Sigma-point Kalman Filter with Nonlinear Unknown Input Estimation via Optimization and Data-driven Approach for Dynamic Systems
This work addresses a restrictive assumption in state estimation for intelligent autonomous systems, offering a method that handles nonlinear unknown inputs without linearization, which is incremental as it builds on sigma-point Kalman filters.
The authors tackled the problem of joint state and unknown input estimation in nonlinear dynamic systems, where existing methods assume linear unknown inputs, by proposing a derivative-free Sigma-point Kalman Filter with a nonlinear unknown input estimator. Their results demonstrate that the proposed filter achieves the lowest state and unknown input estimation errors compared to existing nonlinear filters, as validated in simulation-based rigid robot and physical soft robot case studies.
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.