## 1 Introduction  
As people age, their gait experiences some level of impairment [1]. Elderly gait is commonly characterized by slower speeds, shorter strides, and increased double-support stance phase [2; 3; 4; 5; 6]. Research indicates that individuals aged 70 and above often exhibit these pronounced gait changes [7; 8; 9]. These disturbances to gait can often lead to a reduction in quality of life and limit mobility [10]. Additionally, the risk of gait disorders increase with age, and neurological gait disorders such as Parkinson's Disease become more common [3; 11; 12]. With the world experiencing an aging population problem, the number of persons over 65 is expected to increase. High habitual activity levels and early interventions can help improve gait and reduce gait impairment associated with age [12; 13]. In recent years, elderly gait training using augmented reality (AR) has shown very promising results. Virtual reality (VR) and AR when applied to gait training can lead to significant improvements in balance, gait speed, and overall mobility among older adults [14; 15; 16; 17]. Moreover, research also suggests that holographic displays and AR can further aid in gait coordination in the elderly [18; 16]. The application of AR with real-time feedback has also been explored for its effects on gait function in gait-impaired individuals, highlighting the versatility of AR technologies in addressing various mobility challenges [19]. In addition to these advancements, the integration of avatars in AR for gait training presents a novel approach to enhancing rehabilitation outcomes [20; 21; 22]. By using a synchronized walking avatar, users can receive spatial and temporal cues that mimic natural human movement, thereby promoting better gait patterns and reducing the risk of falls. [PERSON] et al. (2019) emphasized the validity and usability of an avatar-based biofeed-back system for gait training, indicating the feasibility of using avatars to enhance gait training with minimal setup time [23]. This underscores the practicality of incorporating avatar-based biofeedback in gait rehabilitation programs to improve gait performance efficiently [23]. Additionally, [PERSON] and [PERSON] (2021) highlighted the advantages of intentionally synchronizing gait with an avatar in gait training [24]. They suggested that this method can help individuals adjust to gait asymmetries and enhance motor function. By using synchronized avatars, gait training can be customized to meet individual needs, thereby improving the effectiveness of rehabilitation programs. In our previous study [25], we explored the effects of a synchronized walking avatar on the gait of young healthy participants. The study used instantaneous distance changes between the participant and avatar as a visual spatial cue to the participants. The results showed that instantaneous increases and decreases in the distance led to similar increases and decreases, respectively, in the stride length of the user irrespective of the changes in phase difference. Simultaneously, the avatar and participant phase difference changes were provided as temporal cues. Similarly, the increases and decreases in the phase difference had proportional changes in the cycle time of the participant. The study showed that despite simultaneous spatial and temporal cueing, spatial and temporal gait parameters could be targeted largely independently. However, the efficacy of this approach has not been evaluated on elderly participants, and cognitive and physical differences in age could alter the effects [26; 27]. Additionally, while the previous method for human-phase estimation was sufficient for studies involving healthy young individuals with minimal gait variability, it may not be adequate for elderly gait. A more robust phase estimation and synchronization module may be necessary to effectively handle the synchronization between the avatar and elderly users.