Discrete H∞ estimator design of unknown input: Game-theoretic approach

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.