orbitalstate_init_demo.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "### Demonstrate initiation of OrbitalState object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Necessary imports\n",
    "import numpy as np\n",
    "from datetime import datetime\n",
    "from stonesoup.types.array import StateVector\n",
    "\n",
    "# The class in question is\n",
    "from stonesoup.types.orbitalstate import OrbitalState"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### initiate from Cartesian coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The state vector is (in km)\n",
    "orb_st_vec = StateVector([-6045, -3490, 2500, -3.457, 6.618, 2.533])\n",
    "\n",
    "# Create the state, and ensure that the Gravitational parameter is in km^3 s^-2, because by default it's in m^3 s^-2\n",
    "orb_st = OrbitalState(orb_st_vec, grav_parameter=3.986004418e5, timestamp=datetime.now())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check whether that gives you something sensible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StateVector([[1.71211182e-01],\n",
       "             [8.78808177e+03],\n",
       "             [2.67470361e+00],\n",
       "             [4.45546404e+00],\n",
       "             [3.50255117e-01],\n",
       "             [4.96472955e-01]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orb_st.keplerian_elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These should be $e = 0.1712$, $a = 8788$, $i = 2.674$, $\\Omega = 4.456$, $\\omega = 0.3503$, $\\theta = 0.4965$ according to the textbooks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's the simplest way of doing it, but other intiations (from Keplerian elements or Equinocital elements should also work). Of note might be the option of initiating directly from a TLE. See this link: https://gist.github.com/jmbarr/f1ce08fc4c3e2b5a09fde68c0633cb17"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Covariances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n"
     ]
    }
   ],
   "source": [
    "print(orb_st.covar)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default there's no covariance specified (i.e. covar=None). That's deliberate because there's no strong reason to presume that the uncertainty is Gauss-distributed. And certainly not in the Cartesian frame. Note though that if you were to do inference using a Kalman-type filter, you'd be making this assumption implicitly. Many (most?) current inference schemes assume Gaussianity in a different frame (roughly corresponding to radial, along-track, and normal 'RTN' coordinates). `OrbitalState` would have to be adjusted to cope with this. In fact it might be better to derive a new class to do this..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So further developments might create `GaussianOrbitalState`, `ParticleOrbitalState` or somesuch. Or perhaps something like an `RTNGaussianOrbitalState` in which the covar could be used by the Kalman-type filters."
   ]
  }
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