  Real-time identification of electrical equivalent circuit models is a
critical requirement in many practical systems, such as batteries and electric
motors. Significant work has been done in the past developing different types
of algorithms for system identification using reduced equivalent circuit
models. However, little work was done in analyzing the theoretical performance
bounds of these approaches. Proper understanding of theoretical bounds will
help in designing a system that is economical in cost and robust in
performance. In this paper, we analyze the performance of a linear recursive
least squares approach to equivalent circuit model identification and show that
the least squares approach is both unbiased and efficient when the
signal-to-noise ratio is high enough. However, we show that, when the
signal-to-noise ratio is low - resembling the case in many practical
applications - the least squares estimator becomes significantly biased.
Consequently, we develop a parameter estimation approach based on total least
squares method and show it to be asymptotically unbiased and efficient at
practically low signal-to-noise ratio regions. Further, we develop a recursive
implementation of the total least square algorithm and find it to be slow to
converge; for this, we employ a Kalman filter to improve the convergence speed
of the total least squares method. The resulting total Kalman filter is shown
to be both unbiased and efficient in equivalent circuit model parameter
identification. The performance of this filter is analyzed using real-world
current profile under fluctuating signal-to-noise ratios. Finally, the
applicability of the algorithms and analysis in this paper in identifying
higher order electrical equivalent circuit models is explained.
