25 35 Time(seconds) Time (seconds) Time(seconds) (a)CSI waveform for walking (b)CSI waveform for falling (c)CSI waveform for sitting down 25 0.5 Time(seconds) Time (seconds) Time(seconds) (d)Sepctrogram for walking (e)Sepctrogram for falling (f)Sepctrogram for sitting down Figure 5:Waveforms and spectrograms for different activities. stantial energy are on high frequency components.After that,there the wavelength is 5.15 cm.Note that 7.7 m/s is already too fast is a quick transition to the silent state,where the movement energy a speed for a human to move with.Commercial WiFi NICs can reduces to nearly zero.By looking at these transitions between easily sample CSI values at a rate of up to 2500 samples/second, different states.we can infer that the person is possibly falling. which is far greater than the sampling rate required by the Nyquist Similarly,other human activities also contain states with can be criteria for a 300Hz signal.Thus,we can apply signal processing characterized by their movement speeds. techniques on the denoised CSI values and get the frequency com- Hidden Markov Model (HMM)is a suitable tool to build state ponents in CFR power and infer the speed.For slow movements transition models using time-dependent features.It has been ex- that only move a few centimeters per second,CARM utilizes wave- tensively used in several recognition applications such as speech let transforms to extract low frequency components below 1 Hz to recognition [18],handwriting recognition,and gesture recognition capture slow movements such as brushing teeth,see Section 6. in videos [6].Use of HMMs for activity recognition is based on Movement of different body parts:Time-frequency analysis the assumption that the sequence of observed feature vectors cor- tools can separate the movement of different body parts when they responding to an activity is generated by a Markov model,which is move at different speeds.For example,the weak energy bands in a finite state machine that changes state once every time unit.Each frequency components between 50~70 Hz in Figure 5(d)are actu- time a state is entered,a feature vector is generated from a prob- ally caused by swing of legs when walking [25].In general,CFR ability density called output probability density.Furthermore,the power changes caused by the movements of arms/legs have smaller transition from one state to another or back to itself is also prob- in energy compared to torso movements as the reflection areas for abilistic and is governed by a discrete probability called transition arms/legs are smaller.Our feature extraction process captures both probability.Hidden Markov Models are called hidden because in the body movement and arms/legs movements.Therefore,CARM practice,the sequence of feature vectors is known but the underly- can distinguish whether the activity involves the whole body or just ing sequence of states that generated those feature vectors is hid- arms/legs.For example,CARM can recognize falling,running and den. boxing,which are all high speed movements but involve different HMM can capture information from all training samples and body parts. thus works very well even when there is high within-class vari- Scenarios with multiple persons:When there are multiple per- ance.Provided that a sufficient number of representative training sons within the same room,CARM can recognize the activity when samples of an activity are available,an HMM can be constructed only one person is moving.see details in Section 8.When both that implicitly models all of the many sources of variability inherent persons are actively moving,we need multiple sender/receivers in the activity.Compared to existing works which uses statistical to capture the actions.Activities that are closer to the given features along a long period [10,27].HMM based models utilizes sender/receiver introduce higher distortions in CFR power.There- the transitions within the activity that provide more details about fore,we can use blind signal separation methods [15]to extract the activity.For details related to HMM model training and classi- CFR power distortions caused by different person.However,this fication,please refer to Section 7. is out of the scope of this paper and will be studied in our future works. 4.4 Discussion Detection of high-speed and low-speed movements:CARM 5.PCA BASED CSI DENOISING SCHEME can reliably detect both high-speed movement and low-speed CARM builds the HMM model in following three steps as de movements.Commercial WiFi devices provide CSI values with scribed in Sections 5.6,and 7,respectively.First,CARM collects sampling rates high enough to accurately obtain the values of these CSI values and removes the noises in the measurements.Second, frequencies.From our extensive activity dataset.we have observed CARM extracts human movement features from the denoised CSI that indoor human movements introduce frequency components of values using DWT.Third,CARM trains an HMM model for each no more than 300Hz in the CFR power,which corresponds to a top activity and uses the CSI-activity models to recognize activities in human movement speed of about 300 x 0.0515/2=7.7m/s,when real time.2 2.5 3 3.5 4 −15 −10 −5 0 5 10 15 Time (seconds) CSI (a) CSI waveform for walking 0.5 1 1.5 2 −40 −20 0 20 40 Time (seconds) CSI (b) CSI waveform for falling 0 0.5 1 1.5 2 −40 −20 0 20 Time (seconds) CSI (c) CSI waveform for sitting down (d) Sepctrogram for walking (e) Sepctrogram for falling (f) Sepctrogram for sitting down Figure 5: Waveforms and spectrograms for different activities. stantial energy are on high frequency components. After that, there is a quick transition to the silent state, where the movement energy reduces to nearly zero. By looking at these transitions between different states, we can infer that the person is possibly falling. Similarly, other human activities also contain states with can be characterized by their movement speeds. Hidden Markov Model (HMM) is a suitable tool to build state transition models using time-dependent features. It has been ex￾tensively used in several recognition applications such as speech recognition [18], handwriting recognition, and gesture recognition in videos [6]. Use of HMMs for activity recognition is based on the assumption that the sequence of observed feature vectors cor￾responding to an activity is generated by a Markov model, which is a finite state machine that changes state once every time unit. Each time a state is entered, a feature vector is generated from a prob￾ability density called output probability density. Furthermore, the transition from one state to another or back to itself is also prob￾abilistic and is governed by a discrete probability called transition probability. Hidden Markov Models are called hidden because in practice, the sequence of feature vectors is known but the underly￾ing sequence of states that generated those feature vectors is hid￾den. HMM can capture information from all training samples and thus works very well even when there is high within-class vari￾ance. Provided that a sufficient number of representative training samples of an activity are available, an HMM can be constructed that implicitly models all of the many sources of variability inherent in the activity. Compared to existing works which uses statistical features along a long period [10, 27], HMM based models utilizes the transitions within the activity that provide more details about the activity. For details related to HMM model training and classi- fication, please refer to Section 7. 4.4 Discussion Detection of high-speed and low-speed movements: CARM can reliably detect both high-speed movement and low-speed movements. Commercial WiFi devices provide CSI values with sampling rates high enough to accurately obtain the values of these frequencies. From our extensive activity dataset, we have observed that indoor human movements introduce frequency components of no more than 300Hz in the CFR power, which corresponds to a top human movement speed of about 300 × 0.0515/2 = 7.7m/s, when the wavelength is 5.15 cm. Note that 7.7 m/s is already too fast a speed for a human to move with. Commercial WiFi NICs can easily sample CSI values at a rate of up to 2500 samples/second, which is far greater than the sampling rate required by the Nyquist criteria for a 300Hz signal. Thus, we can apply signal processing techniques on the denoised CSI values and get the frequency com￾ponents in CFR power and infer the speed. For slow movements that only move a few centimeters per second, CARM utilizes wave￾let transforms to extract low frequency components below 1 Hz to capture slow movements such as brushing teeth, see Section 6. Movement of different body parts: Time-frequency analysis tools can separate the movement of different body parts when they move at different speeds. For example, the weak energy bands in frequency components between 50∼70 Hz in Figure 5(d) are actu￾ally caused by swing of legs when walking [25]. In general, CFR power changes caused by the movements of arms/legs have smaller in energy compared to torso movements as the reflection areas for arms/legs are smaller. Our feature extraction process captures both the body movement and arms/legs movements. Therefore, CARM can distinguish whether the activity involves the whole body or just arms/legs. For example, CARM can recognize falling, running and boxing, which are all high speed movements but involve different body parts. Scenarios with multiple persons: When there are multiple per￾sons within the same room, CARM can recognize the activity when only one person is moving, see details in Section 8. When both persons are actively moving, we need multiple sender/receivers to capture the actions. Activities that are closer to the given sender/receiver introduce higher distortions in CFR power. There￾fore, we can use blind signal separation methods [15] to extract CFR power distortions caused by different person. However, this is out of the scope of this paper and will be studied in our future works. 5. PCA BASED CSI DENOISING SCHEME CARM builds the HMM model in following three steps as de￾scribed in Sections 5, 6, and 7, respectively. First, CARM collects CSI values and removes the noises in the measurements. Second, CARM extracts human movement features from the denoised CSI values using DWT. Third, CARM trains an HMM model for each activity and uses the CSI-activity models to recognize activities in real time