Minimum-energy filtering on the unit circle using velocity measurements with bias and vectorial state measurements

We consider minimum-energy filtering of a system defined on the unit circle when the angular velocity measurements are contaminated with deterministic measurement error and bias. We propose a second order approximate minimum-energy filter for this system using vectorial measurements. This work extends prior work in two aspects; Firstly, by including a model for slowly time varying angular velocity measurement bias, we estimate and reject the bias in order to estimate the state of the system more accurately. Secondly, rather than using full state measurements we use vector measurements to derive the filter. Both of these two innovations make the filter more practical in real world applications. In simulations we show that the proposed filter is globally convergent and robust to different levels of measurement error and bias.