KalmanPosterior

class probnum.filtsmooth.gaussian.KalmanPosterior(transition, locations=None, states=None, diffusion_model=None)

Bases: TimeSeriesPosterior, ABC

Posterior distribution after approximate Gaussian filtering and smoothing.

Parameters

• locations (Optional[Iterable[FloatLike]]) – Locations / Times of the discrete-time estimates.

• states (Optional[Iterable[randvars.RandomVariable]]) – Estimated states (in the state-space model view) of the discrete-time estimates.

• transition (GaussMarkovPriorTransitionArgType) – Dynamics model used as a prior for the filter.

Return type

None

Attributes Summary

frozen	Whether the posterior is frozen.
locations	Locations of the states of the posterior.
states	States of the posterior.

Methods Summary

__call__(t)	Evaluate the time-continuous posterior at location t
append(location, state)	Append a state to the posterior.
freeze()	Freeze the posterior.
interpolate(t[, previous_index, next_index])	Evaluate the posterior at a measurement-free point.
sample(rng[, t, size])	Draw samples from the filtering/smoothing posterior.
transform_base_measure_realizations(...)	Transform samples from a base measure to samples from the KalmanPosterior.

Attributes Documentation

frozen

Whether the posterior is frozen.

locations

Locations of the states of the posterior.

states

States of the posterior.

Methods Documentation

__call__(t)

Evaluate the time-continuous posterior at location t

Algorithm: 1. Find closest t_prev and t_next, with t_prev < t < t_next 2. Predict from t_prev to t 3. (if self._with_smoothing=True) Predict from t to t_next 4. (if self._with_smoothing=True) Smooth from t_next to t 5. Return random variable for time t

Parameters

t (ArrayLike) – Location, or time, at which to evaluate the posterior.

Raises

ValueError – If time-points are not strictly increasing.

Returns

Estimate of the states at time t.

Return type

randvars.RandomVariable or randvars._RandomVariableList

append(location, state)

Append a state to the posterior.

Parameters

• location (FloatLike) –

• state (RandomVariable) –

Return type

None

freeze()

Freeze the posterior.

Return type

None

abstract interpolate(t, previous_index=None, next_index=None)

Evaluate the posterior at a measurement-free point.

Returns

Dense evaluation.

Return type

randvars.RandomVariable or randvars._RandomVariableList

Parameters

• t (FloatLike) –

• previous_index (Optional[IntLike]) –

• next_index (Optional[IntLike]) –

sample(rng, t=None, size=())

Draw samples from the filtering/smoothing posterior.

If nothing is specified, a single sample is drawn (supported on self.locations). If locations are specified, a single sample is drawn on those locations. If size is specified, more than a single sample is drawn.

Internally, samples from a base measure are drawn and transformed via self.transform_base_measure_realizations.

Parameters

• rng (np.random.Generator) – Random number generator.

• t (Optional[ArrayLike]) – Locations on which the samples are wanted. Default is none, which implies that self.location is used.

• size (Optional[ShapeLike]) – Indicates how many samples are drawn. Default is an empty tuple, in which case a single sample is returned.

Returns

Drawn samples. If size has shape (A1, …, Z1), locations have shape (L,), and the state space model has shape (A2, …, Z2), the output has shape (A1, …, Z1, L, A2, …, Z2). For example: size=4, len(locations)=4, dim=3 gives shape (4, 4, 3).

Return type

np.ndarray

abstract transform_base_measure_realizations(base_measure_realizations, t)

Transform samples from a base measure to samples from the KalmanPosterior.

Here, the base measure is a multivariate standard Normal distribution.

Parameters

• base_measure_realizations (ndarray) – Shape (*size, N, d). Samples from a multivariate standard Normal distribution. N is either the len(self.locations) (if t == None), or len(t) + 1 (if t != None). The reason for the +1 in the latter is that samples at arbitrary locations need to be conditioned on a sample at the final time point.

• t (ArrayLike) – Shape (N,). Time points. Must include self.locations.Shape

Returns

Shape (*size, N, d) Transformed base measure realizations. If the inputs are samples from a multivariate standard Normal distribution, the results are size samples from the Kalman posterior at prescribed locations.

Return type

np.ndarray