# 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. 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. Stopping criteria for iterated filters/smoothers. FixedPointStopping([atol, rtol, …]) Keep updating until the filter recursion arrives at a fixed-point.

# 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¶

 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. Coordinate change transformations as preconditioners in state space models. NordsieckLikeCoordinates(powers, scales, …) Nordsieck-like coordinates.