Observer design for nonlinear systems with multi-rate sampled outputs - Application to attitude estimation

Abstract

The present paper proposes an observer for a class of nonlinear systems with multi-rate sampled outputs. Each output can have irregular and aperiodic sampling rate independent of the others. This work extends previous studies on high gain observer to permit the estimation of multi-rated output systems. The stability is proved by using a Lyapunov approach, providing that the sampling rates of each outputs are respectively smaller than their associated upper bound. The observer is then applied to the attitude estimation problem.

Continuous-Discrete Time Observer Design for Multi-Output Linear Continuous Systems With Aperiodic Asynchronous Measurements

“…Remark 2: The convergence of the proposed observer could be obtained by using similar ideas as in [3]. In this case, the convergence is obtained by considering the Lyapunov function corresponding to the continuous observer error system, its derivative is computed and an inequality is obtained with the derivative on the left hand-side and a term depending on the Lyapunov function and its integral on the right-hand side.…”

“…On the continuous estimate side, a class of nonlinear uniformly observable systems with a cascade structure has been considered in [28], but the use of a constant gain observer lead to very small practical sampling periods. This class of systems has been further considered in [3] where an observer with continuous estimates and based on an output error predictor and an high-gain approach is proposed. The sampling periods can be taken larger than in [28] in practice, but the maximum values for the sampling periods guaranteed by the convergence analysis may be very low.…”

State Observer Under Multi-Rate Sensing Environment and Its Design Using l2-Induced Norm

“…In [20], a moving horizon estimation method of state has been studied for the case when the sampling rates of the sensors are not uniform. Other various studies about multi-rate observers are investigated in many aspects (nonlinear systems [21], continuous systems [22], asynchronous measurement [23]). It is significant to carry out research from the viewpoint of realizing a control system with a short sampling period for control.…”

An Online Interval-Based Inertial Navigation System for Control Purposes of Autonomous Boats

“…• A combination of three low-cost accelerometers together with gyrometers [see, e.g., Mahony et al (2008), Premerlani and Bizard (2009), and Bonargent et al (2020)]. This might require basic bias calibration, and some movement conditions might cause problems during initialization (related to the estimation of the gravity vector direction in the sensor data), even though those situations are commonly unlikely.…”