The increasing prevalence of cognitive disorders among the elderly is a significant consequence of the global aging phenomenon. Wandering stands out as the most prominent and challenging symptom in these patients, with potential irreversible consequences such as loss or even death. Thus, harnessing technological advancements to mitigate caregiving burdens and disease-related repercussions becomes paramount. Numerous studies have developed algorithms and smart healthcare and telemedicine systems for wandering detection. Broadly, these algorithms fall into two categories: those estimating path complexity and those relying on historical trajectory data. However, motion signal processing methods are rarely employed in this context. This paper proposes a motion-signal-processing-based algorithm utilizing the wavelet packet transform (WPT) with a fourth-order Coiflet mother wavelet. The algorithm identifies wandering patterns solely based on patients’ positional data on the current traversed path and variations in wavelet coefficients within the frequency–time spectrum of motion signals. The model’s independence from prior motion behavior data enhances its compatibility with the pronounced instability often seen in these patients. A performance assessment of the proposed algorithm using the Geolife open-source dataset achieved accuracy, precision, specificity, recall, and F-score metrics of 83.06%, 92.62%, 83.06%, 83.06%, and 87.58%, respectively. Timely wandering detection not only prevents irreversible consequences but also serves as a potential indicator of progression to severe Alzheimer’s in patients with mild cognitive impairment, enabling timely interventions for preventing disease progression. This underscores the importance of advancing wandering detection algorithms.