This study investigates a real-time joint channel and hyperparameter estimation method for orthogonal frequency division multiplexing mobile communications. The channel frequency response of the pilot subcarrier and its fixed hyperparameters (such as channel statistics) are estimated using a Liu and West filter (LWF), which is based on the state-space model and sequential Monte Carlo method. For the first time, to our knowledge, we demonstrate that the conventional LWF biases the hyperparameter due to a poor estimate of the likelihood caused by overfitting in noisy environments. Moreover, this problem cannot be solved by conventional smoothing techniques. For this, we modify the conventional LWF and regularize the likelihood using a Kalman smoother. The effectiveness of the proposed method is confirmed via numerical analysis. When both of the Doppler frequency and delay spread hyperparameters are unknown, the conventional LWF significantly degrades the performance, sometimes below that of least squares estimation. By avoiding the hyperparameter estimation failure, our method outperforms the conventional approach and achieves good performance near the lower bound. The coding gain in our proposed method is at most 10 dB higher than that in the conventional LWF. Thus, the proposed method improves the channel and hyperparameter estimation accuracy. Derived from mathematical principles, our proposal is applicable not only to wireless technology but also to a broad range of related areas such as machine learning and econometrics.