(MvNormalMeanCovariance, 4))\n",
    "    setmarginal!(x_k_p_one, vague(MvNormalMeanCovariance, 4))\n",
    "\n",
    "    stream = combineLatest(\n",
    "        (\n",
    "        getmarginal(x_k_p_one, IncludeAll()), \n",
    "        getmarginal(control, IncludeAll()), \n",
    "        getmarginal(intent, IncludeAll()), \n",
    "        data_stream1,\n",
    "        data_stream2\n",
    "        ), PushNew()\n",
    "    )\n",
    "\n",
    "\n",
    "    fe_actor = ScoreActor(Float64)\n",
    "\n",
    "    fe_subscription = subscribe!(score(Float64, BetheFreeEnergy(), model), fe_actor)\n",
    "\n",
    "    finish = Condition()\n",
    "    \n",
    "    subscription = subscribe!(stream |> async() |> take(max_data_points) |> tap_on_complete(() -> notify(finish)), (d) -> begin\n",
    "\n",
    "        x_k_p_one_posterior = d[1]\n",
    "        control_posterior   = d[2] \n",
    "        intent_posterior    = d[3]\n",
    "        data_point1         = d[4]\n",
    "        data_point2         = d[5]\n",
    "\n",
    "        push!(saved_observations, data_point1)\n",
    "\n",
    "        μ, Σ = mean_cov(x_k_p_one_posterior)\n",
    "        pA = getAFromState(μ, δt)\n",
    "        \n",
    "        for k in 1:max_vmp_iterations\n",
    "            update!(x_k_mean, μ)\n",
    "                \n",
    "            update!(x_k_cov, Σ)\n",
    "                \n",
    "            # Update A here\n",
    "            update!(A, pA)\n",
    "\n",
    "            update!(o_x_k_p_one, data_point2)\n",
    "            update!(y_k, data_point1)\n",
    "            # update!(intent, mean(intent_posterior))\n",
    "        end\n",
    "\n",
    "        release!(fe_actor)\n",
    "\n",
    "        index = length(saved_controls)\n",
    "        ii = ii + 1\n",
    "\n",
    "        # Save our result\n",
    "\n",
    "        push!(saved_controls, Rocket.getrecent(getmarginal(control, IncludeAll())))   \n",
    "        push!(saved_position, Rocket.getrecent(getmarginal(x_k_p_one, IncludeAll())))  \n",
    "        push!(saved_intent, Rocket.getrecent(getmarginal(intent, IncludeAll())))  \n",
    "            \n",
    "        # update y_current somehow\n",
    "\n",
    "        #true action\n",
    "        \n",
    "        c_m=zeros(4)\n",
    "        c_m[3]=0.0\n",
    "        c_m[4]=0.0\n",
    "\n",
    "\n",
    "        y_own=own_ship_moving(data_point2,δt,mode)\n",
    "        push!(saved_own_position,y_own)\n",
    "        next!(data_stream2, y_own)\n",
    "        \n",
    "        y_next = generateNewObservation(ii, δt, data_point1+data_point2, c_m,mode)  \n",
    "\n",
    "        y_relative=y_next-y_own\n",
    "\n",
    "\n",
    "        \n",
    "            \n",
    "        next!(data_stream1, y_relative)\n",
    "\n",
    "    end)\n",
    "\n",
    "    # Start to initial\n",
    "    if mode==\"head-on\"\n",
    "        y_initial=[10.0;10.0 ;π/2.001;1.0]\n",
    "        y_own_initial=[0.0;800.0 ;-π/2;1.0]\n",
    "    end\n",
    "    if mode==\"overtaking\"\n",
    "        y_initial=[10.0;10.0 ;π/2.001;0.8]\n",
    "        y_own_initial=[-20.0;100.0;π/2.00001;1.0]\n",
    "    end\n",
    "\n",
    "    if mode==\"crossing\"\n",
    "        y_initial=[-10.0;10.0 ;π/2.001;2.0]\n",
    "        y_own_initial=[-700.0;410.0;0.00001;5.0]\n",
    "    end\n",
    "    next!(data_stream2, y_own_initial) # Initial state\n",
    "    next!(data_stream1, y_initial-y_own_initial) # Initial state\n",
    "\n",
    "    \n",
    "    wait(finish)\n",
    "\n",
    "    # unsubscribe!(subscription)\n",
    "    \n",
    "    return saved_controls, saved_observations, saved_position, saved_intent, getvalues(fe_actor),saved_own_position\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "δt = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RandomVariable(intent)\n"
     ]
    }
   ],
   "source": [
    "rng= MersenneTwister(1234)\n",
    "mode=\"overtaking\"\n",
    "controls, obs, pos,intents, fe ,own_ship= inference(δt, 500, 25,mode);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500-element Vector{Any}:\n",
       " [30.0, -90.0, -0.0007771517182029175, -0.19999999999999996]\n",
       " [30.000705723305714, -90.19977815696893, -0.0007283759112324262, -0.20002627062530953]\n",
       " [30.00130003852668, -90.39961884647016, -0.0008155917530758838, -0.20001524172089558]\n",
       " [30.002109384905363, -90.59977439680034, -0.0007101140855183541, -0.2001244112827908]\n",
       " [30.00265081556647, -90.79995920292596, -0.0008432322821578797, -0.20002544884548557]\n",
       " [30.003417013941096, -91.00003624507677, -0.0009248541069040161, -0.2001801127565368]\n",
       " [30.00402395909159, -91.20022704219865, -0.0009126898936073768, -0.20022064112250992]\n",
       " [30.004690448372465, -91.4005187505393, -0.0009491690584899626, -0.20016861579009526]\n",
       " [30.005346660258997, -91.60078611755561, -0.0008071971250787069, -0.20022084305487553]\n",
       " [30.006036681674672, -91.80094516564137, -0.0007943856837457908, -0.20001409359692635]\n",
       " [30.00652236822157, -92.00115712295056, -0.0007909934673422381, -0.19993433085828594]\n",
       " [30.00708338476511, -92.20107215750048, -0.0009104775292432254, -0.19985265947991437]\n",
       " [30.007847223877864, -92.40081980219693, -0.0007759953310539913, -0.19984434795656436]\n",
       " ⋮\n",
       " [-67.80345516787588, 140.85733965400675, 0.0788817767921548, 0.8049232776823101]\n",
       " [-67.94755754629388, 141.65626456196367, 0.0791536561078876, 0.8051162887701553]\n",
       " [-68.09212531386463, 142.4552308484474, 0.07913013884114051, 0.8052310775515876]\n",
       " [-68.23688703300036, 143.25445836944562, 0.07915891070912906, 0.8053821572393854]\n",
       " [-68.38179415453128, 144.05385362127572, 0.07903648435930943, 0.80538098769074]\n",
       " [-68.52633255080013, 144.853141935581, 0.07905398954630605, 0.8051337058395641]\n",
       " [-68.67087160727615, 145.65222532378357, 0.07901366807437715, 0.8050279599325515]\n",
       " [-68.81527886703252, 146.45140618779965, 0.07909128558277301, 0.8050828630870275]\n",
       " [-68.95981581536107, 147.25057383377293, 0.0793070963728999, 0.8049950659777522]\n",
       " [-69.1047326022005, 148.04954219358603, 0.07933059836894252, 0.8050529351349948]\n",
       " [-69.24980261147286, 148.8485286269331, 0.07932928315340759, 0.8051091034737805]\n",
       " [-69.3950212704816, 149.64774775762532, 0.07919210073712968, 0.8052224150797672]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 33,
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   "source": [
    "\n",
    "plot(fe)"
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  {
   "cell_type": "code",
   "execution_count": 34,
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     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = scatter(map(o -> o[1], obs), map(o -> o[2], obs),  ms = 2, label=\"Relative position\",xlim=[-800,800])\n",
    "# p1 = scatter(map(o -> o[1], mean.(pos)), map(o -> o[2], mean.(pos)),  ms = 2)\n",
    "p2=plot(map(o -> o[1],own_ship), map(o -> o[2],own_ship),label=\"Own ship\",xlim=[-800,800])\n",
    "p2 = plot!(map(o -> o[1], mean.(pos)), map(o -> o[2], mean.(pos)),  ms = 2,label=\"Other ship\")\n",
    "if mode==\"head-on\"\n",
    "    indexofown=[100, 250, 380]\n",
    "    indexofcompare=[158,338,498]\n",
    "end\n",
    "if mode==\"overtaking\"\n",
    "    indexofown=[100, 200, 300]\n",
    "    indexofcompare=[148,281,499]\n",
    "end\n",
    "if mode==\"crossing\"\n",
    "    indexofown=[100, 200, 310]\n",
    "    indexofcompare=[112,140,165,500]\n",
    "end\n",
    "\n",
    "p2=scatter!(map(o -> o[1], mean.(pos))[indexofown], map(o -> o[2], mean.(pos)[indexofown]),label=\"Message passing method\")\n",
    "p2=scatter!(map(o -> o[1], mean.(pos))[indexofcompare], map(o -> o[2], mean.(pos)[indexofcompare]),shape=:star5,label=\"DP method\")\n",
    "\n",
    "# p2 = plot(map(o -> o[1], obs))\n",
    "# p3 = plot(map(o -> o[2], obs))\n",
    "\n",
    "plot(p1, p2, layout = @layout([ a b ]), size = (1000, 400))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean.(controls);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(map(c -> c[3] / δt, mean.(controls)), label = \"Turning rate\")\n",
    "# plot(map(c -> c[3] / δt, mean.(controls)), ribbon = map(c -> c[3] / δt, var.(controls)), label = \"c[3]\")\n",
    "plot!(map(c -> c[4] / δt, mean.(controls)), label = \"Acceleration\")\n",
    "# plot!(map(c -> c[3] / δt, var.(controls)), label = \"c[3]\")\n",
    "# plot!(map(c -> c[4] / δt, var.(controls)), label = \"c[4]v\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.019894367886486918"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/16π"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(mean.(intents),label = \"Intent\")\n",
    "# println(var.(intents))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Matrix{Float64}:\n",
       " 0.166667     1.16683e-59   2.20589e-63   2.67852e-61\n",
       " 1.16683e-59  0.166667      2.20589e-63   2.67852e-61\n",
       " 2.20589e-63  2.20589e-63   5.84125      -7.29665e-10\n",
       " 2.67852e-61  2.67852e-61  -7.29665e-10   2.84217"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov.(controls)[2]"
   ]
  }
 ],
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   "file_extension": ".jl",
   "mimetype": "application/julia",
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