  Most works on joint state and unknown input (UI) estimation require the
assumption that the UIs are linear; this is potentially restrictive as it does
not hold in many intelligent autonomous systems. To overcome this restriction
and circumvent the need to linearize the system, we propose a derivative-free
Unknown Input Sigma-point Kalman Filter (SPKF-nUI) where the SPKF is
interconnected with a general nonlinear UI estimator that can be implemented
via nonlinear optimization and data-driven approaches. The nonlinear UI
estimator uses the posterior state estimate which is less susceptible to state
prediction error. In addition, we introduce a joint sigma-point transformation
scheme to incorporate both the state and UI uncertainties in the estimation of
SPKF-nUI. An in-depth stochastic stability analysis proves that the proposed
SPKF-nUI yields exponentially converging estimation error bounds under
reasonable assumptions. Finally, two case studies are carried out on a
simulation-based rigid robot and a physical soft robot, i.e., robots made of
soft materials with complex dynamics to validate effectiveness of the proposed
filter on nonlinear dynamic systems. Our results demonstrate that the proposed
SPKF-nUI achieves the lowest state and UI estimation errors when compared to
the existing nonlinear state-UI filters.
