## 1 Introduction  
The Kalman filter has been widely investigated and applied in various engineering fields owing to its optimality and computational efficiency [1; 2; 3; 4; 5]. However, the optimality of the Kalman filter is guaranteed only if the system model is accurate and the information of the noise statistics is exactly known. In practical applications, an accurate model is difficult to obtain and the noise characteristics of the system are generally unknown. Thus, the estimation performance of the Kalman filter may degrade or diverge in the presence of model uncertainties and numerical errors [5; 6]. To address the issue of the divergence of the conventional Kalman filter, fading memory Kalman filters were investigated to improve the filtering robustness. Because heavy weighting of recent measurements increases the stability margin of the Kalman filter, the fading-memory algorithm provides robustness to the filter and an effective way of preventing the divergence of the Kalman filter. Moreover, it can facilitate a more general solution than conventional Kalman filters, because the fading-memory Kalman filter is reduced and equivalent to a conventional Kalman filter when the fading factor is taken as one. Another solution to solve the divergence problem of the conventional Kalman filter is by using the receding horizon (RH) estimation method. Unlike Kalman-filter-based approaches, the state estimation of an RH filter uses only recent finite measurements; thus, it is insensitive to erroneous modeling of the system and numerical errors. RH estimation has good properties such as bounded-input bounded-output (BIBO) stability, dead-beat property, fast-tracking ability, and robustness against modeling uncertainties and numerical errors. Furthermore, the RH estimators in [7; 8; 9; 10; 11; 12; 13; 14] do not require a priori knowledge of initial information. Thus, as an alternative to Kalman-filter-based methods, RH estimators have been extensively investigated recently [7; 8; 9; 10; 11; 12; 13; 14]. To achieve a better estimation performance, adopting the fading-memory method for designing the RH estimators is of significance. By combining the RH estimation and fading-memory methods, the robust characteristics of both the methods can be simultaneously incorporated into the design of RH estimators. With a constant fading factor, the fading-memory RH filters were proposed for linear continuous time-invariant and discrete time-varying state-space models in [17] and [10], respectively. For the RH smoothing problem, the fading-memory algorithm was applied to the fixed-lag RH smoother with a recursive form in [11]. The results in these approaches show that the combination of RH estimation and fading-memory strategy can provide faster tracking ability and better robustness concerning temporary modeling uncertainties than the fading Kalman filter and nonfading-memory RH filter. Thus, fading-memory RH estimation is reasonable and expected to improve estimation performance. However, previous approaches have only considered a constant fading factor, which makes it difficult to achieve the desired estimation performance for unpredictable disturbances. Moreover, although optimal RH estimators are combined with the fading-memory method, fading-memory RH estimators with a constant fading factor cannot guarantee optimal filtering [20]. Furthermore, a large fading-factor value may cause a loss of filtering accuracy. These problems can be solved by integrating the adaptive fading-memory algorithm into RH estimation and the estimation performance of an RH filter can be considerably improved compared to that of the constant one. In the case of fading-memory Kalman filtering, many adaptive fading-memory (AFM) Kalman filters have been proposed to adjust the fading factors [6; 20; 21; 22; 23; 24; 25; 26; 27]. However, the contribution to RH estimation based on the adaptive fading-memory strategy is limited.