Discrete Unilateral Constrained Extended Kalman Filter in an Embedded System

Since its publication in the 1960s, the Kalman Filter (KF) has been a powerful tool in optimal state estimation. However, the KF and most of its variants have mainly focused on the state estimation of smooth systems. In this work, we propose a new algorithm called the Discrete Unilateral Constrained Extended Kalman Filter (DUCEKF) that expands the capabilities of the Extended Kalman Filter (EKF) to a class of hybrid mechanical systems known as systems with unilateral constraints. Such systems are non-smooth in position and discontinuous in velocity. Lyapunov stability theory is invoked to establish sufficient conditions for the estimation error stability of the proposed algorithm. A comparison of the proposed algorithm with the EKF is conducted in simulation through a case study to demonstrate the superiority of the DUCEKF for the state estimation tasks in this class of systems. Simulations and an experiment were developed in this case study to validate the performance of the proposed algorithm. The experiment was conducted using electronic hardware that consists of an Embedded System (ES) called "Mikromedia for dsPIC33EP" and an external DAC-12 Click board, which includes a Digital-to-Analog Converter (DAC) from Texas Instruments.