If the state process is \(X(t) = (x_{1}(t),x_{2}(t))\), then
$$X(t+1) = \alpha X(t) + \sigma \epsilon(t),$$
where \(\alpha\) and \(\sigma\) are 2x2 matrices, \(\sigma\) is lower-triangular, and \(\epsilon(t)\) is standard bivariate normal.
The observation process is \(Y(t) = (y_1(t),y_2(t))\), where \(y_i(t) \sim \mathrm{normal}(x_i(t),\tau)\).
The functions rprocess
, dprocess
, rmeasure
, dmeasure
, and skeleton
are implemented using compiled C code for computational speed:
see the source code for details.