Remote Estimation for Energy Harvesting Systems Under Multiplicative Noises: A Binary Encoding Scheme With Probabilistic Bit Flips

In this article, we investigate the state estimation problem for a class of networked systems with energy harvesting technologies, where the sensor is capable of replenishing energy from the environment. The underlying system is subject to both additive and multiplicative stochastic noises, and the measurement is transmitted to the remote estimator only when the current energy storage is larger than the transmission energy consumption. A binary encoding scheme is utilized in the communication process, under which the measurements are quantized into a bit string, transmitted via memoryless binary symmetric channels with certain probabilistic bit flips, and recovered at the receiver. A minmax robust estimator is designed to minimize the worst-case covariance of the estimation error in terms of the solutions to Riccati-like difference equations. Furthermore, the influence of the length of bit stream on the transmission rate and the estimation performance is discussed, and conditions guaranteeing the boundedness of the proposed estimator are provided. Finally, a numerical example is exploited to verify the effectiveness of the results.