  Predicting future human motion plays a significant role in human-machine
interactions for various real-life applications. A unified formulation and
multi-order modeling are two critical perspectives for analyzing and
representing human motion. In contrast to prior works, we improve the
multi-order modeling ability of human motion systems for more accurate
predictions by building a deep state-space model (DeepSSM). The DeepSSM
utilizes the advantages of both the state-space theory and the deep network.
Specifically, we formulate the human motion system as the state-space model of
a dynamic system and model the motion system by the state-space theory,
offering a unified formulation for diverse human motion systems. Moreover, a
novel deep network is designed to parameterize this system, which jointly
models the state-state transition and state-observation transition processes.
In this way, the state of a system is updated by the multi-order information of
a time-varying human motion sequence. Multiple future poses are recursively
predicted via the state-observation transition. To further improve the model
ability of the system, a novel loss, WT-MPJPE (Weighted Temporal Mean Per Joint
Position Error), is introduced to optimize the model. The proposed loss
encourages the system to achieve more accurate predictions by increasing
weights to the early time steps. The experiments on two benchmark datasets
(i.e., Human3.6M and 3DPW) confirm that our method achieves state-of-the-art
performance with improved accuracy of at least 2.2mm per joint. The code will
be available at: \url{https://github.com/lily2lab/DeepSSM.git}.
