Kalman-Like Filter Under Binary Sensors

This article is concerned with the Kalman-like filtering (KLF) problem for linear and nonlinear dynamic systems observed by binary sensors. Binary sensors are a special class of sensors that output only one bit of data and have considerable advantages in terms of energy consumption and economic costs. However, it is difficult to directly use binary sensors to estimate system states since the available information is compressed to the extreme and is difficult to be extracted. To address this problem, this article proposes an uncertainty measurement model to capture the innovations generated from binary sensors by analyzing their characteristics. Based on the proposed model, the KLFs are constructed for linear and nonlinear dynamical systems. Then, to deal with the uncertainties induced by binary sensors, conservative error covariances with adjustable parameters are derived for the KLFs via matrix inequalities and unscented transform. The optimal filter gains and some adjustable parameters are obtained by minimizing the traces and the upper bounds of the conservative covariances, respectively. Finally, arterial O
₂
system and damped mass-spring system are employed to show the effectiveness and advantages of the proposed methods.