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achieved by the EKF estimates In addition, scaling parameters used for sigma-point selection
can be optimized to capture certain characteristic of the prior distribution if known, e g the
algorithm can be modified to work with distributions that have heavier tail than Gaussian
distributions such as Cauchy or Student-t distributions The new filter that results from using a
UKF for importance proposal distribution generation within a particle filter framework is
called the unscentedparticle filter (UPF)
3. NUMERICAL SIMULATIONS
Identification of nonlinear SDOF system: the EKF and the UKF
In this numerical simulation, performance of the UKF and the EKF was evaluated on
single-degree-of-freedom Bouc-Wen's hysteretic model as following
u
(3 1)
(32)
f (3 3)
where u(t) is displacement, ® n is natural frequency, £ is damping ratio, $ is
Bouc-Wen's nonlinear displacement related to nonlinear restoring force, u is ground
acceleration and / & y are shape-control parameters to be identified X is^state vector
used in the filtering techniques
Estimation performance was compared for 13 by 13 cases of initial guesses of £(0 | 0) and
(0 | 0) and estimation error (RMSE in percentile) was shown in Fig. 3 1 Performance
between the EKF and the UKF is strongly distinct The EKF diverges almost region of
simulation but the UKF shows robust estimation capability about the initial guesses of £(0 | 0)
and P(0|0)
%(0\0"> ieU '
a) The extended Kalman filter b) The unscented Kalman filter
Fig. 3 1 Root mean square error (RJVISE) of estimation