Event-based state estimation under constrained bit rate: An encoding–decoding approach

This paper is concerned with the state estimation problem for a class of linear continuous-time systems under bit rate constraints. The data transmission between the sensors and the estimator is implemented through a digital communication network with limited bandwidth. By resorting to the singular value decomposition technique, an event-based encoding strategy is developed to encode the measurement signals into 1-bit codewords so as to reduce network resource consumption. The Zeno phenomenon is first proven to be excluded, and then a sufficient condition is established under which the decoding error is ultimately bounded. Subsequently, a necessary condition is proposed to derive a lower bound of the bit rate below which the decoding error diverges. Moreover, the explicit expression of the desired state estimator is parameterized and the boundedness of the estimation errors is also analyzed. Finally, two simulation examples are presented to validate the effectiveness of the proposed theoretical results.