probnum.filtsmooth

Bayesian Filtering and Smoothing.

This package provides different kinds of Bayesian filters and smoothers which estimate the distribution over observed and hidden variables in a sequential model. The two operations differ by what information they use. Filtering considers all observations up to a given point, while smoothing takes the entire set of observations into account.

Classes

Kalman(dynamics_model, measurement_model, initrv)	Gaussian filtering and smoothing, i.e. Kalman-like filters and smoothers.
ContinuousEKFComponent(non_linear_sde, num_steps)	Continuous extended Kalman filter transition.
DiscreteEKFComponent(disc_model)	Discrete extended Kalman filter transition.
ContinuousUKFComponent(non_linear_sde, dimension)	Continuous unscented Kalman filter transition.
DiscreteUKFComponent(disc_model, dimension)	Discrete extended Kalman filter transition.
UnscentedTransform(dimension[, spread, …])	Used for unscented Kalman filter.
FiltSmoothPosterior()	Posterior Distribution over States after Filtering/Smoothing.
KalmanPosterior(locations, state_rvs, …)	Posterior Distribution after (Extended/Unscented) Kalman Filtering/Smoothing.
IteratedKalman(kalman[, stoppingcriterion])	Iterated filter/smoother based on posterior linearisation.
StoppingCriterion([…])	Stopping criteria for iterated filters/smoothers.
FixedPointStopping([atol, rtol, …])	Keep updating until the filter recursion arrives at a fixed-point.

Class Inheritance Diagram

probnum.filtsmooth.statespace

Probabilistic State Space Models.

This package implements continuous-discrete and discrete-discrete state space models, which are the basis for Bayesian filtering and smoothing, but also probabilistic ODE solvers.

Functions

linear_sde_statistics(rv, start, stop, step, …)	Computes mean and covariance of SDE solution.
matrix_fraction_decomposition(driftmat, …)	Matrix fraction decomposition (without force).
generate(dynmod, measmod, initrv, times[, …])	Samples true states and observations at pre-determined timesteps “times” for a state space model.

Classes

Transition()	Markov transition rules in discrete or continuous time.
SDE(driftfun, dispmatfun, jacobfun)	Stochastic differential equation.
LinearSDE(driftmatfun, forcevecfun, dispmatfun)	Linear stochastic differential equation (SDE),
LTISDE(driftmat, forcevec, dispmat)	Linear time-invariant continuous Markov models of the form.
Integrator(ordint, spatialdim)	An integrator is a special kind of SDE, where the \(i\) th coordinate models the \(i\) th derivative.
IBM(ordint, spatialdim, diffconst)	Integrated Brownian motion in \(d\) dimensions.
IOUP(ordint, spatialdim, driftspeed, diffconst)	Integrated Ornstein-Uhlenbeck process in \(d\) dimensions.
Matern(ordint, spatialdim, lengthscale, …)	Matern process in \(d\) dimensions.
DiscreteGaussian(dynamicsfun, diffmatfun[, …])	Random variable transitions with additive Gaussian noise.
DiscreteLinearGaussian(dynamicsmatfun, …)	Discrete, linear Gaussian transition models of the form.
DiscreteLTIGaussian(dynamicsmat, forcevec, …)	Discrete, linear, time-invariant Gaussian transition models of the form.
Preconditioner()	Coordinate change transformations as preconditioners in state space models.
NordsieckLikeCoordinates(powers, scales, …)	Nordsieck-like coordinates.

Class Inheritance Diagram