Structural Time Series Models and the Kalman Filter: A Concise Review

The Particle Filter and Extended Kalman Filter methods for the structural system identification considering various uncertainties

Structural system identification using recursive methods has been a research direction of increasing interest in recent decades. The two prominent methods, including the Extended Kalman Filter (EKF) and the Particle Filter (PF), also known as the Sequential Monte Carlo (SMC), are advantageous in this field. In this study, the system identification of a shake table test of a 4-story steel struct...

The Role of the Kalman Filter in Time Series Econometrics

E conomic time series display features such as trend, seasonal, and cycle that we do not observe directly from the data. The cycle is of particular interest to economists as it is a measure of the fl uctuations in economic activity. An unobserved components model attempts to capture the features of a time series by assuming that they follow stochastic processes that, when put together, yield th...

Structural Time Series Models

1 Trend and Cycle Decomposition y t = t + t where y t is an n 1 vector and t and t represent trend and cycle components respectively. This decomposition into components is not unique. Beveridge and Nelson (1981) and Stock and Watson (1988) derive the following decomposition: y t = C(L)" t = C(1)" t + (1 L)C (L)" t Integrating up gives: y t = C(1) 1 X i=0 " ti | {z } + C (L)" t | {z } trend cycl...

Space–time Kalman filter

Design and Implementation of a Kalman Filter-Based Time-Varying Harmonics Analyzer

Nowadays with increasing use of numerous nonlinear loads, voltage and current harmonics in power systems are one of the most important problems power engineers encounter. Many of these nonlinear loads, because of their dynamic natures, inject time-varying harmonics into power system. Common techniques applied for harmonics measurement and assessment such as FFT have significant errors in presen...