Sigma-point Kalman Filter with Nonlinear Unknown Input Estimation via
  Optimization and Data-driven Approach for Dynamic Systems
Junn Yong Loo Ze Yang Ding Vishnu Monn Baskaran Surya Girinatha Nurzaman Chee Pin Tan
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.