In this paper, a new deconvolution estimator design method is proposed to solve the problems caused by unknown input for a discrete time-varying linear system (DTVLS). These problems arise in cases of image restoration or geological exploration. Our proposed method modifies the state estimate error x(k)-x(k) of traditional performance measures to the input estimate error u(k)-u(k) to develop a deconvolution estimator via game theory in an H∞ setting. In this paper, unknown input is estimated using noisy measurements, and statistical information about the process and measurement noises is not necessarily required in an H∞ setting. The new deconvolution estimator yields an estimated input that is close to the actual input and that leads to improvements in terms of MSE and PSNR for performance. © 2010 Elsevier B.V. All rights reserved.
Rho, H., Kang, Y. B., Hyun, S., & Kim, H. (2011). Discrete H∞ estimator design of unknown input: Game-theoretic approach. Signal Processing, 91(5), 1168–1181. https://doi.org/10.1016/j.sigpro.2010.11.003