lmlib.statespace.cost.RLSAlssmSteadyState#

class lmlib.statespace.cost.RLSAlssmSteadyState(cost_model, steady_state_method='closed_form', **kwargs)#

Bases: lmlib.statespace.cost.RLSAlssmBase

Filter and Data container for Recursive Least Sqaure Alssm Filters in Steady State Mode

With RLSAlssmSteadyState a common \(W_k = W_{steady}\) is used for all samples (faster computation). Note that using a common \(W_k\) potentially leads to border missmatch effects and to completely invalid results when samples have individual sample weights.

See also

RLSAlssm

Methods

`__init__`(cost_model[, steady_state_method])
`eval_errors`(xs[, ks])	Evaluation of the squared error for multiple state vectors xs.
`filter`(y[, v])	Computes the intermediate parameters for subsequent squared error computations and minimizations.
`filter_minimize_x`(y[, v, H, h])	Combination of `RLSAlssmSteadyState.filter()` and `RLSAlssmSteadyState.minimize_x()`.
`minimize_v`([H, h, return_constrains])	Returns the state vector v of the squared error minimization with linear constraints
`minimize_x`([H, h])	Returns the state vector x of the squared error minimization with linear constraints
`set_backend`(backend)	Setting the backend computations option

Attributes

`W`	Filter Parameter \(W\)
`betas`	Segment scalars weights the cost function per segment
`cost_model`	Cost Model
`kappa`	Filter Parameter \(\kappa\)
`nu`	Filter Parameter \(\nu\)
`xi`	Filter Parameter \(\xi\)

property W#

Filter Parameter \(W\)

Type: ndarray

property betas#

Segment scalars weights the cost function per segment

Type: ndarray

property cost_model#

Cost Model

Type: CostSegment, CompositeCost

eval_errors(xs, ks=None)#: Evaluation of the squared error for multiple state vectors xs.

See also

RLSAlssm.eval_error

filter(y, v=None)#

Computes the intermediate parameters for subsequent squared error computations and minimizations.

Computes the intermediate parameters using efficient forward- and backward recursions. The results are stored internally, ready to solve the least squares problem using e.g., minimize_x() or minimize_v(). The parameter allocation allocate() is called internally, so a manual pre-allcation is not necessary.

Parameters

y (array_like) –
Input signal
RLSAlssm or RLSAlssmSteadyState

Single-channel signal is of shape =(K,) for
Multi-channel signal is of shape =(K,L)

RLSAlssmSet or RLSAlssmSetSteadyState
Single-channel set signals is of shape =(K,S) for
Multi-channel set signals is of shape =(K,L,S)

Multi-channel-sets signal is of shape =(K,L,S)
v (array_like, shape=(K,), optional) – Sample weights. Weights the parameters for a time step k and is the same for all multi-channels. By default the sample weights are initialized to 1.

K : number of samples
L : output order / number of signal channels
S : number of signal sets

filter_minimize_v(y, v=None, H=None, h=None)#

Combination of RLSAlssmSteadyState.filter() and RLSAlssmSteadyState.minimize_v().

This method has the same output as calling the methods

rls.filter(y)
xs = rls.minimize_v()