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¶
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Gaussian filtering and smoothing, i.e. Kalman-like filters and smoothers. |
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Continuous extended Kalman filter transition. |
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Discrete extended Kalman filter transition. |
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Continuous unscented Kalman filter transition. |
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Discrete extended Kalman filter transition. |
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Used for unscented Kalman filter. |
Posterior Distribution over States after Filtering/Smoothing. |
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Posterior Distribution after (Extended/Unscented) Kalman Filtering/Smoothing. |
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Iterated filter/smoother based on posterior linearisation. |
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Stopping criteria for iterated filters/smoothers. |
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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¶
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Computes mean and covariance of SDE solution. |
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Matrix fraction decomposition (without force). |
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Samples true states and observations at pre-determined timesteps “times” for a state space model. |
Classes¶
Markov transition rules in discrete or continuous time. |
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Stochastic differential equation. |
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Linear stochastic differential equation (SDE), |
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Linear time-invariant continuous Markov models of the form. |
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An integrator is a special kind of SDE, where the \(i\) th coordinate models the \(i\) th derivative. |
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Integrated Brownian motion in \(d\) dimensions. |
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Integrated Ornstein-Uhlenbeck process in \(d\) dimensions. |
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Matern process in \(d\) dimensions. |
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Random variable transitions with additive Gaussian noise. |
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Discrete, linear Gaussian transition models of the form. |
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Discrete, linear, time-invariant Gaussian transition models of the form. |
Coordinate change transformations as preconditioners in state space models. |
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Nordsieck-like coordinates. |