  Human Activity Recognition (HAR) is a cornerstone of ubiquitous computing,
with promising applications in diverse fields such as health monitoring and
ambient assisted living. Despite significant advancements, sensor-based HAR
methods often operate under the assumption that training and testing data have
identical distributions. However, in many real-world scenarios, particularly in
sensor-based HAR, this assumption is invalidated by out-of-distribution
($\displaystyle o.o.d.$) challenges, including differences from heterogeneous
sensors, change over time, and individual behavioural variability. This paper
centres on the latter, exploring the cross-user HAR problem where behavioural
variability across individuals results in differing data distributions. To
address this challenge, we introduce the Deep Temporal State Domain Adaptation
(DTSDA) model, an innovative approach tailored for time series domain
adaptation in cross-user HAR. Contrary to the common assumption of sample
independence in existing domain adaptation approaches, DTSDA recognizes and
harnesses the inherent temporal relations in the data. Therefore, we introduce
'Temporal State', a concept that defined the different sub-activities within an
activity, consistent across different users. We ensure these sub-activities
follow a logical time sequence through 'Temporal Consistency' property and
propose the 'Pseudo Temporal State Labeling' method to identify the
user-invariant temporal relations. Moreover, the design principle of DTSDA
integrates adversarial learning for better domain adaptation. Comprehensive
evaluations on three HAR datasets demonstrate DTSDA's superior performance in
cross-user HAR applications by briding individual behavioral variability using
temporal relations across sub-activities.
