DiscreteUKFComponent¶
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class
probnum.filtsmooth.
DiscreteUKFComponent
(non_linear_model, spread=0.0001, priorpar=2.0, special_scale=0.0)[source]¶ Bases:
probnum.filtsmooth.gaussfiltsmooth.unscentedkalman.UKFComponent
,probnum.statespace.discrete_transition.DiscreteGaussian
Discrete unscented Kalman filter transition.
Attributes Summary
- rtype
Methods Summary
assemble_sigma_points
(at_this_rv)Assemble the sigma-points.
backward_realization
(realization_obtained, rv)Backward-pass of a realisation of a state, according to the transition.
backward_rv
(rv_obtained, rv[, rv_forwarded, …])Backward-pass of a state, according to the transition.
forward_realization
(realization, t[, …])Forward-pass of a realization of a state, according to the transition.
forward_rv
(rv, t[, compute_gain, …])Forward-pass of a state, according to the transition.
from_ode
(ode, prior[, evlvar])jointly_sample_list_backward
(rv_list, locations)Jointly sample from a list of random variables, according to the present transition.
smooth_list
(rv_list, locations[, …])Apply smoothing to a list of random variables, according to the present transition.
Attributes Documentation
Methods Documentation
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backward_realization
(realization_obtained, rv, rv_forwarded=None, gain=None, t=None, _diffusion=1.0, _linearise_at=None, **kwargs)[source]¶ Backward-pass of a realisation of a state, according to the transition. In other words, return a description of
\[p(x(t) \,|\, {\mathcal{G}_t(x(t)) = \xi})\]for an observed realization \(\xi\) of \({\mathcal{G}_t}(x(t))\). For example, this function is called in a Kalman update step.
- Parameters
realization_obtained – Observed realization \(\xi\) as an array.
rv – “Current” distribution \(p(x(t))\) as a RandomVariable.
rv_forwarded – “Forwarded” distribution (think: \(p(\mathcal{G}_t(x(t)) \,|\, x(t))\)) as a RandomVariable. Optional. If provided (in conjunction with gain), computation might be more efficient, because most backward passes require the solution of a forward pass. If rv_forwarded is not provided,
forward_rv()
might be called internally (depending on the object) which is skipped if rv_forwarded has been providedgain – Expected gain. Optional. If provided (in conjunction with rv_forwarded), some additional computations may be avoided (depending on the object).
t – Current time point.
dt – Increment \(\Delta t\). Ignored for discrete-time transitions.
_diffusion – Special diffusion of the driving stochastic process, which is used internally.
_linearise_at – Specific point of linearisation for approximate forward passes (think: extended Kalman filtering). Used internally for iterated filtering and smoothing.
- Returns
RandomVariable – New state, after applying the backward-pass.
Dict – Information about the backward-pass.
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backward_rv
(rv_obtained, rv, rv_forwarded=None, gain=None, t=None, _diffusion=1.0, _linearise_at=None, **kwargs)[source]¶ Backward-pass of a state, according to the transition. In other words, return a description of
\[p(x(t) \,|\, z_{\mathcal{G}_t}) = \int p(x(t) \,|\, z_{\mathcal{G}_t}, \mathcal{G}_t(x(t))) p(\mathcal{G}_t(x(t)) \,|\, z_{\mathcal{G}_t})) d \mathcal{G}_t(x(t)),\]for observations \(z_{\mathcal{G}_t}\) of \({\mathcal{G}_t}(x(t))\). For example, this function is called in a Rauch-Tung-Striebel smoothing step, which computes a Gaussian distribution
\[p(x(t) \,|\, z_{\leq t+\Delta t}) = \int p(x(t) \,|\, z_{\leq t+\Delta t}, x(t+\Delta t)) p(x(t+\Delta t) \,|\, z_{\leq t+\Delta t})) d x(t+\Delta t),\]from filtering distribution \(p(x(t) \,|\, z_{\leq t})\) and smoothing distribution \(p(x(t+\Delta t) \,|\, z_{\leq t+\Delta t})\), where \(z_{\leq t + \Delta t}\) contains both \(z_{\leq t}\) and \(z_{t + \Delta t}\).
- Parameters
rv_obtained – “Incoming” distribution (think: \(p(x(t+\Delta t) \,|\, z_{\leq t+\Delta t})\)) as a RandomVariable.
rv – “Current” distribution (think: \(p(x(t) \,|\, z_{\leq t})\)) as a RandomVariable.
rv_forwarded – “Forwarded” distribution (think: \(p(x(t+\Delta t) \,|\, z_{\leq t})\)) as a RandomVariable. Optional. If provided (in conjunction with gain), computation might be more efficient, because most backward passes require the solution of a forward pass. If rv_forwarded is not provided,
forward_rv()
might be called internally (depending on the object) which is skipped if rv_forwarded has been providedgain – Expected gain from “observing states at time \(t+\Delta t\) from time \(t\)). Optional. If provided (in conjunction with rv_forwarded), some additional computations may be avoided (depending on the object).
t – Current time point.
dt – Increment \(\Delta t\). Ignored for discrete-time transitions.
_diffusion – Special diffusion of the driving stochastic process, which is used internally.
_linearise_at – Specific point of linearisation for approximate forward passes (think: extended Kalman filtering). Used internally for iterated filtering and smoothing.
- Returns
RandomVariable – New state, after applying the backward-pass.
Dict – Information about the backward-pass.
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forward_realization
(realization, t, _diffusion=1.0, _linearise_at=None, **kwargs)[source]¶ Forward-pass of a realization of a state, according to the transition. In other words, return a description of
\[p(\mathcal{G}_t[x(t)] \,|\, x(t)=\xi),\]for some realization \(\xi\).
- Parameters
realization – Realization \(\xi\) of the random variable \(x(t)\) that describes the current state.
t – Current time point.
dt – Increment \(\Delta t\). Ignored for discrete-time transitions.
compute_gain – Flag that indicates whether the expected gain of the forward transition shall be computed. This is important if the forward-pass is computed as part of a forward-backward pass, as it is for instance the case in a Kalman update.
_diffusion – Special diffusion of the driving stochastic process, which is used internally.
_linearise_at – Specific point of linearisation for approximate forward passes (think: extended Kalman filtering). Used internally for iterated filtering and smoothing.
- Returns
RandomVariable – New state, after applying the forward-pass.
Dict – Information about the forward pass. Can for instance contain a gain key, if compute_gain was set to True (and if the transition supports this functionality).
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forward_rv
(rv, t, compute_gain=False, _diffusion=1.0, _linearise_at=None, **kwargs)[source]¶ Forward-pass of a state, according to the transition. In other words, return a description of
\[p(\mathcal{G}_t[x(t)] \,|\, x(t)),\]or, if we take a message passing perspective,
\[p(\mathcal{G}_t[x(t)] \,|\, x(t), z_{\leq t}),\]for past observations \(z_{\leq t}\). (This perspective will be more interesting in light of
backward_rv()
).- Parameters
rv – Random variable that describes the current state.
t – Current time point.
dt – Increment \(\Delta t\). Ignored for discrete-time transitions.
compute_gain – Flag that indicates whether the expected gain of the forward transition shall be computed. This is important if the forward-pass is computed as part of a forward-backward pass, as it is for instance the case in a Kalman update.
_diffusion – Special diffusion of the driving stochastic process, which is used internally.
_linearise_at – Specific point of linearisation for approximate forward passes (think: extended Kalman filtering). Used internally for iterated filtering and smoothing.
- Return type
- Returns
RandomVariable – New state, after applying the forward-pass.
Dict – Information about the forward pass. Can for instance contain a gain key, if compute_gain was set to True (and if the transition supports this functionality).
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jointly_sample_list_backward
(rv_list, locations, _previous_posterior=None)¶ Jointly sample from a list of random variables, according to the present transition.
An explanation of the algorithm can be found in, for instance, this link 1.
References
- Parameters
rv_list (_RandomVariableList) – List of random variables to be sampled from (jointly).
locations – Locations \(t\) of the random variables in the time-domain. Used for continuous-time transitions.
_previous_posterior – Specify a previous posterior to improve linearisation in approximate backward passes. Used in iterated smoothing based on posterior linearisation.
- Returns
List of smoothed random variables.
- Return type
_RandomVariableList
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proc_noise_cov_cholesky_fun
(t)¶
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smooth_list
(rv_list, locations, _previous_posterior=None)¶ Apply smoothing to a list of random variables, according to the present transition.
- Parameters
rv_list (_RandomVariableList) – List of random variables to be smoothed.
locations – Locations \(t\) of the random variables in the time-domain. Used for continuous-time transitions.
_previous_posterior – Specify a previous posterior to improve linearisation in approximate backward passes. Used in iterated smoothing based on posterior linearisation.
- Returns
List of smoothed random variables.
- Return type
_RandomVariableList