Unscented Incremental Kalman Filter for Nonlinear Under Observed Systems

With the rapid development of tracking, navigation, signal processing, and image processing, nonlinear systems with multiplicative noise have been widely used in these fields. However, in practical engineering, unknown errors are introduced due to measurement errors and environmental factors, and traditional Kalman filtering methods are not suitable for state estimation problems in such situations. For nonlinear under observation systems with multiplicative noise and correlated noise, a decorrelation algorithm is first used to convert correlated noise into uncorrelated noise. Secondly, by introducing virtual state vectors and virtual noise, a virtual state equation is established to derive the system expression without multiplicative noise, and an incremental observation equation is introduced to eliminate unknown errors and simplify the model. Based on the simplified model, a unscented incremental Kalman filtering algorithm was proposed. Simulation examples demonstrate that the proposed algorithm can effectively address the impact of unobserved noise.