Filter and Data container for Recursive Least Sqaure Alssm Filters using Sets 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.

RLSAlssmSet

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 RLSAlssmSetSteadyState.filter() and RLSAlssmSetSteadyState.minimize_x(). minimize_v([H, h, broadcast_h, ...]) Returns the state vector v of the squared error minimization with linear constraints minimize_x([H, h, broadcast_h]) Returns the state vector x of the squared error minimization with linear constraints set_backend(backend) Setting the backend computations option set_kappa_diag(b)

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
eval_errors(xs, ks=None)#

Evaluation of the squared error for multiple state vectors xs.

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

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

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_x(y, v=None, H=None, h=None, **kwargs)#

property kappa#

Filter Parameter $$\kappa$$

Type

ndarray

Returns the state vector v of the squared error minimization with linear constraints

Returns the state vector x of the squared error minimization with linear constraints

property nu#

Filter Parameter $$\nu$$

Type

ndarray

set_backend(backend)#

Setting the backend computations option

Parameters

backend (str) – ‘py’, for python backend, ‘jit’ for Just in Time backend

property xi#

Filter Parameter $$\xi$$

Type

ndarray