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.

翻译：联合状态与未知输入估计的大多数工作均假定未知输入为线性；这一假设在许多智能自主系统中往往不成立，具有潜在局限性。为突破此限制并避免系统线性化，我们提出一种无导数未知输入Sigma-point卡尔曼滤波器，其中SPKF与可通过非线性优化及数据驱动方法实现的一般非线性未知输入估计器相耦合。该非线性未知输入估计器利用对状态预测误差敏感度较低的后验状态估计值。此外，我们引入联合Sigma-point变换策略，将状态与未知输入不确定性共同纳入SPKF-nUI的估计框架。深入的随机稳定性分析证明，在合理假设条件下，所提出的SPKF-nUI可生成指数收敛的估计误差界。最后，在基于仿真的刚性机器人与物理软体机器人（即由软材料制成且具有复杂动力学的机器人）两个案例中验证了所提滤波器对非线性动态系统的有效性。结果表明，与现有非线性状态-未知输入滤波器相比，所提出的SPKF-nUI在状态与未知输入估计误差方面均达到最低水平。