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Förfiltrering av singnaler med kalmanfilter

Bengtsson, Gunnar (1969) In MSc Theses
Department of Automatic Control
Abstract
In this paper we discuss the problem of finding a suitable filter used as prefilter at digital Kalman filtering. The process is described by a stochastic state model. Two different filters are analyzed: a low-pass filter and a mean value filter. Especially we examine optimal choices of the parameters of the filters i.e. optimal integration area in the mean value filter and optimal time constant in the low-pass filter. In the analysis of the mean value filter it is supposed that the integration area h doesn't exceed the length of the sampling interval T. The analysis is carried out in a more general way and the results are applied to special dynamical systems: 1. A system of first order which can be described by a constant + noise. 2. A... (More)
In this paper we discuss the problem of finding a suitable filter used as prefilter at digital Kalman filtering. The process is described by a stochastic state model. Two different filters are analyzed: a low-pass filter and a mean value filter. Especially we examine optimal choices of the parameters of the filters i.e. optimal integration area in the mean value filter and optimal time constant in the low-pass filter. In the analysis of the mean value filter it is supposed that the integration area h doesn't exceed the length of the sampling interval T. The analysis is carried out in a more general way and the results are applied to special dynamical systems: 1. A system of first order which can be described by a constant + noise. 2. A system of second order which is oscillating and disturbed by noise. We find in these cases optimal choices of h and a (a denotes the time constant in the low-pass filter). In some cases it seems optimal to take h > T. This appears especially when the sampling interval is short. At long sampling intervals, on the other hand, we often get a considerable improvement by choosing h < T in comparison with the case h = T. In the studied cases the low-pass filter has proved to be the best. However, we get only a slight decrease in the information function when we choose a mean value filter with a suitable integration time. (Less)
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author
Bengtsson, Gunnar
supervisor
organization
year
type
H3 - Professional qualifications (4 Years - )
subject
publication/series
MSc Theses
report number
TFRT-5058
ISSN
0346-5500
language
Swedish
id
8850809
date added to LUP
2016-03-29 16:53:12
date last changed
2016-03-29 16:53:12
@misc{8850809,
  abstract     = {In this paper we discuss the problem of finding a suitable filter used as prefilter at digital Kalman filtering. The process is described by a stochastic state model. Two different filters are analyzed: a low-pass filter and a mean value filter. Especially we examine optimal choices of the parameters of the filters i.e. optimal integration area in the mean value filter and optimal time constant in the low-pass filter. In the analysis of the mean value filter it is supposed that the integration area h doesn't exceed the length of the sampling interval T. The analysis is carried out in a more general way and the results are applied to special dynamical systems: 1. A system of first order which can be described by a constant + noise. 2. A system of second order which is oscillating and disturbed by noise. We find in these cases optimal choices of h and a (a denotes the time constant in the low-pass filter). In some cases it seems optimal to take h > T. This appears especially when the sampling interval is short. At long sampling intervals, on the other hand, we often get a considerable improvement by choosing h < T in comparison with the case h = T. In the studied cases the low-pass filter has proved to be the best. However, we get only a slight decrease in the information function when we choose a mean value filter with a suitable integration time.},
  author       = {Bengtsson, Gunnar},
  issn         = {0346-5500},
  language     = {swe},
  note         = {Student Paper},
  series       = {MSc Theses},
  title        = {Förfiltrering av singnaler med kalmanfilter},
  year         = {1969},
}