Estimation of Toolface for Dynamic Point-the-bit Rotary Steerable Systems via Nonlinear Polynomial Filtering

In this article, the estimation problem of Toolface is investigated for the dynamic point-the-bit rotary steerable system (DPRSS), and it is essentially a nonlinear filtering problem under strong interference. First, the DPRSS is modeled by a continuous-time nonlinear system, which involves polynomial nonlinearities and strong interference whose amplitude is much larger than that of system states. By employing the Carleman approximation approach, a linear parameter varying system is derived from the polynomial nonlinear system, and a novel polynomial filter is constructed. Subsequently, several sufficient conditions in terms of parameter-dependent linear matrix inequalities (PDLMIs) are obtained to ensure the input-to-state stability of the filtering error system. Furthermore, the filter parameter can be calculated by solving PDLMIs through the sum of squares decomposition method. Finally, an experimental study on the DPRSS prototype is provided to show the effectiveness and applicability of the developed filtering scheme.