  In this technical note, a recursive set-membership filtering algorithm for
discrete-time nonlinear dynamical systems subject to unknown but bounded
process and measurement noises is proposed. The nonlinear dynamics is
represented in a pseudo-linear form using the state dependent coefficient (SDC)
parameterization. Matrix Taylor expansions are utilized to expand the state
dependent matrices about the state estimates. Upper bounds on the norms of
remainders in the matrix Taylor expansions are calculated on-line using a
non-adaptive random search algorithm at each time step. Utilizing these upper
bounds and the ellipsoidal set description of the uncertainties, a two-step
filter is derived that utilizes the `correction-prediction' structure of the
standard Kalman Filter variants. At each time step, correction and prediction
ellipsoids are constructed that contain the true state of the system by solving
the corresponding semi-definite programs (SDPs). Finally, a simulation example
is included to illustrate the effectiveness of the proposed approach.
