Stochastics#
Class to manage random operations of GPS tracks
- tracklib.algo.Stochastics.gaussian_process(self, timestamps, kernel, factor=1.0, sigma=0.0, cp_var=False)[source]#
Track interpolation and smoothing with Gaussian Process (GP)
- Parameters
timestamps – points where interpolation must be computed. May be a list of timestamps, a track or a number of seconds
kernel –
a symetric function k(xi-xj) describing the statistical similarity between the coordinates X,Y,Z taken in two points :
\[ \begin{align}\begin{aligned}k(t2-t1) = Cov(X(t1), X(t2))\\k(t2-t1) = Cov(X(t1), X(t2))\\k(t2-t1) = Cov(Z(t1), Z(t2))\end{aligned}\end{align} \]factor – unit factor of variance if the kernel must be scaled
sigma – observation noise standard deviation (in coords units)
cp_var – compute covariance matrix and store pointwise sigmas
- Returns
interpolated/smoothed track (without AF)
- tracklib.algo.Stochastics.noise(track, sigma=[1], kernel=[<tracklib.core.Kernel.DiracKernel object>], distribution=1, mode='linear', force=False, cycle=False)[source]#
Track noising with Cholesky factorization of gaussian process covariance matrix:
\[h(x2-x1)=\exp-\left(\frac{x2-x1}{scope}\right)^2\]If \(X\) is a gaussian white noise, \(Cov(LX) = L^t*L\) => if \(L\) is a Cholesky factorization of a semi-postive-definite matrix \(S\), \(then Cov(LX) = L^T*L = S\) and \(Y=LX\) has \(S\) as covariance matrix.
- Parameters
track – the track to be smoothed (input track is not modified)
sigma – noise amplitude(s) (in observation coordinate units)
kernel – noise autocovariance function(s) :param mode: ‘linear’ (default), ‘circular’ or ‘euclidian’ :param force: force definite-positive matrix with removal of negative eigen values
- tracklib.algo.Stochastics.randomizer(input, f, sigma=[7], kernel=[<tracklib.core.Kernel.GaussianKernel object>], N=10)[source]#
Randomizing traces for sensitivity analysis on output f
- Parameters
input – a track, or list of tracks to be randomized
f – a function taking a list of tracks as input
sigma – noise amplitude (in observation coordinate units)
N – number of simulations to generate (default is 100)
scope_s – spatial autocorrelation scope (measured along track curvilinear abscissa in observation coordinate units)