Statistical Analysis of Kalman Filters by Conversion to Gauss-Helmert Models with Applications to Process Noise Estimation

2010 ◽  
Author(s):  
Arne Petersen ◽  
Reinhard Koch
Keyword(s):  
Statistical Analysis ◽  
Kalman Filters ◽  
Noise Estimation ◽  
Process Noise

scholarly journals On-Line Learning of Linear Dynamical Systems: Exponential Forgetting in Kalman Filters

2019 ◽  
Vol 33 ◽  
pp. 4098-4105 ◽  
Author(s):  
Mark Kozdoba ◽  
Jakub Marecek ◽  
Tigran Tchrakian ◽  
Shie Mannor
Keyword(s):  
Kalman Filter ◽  
Kalman Filters ◽  
Linear Dynamical System ◽  
Process Noise ◽  
Linear Dynamical Systems ◽  
The Past ◽  
On Line ◽  
Regression Depth ◽  
Regret Bounds ◽  
On Line Learning

The Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter may be approximated by regression on a few recent observations. Surprisingly, we also show that having some process noise is essential for the exponential decay. With no process noise, it may happen that the forecast depends on all of the past uniformly, which makes forecasting more difficult.Based on this insight, we devise an on-line algorithm for improper learning of a linear dynamical system (LDS), which considers only a few most recent observations. We use our decay results to provide the first regret bounds w.r.t. to Kalman filters within learning an LDS. That is, we compare the results of our algorithm to the best, in hindsight, Kalman filter for a given signal. Also, the algorithm is practical: its per-update run-time is linear in the regression depth.

scholarly journals Adaptive Sigma-Point Kalman Filtering for Wind Turbine State and Process Noise Estimation

2018 ◽  
Vol 1037 ◽  
pp. 032003 ◽  
Author(s):  
B Ritter ◽  
E Mora ◽  
T Schlicht ◽  
A Schild ◽  
U Konigorski
Keyword(s):  
Wind Turbine ◽  
Kalman Filtering ◽  
Noise Estimation ◽  
Process Noise ◽  
Sigma Point

Statistical analysis of classification

1966 ◽  
Vol 24 ◽  
pp. 188-189
Author(s):  
T. J. Deeming
Keyword(s):  
Multivariate Analysis ◽  
Statistical Analysis ◽  
Classification Scheme ◽  
Analytical Procedure ◽  
Narrow Band ◽  
Scientific Research ◽  
Maximum Amount ◽  
Amount Of Information

If we make a set of measurements, such as narrow-band or multicolour photo-electric measurements, which are designed to improve a scheme of classification, and in particular if they are designed to extend the number of dimensions of classification, i.e. the number of classification parameters, then some important problems of analytical procedure arise. First, it is important not to reproduce the errors of the classification scheme which we are trying to improve. Second, when trying to extend the number of dimensions of classification we have little or nothing with which to test the validity of the new parameters.Problems similar to these have occurred in other areas of scientific research (notably psychology and education) and the branch of Statistics called Multivariate Analysis has been developed to deal with them. The techniques of this subject are largely unknown to astronomers, but, if carefully applied, they should at the very least ensure that the astronomer gets the maximum amount of information out of his data and does not waste his time looking for information which is not there. More optimistically, these techniques are potentially capable of indicating the number of classification parameters necessary and giving specific formulas for computing them, as well as pinpointing those particular measurements which are most crucial for determining the classification parameters.

Sign in / Sign up

Export Citation Format

Share Document