

Title of Thesis
Adaptive Estimation Using State Space Methods 
Author(s)
Maj Muhammad
Salman 
Institute/University/Department
Details College of Electrical and Mechanical Engineering
/ National University of Sciences and Technology, Rawalpindi 
Session 2009 
Subject Engineering Electrical 
Number of Pages 129 
Keywords (Extracted from title, table of contents and
abstract of thesis) Spectrum, Development, Leakage,
Adaptive, Methods, State, Prediction, Space, Using, Mathematical,
Estimation 
Abstract This thesis focuses
on the development of new variants of adaptive filters. Built around
statespace framework, the proposed filters are especially suitable
for applications like tracking, output feedback control and
recursive spectrum estimation. They operate without prior knowledge
of process and observation noise statistics and exhibit good
stability properties.The development in this thesis can broadly be
classified into statespace least mean square (SSLMS) and finite
memory leastsquares filters.
SSLMS is a generalization of the wellknown least mean square (LMS)
filter. Incorporating linear timevarying statespace model of the
underlying environment, SSLMS exhibits marked improvement in its
tracking performance over the standard LMS. An extension of SSLMS is
SSLMS with adaptive memory (SSLMSWAM).SSLMSWAM iteratively tunes the
stepsize parameter by stochastic gradient method in an attempt to
yield its most appropriate value.This filter is useful for
situations where a suitable value of stepsize parameter is
difficult to obtain beforehand.
Recursive nature of an adaptive filter brings with it stability
issues. The concept of finite memory (or receding horizon) for an
adaptive filter is appealing because it ensures stability.This
motivates the development of finite memory filters, both for
unforced and forced systems. Finite impulse response (FIR) adaptive
filter, built around structure of an unforced system, uses weighted
observations on a finite interval. Uniform weighting of the
observations results in rectangular RLS (RRLS). Additional
flexibility is achieved by developing an adaptive memory variant of
FIR adaptive filter.Similar to SSLMSWAM, the data window size is
iteratively tuned so as to minimize the prediction error. For the
forced system case, a useful solution in the form of receding
horizon state observer is obtained. It finds utility in output
feedback control of linear timevarying systems. An insight into
convergence properties of finite memory based filters is provided by
the convergence analyses.
Spectrum update with the arrival of new data is a desirable feature
in realtime spectrum estimation applications.The mathematical
equivalence of RRLS resonator bank and recursive discrete Fourier
transform (DFT) gives the rationale for using the newly developed
filters for recursive spectrum estimation. A symmetric windowed
variant of RRLS called ‘truncated exponential RLS (TERLS)’ is useful
for reducing spectral leakage.Same is true for an SSLMS resonator,
which has an attractive feature that spectral side levels and main
lobe width may be reduced simultaneously by reducing the stepsize
parameter. The higher order resonator (HOR), constructed from
several SSLMS resonators, exhibits close resemblance to an ideal
(rectangular) frequency bin, thus minimizing spectral leakage and
increasing resolution. 
