Optimal enforcement of causality in non-parametric transfer function estimation

• Traditionally, non-parametric impulse and frequency response functions are estimated by taking the ratio of power spectral density estimates. However, this approach may often lead to non-causal estimates. In this letter, we derive a closed form expression for the impulse response estimator by smoothed empirical transfer function estimate, which allows optimal enforcement of causality on non-parametric estimators based on spectral analysis. The new method is shown to be asymptotically unbiased and of minimum covariance in a positive semidefinite sense among a broad class of linear estimators. Numerical simulations illustrate the performance of the new estimator. 

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Causality

ETFE

Non-parametric estimation

Spectral analysis

System identification

Frequency response

Identification (control systems)

Impulse response

Spectral density

Spectrum analysis

Transfer functions

Closed-form expression

Empirical transfer function estimates

Frequency response functions

Non-parametric estimations

Positive semidefinite

Transfer function estimation

Parameter estimation

Publication and Content Type

ref (subject category)

art (subject category)