The Sliding Innovation Filter

Abstract

In this paper, a new filter referred to as the sliding innovation filter (SIF) is presented. The SIF is an estimation strategy formulated as a predictor-corrector that makes use of a switching gain and innovation term. In estimation theory, a trade-off exists between robustness to disturbances and optimality in terms of estimation error. Unlike the Kalman filter (KF), the SIF is a sub-optimal filter in the sense that it does not provide the optimal solution to the linear estimation problem. However, the switching gain provides an inherent amount of robustness to estimation problems that may be ill-conditioned or contain modeling uncertainties and disturbances. The paper includes the proof of stability and explanation of the SIF gain. Furthermore, the SIF is extended to nonlinear estimation problems using a Jacobian matrix, resulting in the extended sliding innovation filter (ESIF). The methods are applied to a linear and nonlinear aerospace actuator system under the presence of a leakage fault. The results of the simulation demonstrate the improved performance of the SIF and ESIF strategies over popular KF-based methods.

An Adaptive Formulation of the Sliding Innovation Filter

“…The sliding innovation filter (SIF) is a predictor-corrector estimator based on sliding mode concepts [25]. The difference between the KF and SIF is the structure of the corrective gain matrix.…”

“…The SIF gain is calculated using the measurement matrix, innovation, and sliding boundary layer term. An initial estimate is pushed towards the sliding boundary layer which is based on the upper limit of uncertainties in the estimation process [25]. If the estimate is within the sliding boundary layer, the estimates are forced to switch about the true state trajectory by the SIF gain.…”

“…Equations (2.1) through (2.6) represent the SIF estimation process for linear systems and measurements. The SIF proof of stability was discussed in detail in [25]. A Lyapunov function was defined based on the updated innovation, and was used to prove stability.…”

“…This method has demonstrated robustness to modeling uncertainties while providing a sub-optimal solution in terms of estimation accuracy [4,23,24]. More recently, the sliding innovation filter (SIF) was proposed, and it utilizes a simpler gain and yields a more accurate solution when compared with the SVSF [25]. A nonlinear version, similar to the EKF, was also presented called the extended SIF (ESIF).…”

“…A nonlinear version, similar to the EKF, was also presented called the extended SIF (ESIF). The SIF and ESIF applied in [25] utilized a fixed-width sliding boundary layer which assumes a constant upper limit to modeling uncertainty and noise.…”