Roll and Pitch Estimation From IMU Data Using an LPV H Filter.

Fusion schemes used for estimating roll and pitch angles from inertial measurement unit (IMU) data typically suffer from one or more of the following limitations: sensitivity to inaccurate initial estimate, computational burden, and sensitivity to inaccurate noise model. This article introduces a new fusion algorithm called the linear parameter varying (LPV) $H_{\infty} $ filter, which aims to effectively address these limitations and strike a balance between them. The proposed LPV $H_{\infty} $ filter is a weighted sum of a number of local linear $H_{\infty} $ filters. Each local filter corresponds to a specific set of parameters, allowing for adaptability to different situations. By combining these local filters with their validity weights, the overall filter achieves robustness in the estimation process. The local filters and the overall filter are designed to be stable with fast dynamics, making the scheme less sensitive to inaccurate initial estimates. Moreover, the synthesis of the local filter gains is performed offline (beforehand), which reduces the computational burden during online implementation, making the proposed scheme more efficient and practical for real-time applications. To evaluate the effectiveness of the proposed scheme, a comparative study is conducted against two benchmark and most popular fusion schemes, namely, the highly accurate but computationally demanding fusion scheme of extended Kalman filter (EKF) as well as the adequately accurate yet computationally simple algorithm of explicit complementary filter (ECF). Through this comparative study, the performance of the LPV $H_{\infty} $ filter, using synthetic and experimental data, is assessed in terms of estimation accuracy/robustness against varying noise characteristics, computational efficiency, and sensitivity to inaccurate initial estimate.