**1. Introduction**

Locomotion activity has recently raised great research interest because of its significant potentials in many fields, e.g., rehabilitation for injured people [1], surveillance systems or health care for the elderly [2], daily activity management. Among these researches [3], many different types of sensors are used, such as camera, wireless beacon, electromyogram (EMG) sensors, electrocardiography (ECG) sensors, and inertial measurement units (IMUs). In a smart home, camera system or wireless beacon can help to understand the activity pattern of the host, and then provide suggestions for a healthy life or make a decision when an emergency is coming [4]. On the other hand, for the wearable sensors, EMGs can measure the electrical signal of muscles, while ECGs placed on specific body parts can monitor the heart rate. These kinds of signals can be used for evaluating the activity intensity. However, camera systems need to be pre-installed and calibrated, and they are also sensitive to the light. EMGs and ECGs have cables with the host, and they are sensitive to the moisture. By contrast, IMU sensors are small enough to be placed on the body and can be taken anywhere, providing information like 3D acceleration, angular rate, and magnetic field readings. In this work, given the advantages of using IMUs, we propose to use these sensors to collect the acceleration and angular rate of motion for the purpose of activity recognition.

Numerous single sensor-based and multiple sensors-based applications were developed under different scenarios. It seems that using multiple sensors is quite interesting and can help to recognize more complex activities. For example, Hsu et al. [5] utilized two IMU sensors placed on wrist and ankle to detect 10 daily activities and 11 sport activities. Xie et al. [6] used a hybrid system of inertial sensor and barometer to detect locomotion and static activities. In this paper, we are studying a generic model that can be applied to the recognition of lower limb locomotion activity, this kind of model can work for both single sensor-based and multiple sensors-based applications; the difference is that multiple sensors generate a higher observation dimension than a single sensor. For simplification, the proposed model will be validated through only one IMU sensor placed on the lower limb.

The work proposed here is, to some extent, the continuation of our previous work [7], where a non-parametric triplet Markov chain (TMC-HIST) was designed to detect four lower limb locomotion activities: walking, running, stair ascent and stair descent. TMC [8,9] is an extension of the hidden Markov chain model (HMC) that includes: the observation *Y* and hidden state *X* processes and a third auxiliary hidden state *U* process. While it keeps a similar parameter estimation and restoration algorithm as HMC, in the TMC-HIST, the hidden state process represented the considered activities, the auxiliary one modelized the gait cycle, and histograms were used to represent the non-Gaussian observation density conditioned on each hidden state. We also developed an adaptive on-line algorithm that is based on TMC-HIST to recognize the targeted activities. Results showed that the combination of lower limb activity and gait cycle can significantly improve the recognition performance, and the adaptive parameter updating can gradually fit the motion pattern of people. However, the non-parametric histogram represented the marginal density of observation along one sensor axis, it does not involve the correlation among the three axes of sensor. As a consequence, this weakness may cause a failure when recognizing the activity. In addition, the precision of histogram is highly dependent on the volume of data and the width of bins, which require large storage memory and will slow down the processing speed of on-line recognition.

In this work, in order to overcome the weaknesses of TMC-HIST, we focus on developing a new parametric TMC model that can recognize lower limb locomotion activities using one single IMU sensor. Besides, the proposed algorithm should be adaptive and on-line applicable as well, i.e., it can adjust its parameters at run-time to suit for the user. By introducing a sojourn hidden state process to form semi-Markov structure, it allows the hidden states *X* and *U* keep the same for a while, which is consistent with the activity and gait transition during the motion. Semi-Markov structure is embedded into the TMC to better mimic the real state transition properties. Multi-dimensional Gaussian mixture model (GMM) is introduced to represent the non-Gaussian conditioned observation densities, in the meantime, it involves the observation correlation among the sensor axes. With the introduction of semi-Markov structure and Gaussian mixture density, the specific TMC model will be referred to as SemiTMC-GMM in the remaining of this paper. Because of the parametric densities, an on-line parameter learning algorithm based on EM is applied. Therefore, our claimed contributions in this paper are:


The remaining of the paper is organized as follows. Section 2 depicts the state-of-the-art works in the field of activity recognition using wearable sensors. Section 3 gives the definition of conventional TMC model and gradually extends the model to SemiTMC-GMM. Then, how to apply the proposed model to recognize lower limb locomotion activities is presented in detail at the end of this Section. Section 4 depicts both batch mode and on-line mode parameter learning for the proposed model. In Section 5, the proposed recognition algorithm is tested on two datasets: one is the public dataset [10], and the other is our own dataset. In addition, the performance of the proposed algorithm is discussed

compared to the competitive works. Finally, conclusions and future work are presented in the last Section.
