Reduced Fuzzy Recursive Least-Squares Algorithm For Real Time Estimation
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Date
2018-04
Authors
Cheah, Kah Wai
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Adaptive filtering is an online signal processing application that is capable of estimating
parameters for the characterization of a real time system. The estimation is done based on the
mean-square error (MSE) minimization of the difference between some desired output and the
output of the adaptive filter. The unknown transfer function is assumed to be a known structure
and is realized by three different structures which are commonly used in conventional adaptive
filtering: (i) the finite-duration impulse response (FIR) filter, (ii) the infinite-duration impulse
response (IIR) filter, and (iii) the nonlinear filter. However, there are limitations on each struc-
tures: (i) the FIR filter is limited for linear and almost linear system, (ii) the IIR filter works
well with linear feedback system but encounters some instability issue when implementing the
structure in practice, and (iii) the nonlinear filter requires higher order to describe the unknown
nonlinearity and it is prone to ill-conditioned system. Motivated by the fuzzy approach, this
thesis seeks to investigate the capabilities of the fuzzy system in overcoming the limitations
above. By formulating the adaptive filter as a generalized transfer function to include both
feedforward and feedback mechanism, an interesting connection between adaptive filtering
and fuzzy system is established. It is discovered that fuzzy mapping can be used to realize the
unknown input-output relationship in adaptive filtering without prior assumption on the adap-
tive filter structure. This thesis extends the fuzzy recursive least-squares (FRLS) algorithm
proposed by Wang and Mendel (1993a) to develop a more computational simplified algorithm
which is the reduced FRLS algorithm. The reduced fuzzy basis function associated with the
reduced FRLS algorithm is defined based on the Triangular-shaped membership function. In
literature, the Triangular-shaped membership function may not be well-defined in the metric
space due to the possibility of zero total partitioned space.
Description
Keywords
Reduced fuzzy recursive Ieast-squares algorithm , for real time estimation