Wi-Fi has shown enormous potential for indoor localization because of its wide utilization and availability. Enabling the use of Wi-Fi for indoor localization necessitates the construction of a fingerprint and the adoption of a learning algorithm. The goal is to enable the use of the fingerprint in training the classifiers for predicting locations. Existing models of machine learning Wi-Fi-based localization are brought from machine learning and modified to accommodate for practical aspects that occur in indoor localization. The performance of these models varies depending on their effectiveness in handling and/or considering specific characteristics and the nature of indoor localization behavior. One common behavior in the indoor navigation of people is its cyclic dynamic nature. To the best of our knowledge, no existing machine learning model for Wi-Fi indoor localization exploits cyclic dynamic behavior for improving localization prediction. This study modifies the widely popular online sequential extreme learning machine (OSELM) to exploit cyclic dynamic behavior for achieving improved localization results. Our new model is called knowledge preserving OSELM (KP-OSELM). Experimental results conducted on the two popular datasets TampereU and UJIndoorLoc conclude that KP-OSELM outperforms benchmark models in terms of accuracy and stability. The last achieved accuracy was 92.74% for TampereU and 72.99% for UJIndoorLoc.