# smooth_rts¶

probnum.filtsmooth.smooth_rts(observations, locations, F, L, H, R, m0, C0, prior_model='continuous')[source]

Estimate a trajectory with a Rauch-Tung-Striebel smoother.

A Rauch-Tung-Striebel smoother estimates the unknown trajectory $$X$$ from a set of observations Y. There is a continuous-discrete and a discrete-discrete version (describing whether the prior model and measurement model are continuous/discrete).

In a continuous-discrete model, the prior distribution is described by the SDE

$\text{d}X(t) = F X(t) \text{d}t + L \text{d}W(t)$

driven by Wiener process $$W$$ and subject to initial condition

$X(t_0) \sim N(m_0, C_0).$

By default, $$t_0$$ is set to the location of the first observation.

In a discrete-discrete model, the prior distribution is described by the transition

$X_{n+1} \,|\, X_n \sim N(F X_n, L)$

subject to the same initial condition.

In both cases, the measurement model is (write $$X(t_n)=X_n$$ in the continuous case)

$Y_n \,|\, X_n \sim N(H X_n, R)$

and the Rauch-Tung-Striebel smoother estimates $$X$$ given $$Y_n=y_n$$, $$Y=[y_1, ..., y_N]$$.

Parameters
Raises

ValueError – If prior_model is neither discrete nor continuous.

Returns

Smoothing distribution as returned by the Rauch-Tung-Striebel smoother.

Return type

gaussian.SmoothingPosterior