ture the detailed walking patterns of a human subject.In other words,the energy distribution can serve as the"signature"for a human gait pattern. We extract the spectrogram signature as follows.First,we use the cycle time measured in the previous section to help us to find peaks on the torso contour curve.We then cut the spec- trograms into half-gait-cycles using these peaks.Each half- ce (cycles per gait-cycle contains the process of swinging one leg,which cond) could be the left or the right leg.We further divide the half- Figure 6.Distribution of cadence and torso speed. gait-cycle into 4 stages with equal length in time,which rep- resent the different stages for leg swinging.On each stage, we calculate the normalized energy on 40 frequency points by 人A0A人 averaging the FFT magnitudes during the stage.The shape of energy change in the frequency domain serves as the spectro- gram signature for the subject. The spectrogram signature can serve as a fingerprint of the Figure 7.Spectrogram signatures for five human subjects on stage 2 of gait pattern.Figure 7 plots signatures on stage 2 for five sub- the half-gait-cvcle. jects.For each subject,we plot the signature curve for 50 walking samples on the same graph.We observe that the sig- ject changes his walking speed for some tests,as the walking nature curves for the same subject are clustered together so speed actually increase linearly with the cadence for these that they appear to be a"thick"curve,while different subjects outliers.As tall people tend to have longer step lengths,we have very different signatures.These signatures are determ- also give the heights of these five subjects in Table 1.The ined by the gait patterns and other complex factors such as samples for subject C and E appear on a line with different the height and size of the person.Therefore,they can serve slope in Figure 6 than those for subject A,B and D because as unique characters for a human they are taller and have longer step lengths than others In WifU,we extract a set of 170 features for each walking To understand the relationship between footstep length and sample,including gait cycle length,estimated footstep length, height,we further run the footstep length estimation on a lar- the maximum,minimum,average,and variance for torso and ger data set that contains 49 persons,using the product of leg speeds during the gait cycle,and spectrogram signatures torso speed and cycle time as the estimator of the step size. for the 4 stages in the half-gait-cycle on 40 frequency points. The Pearson correlation coefficient between the height and the footstep length of the subject is 0.405 and the p-value is TRAINING AND CLASSIFICATION 0.0039.This shows that there is actually a positive correla- In this section,based on the features that we extract from tion between the estimated footstep length and the height of WiFi signals,we use machine learning techniques to build the subject.Note that due to the variance in human behavior, a gait recognition system.The first step for human recog- there are subjects that varies footstep length significantly dur- nition is enrollment.In this step,we collect gait instances ing the test and some subject have non proportional step size of the target human subject,which will be used as training to their heights.Nevertheless,the footstep length still can data.Our experimental results show that the number of gait serve as a useful feature for gait based recognition instances that WifiU needs is around 40.Although the target human subject needs to walk for a distance of 5~6 meters for Spectrogram Signatures 40 times in the enrollment phase,we can collect training data We propose a new set of features,called spectrogram signa- when the individual is using traditional identification mech- tures,to further describe the gait patterns in detail.As hu- anisms(such as access tokens)to identify himself to reduce mans may walk with similar speed and cadence,simply using the data collection effort. the two metrics of gait cycle time and torso speed may not sufficiently recognize an individual among a large candidate Using the data gathered in enrollment phase,WifiU trains a set.The spectrogram in Figure 3 actually provides more in- gait model for the target human subject,which can be either used for single user identification or multiple user recogni- formation than the gait cycle time and torso speed.For ex- tion applications.The single user identification application ample,the small green downward spikes appeared in almost every cycle,e.g.,at 1.7 and 2.3 seconds,are possibly caused answers the question whether the subject is the target person or a stranger and the multiple user recognition application an- by the lower leg or the foot of the supporting leg that has swers the question who the subject is among the given set of lower speed than the torso [27].Such detailed information enables us to characterize human gait patterns.To capture users.We use the LibSVM tool [5]with the Radial Basis human gait patterns from spectrograms,we use the distribu- Function(RBF)kernel in the training.The optimal values for parameters v and y for the RBF kernel are selected through tion of reflected energy on predetermined frequency points to serve as"signatures"of the spectrogram.These energy dis- grid search. tributions give an overview on how different body parts are To train a gait model for single user identification,we build a moving at a given stage of walking.Thus,they help to cap- classifier that can classify gait instances into two classes,one0.7 0.8 0.9 1 1.1 0.7 0.8 0.9 1 1.1 Cadence (cycles per second) Torso speed (m/s) A B C D E Figure 6. Distribution of cadence and torso speed. 50 100 0 0.05 0.1 Freq (Hz) Energy Subject A 50 100 0 0.05 0.1 Freq (Hz) Energy Subject B 50 100 0 0.05 0.1 Freq (Hz) Energy Subject C 50 100 0 0.05 0.1 Freq (Hz) Energy Subject D 50 100 0 0.05 0.1 Freq (Hz) Energy Subject E Figure 7. Spectrogram signatures for five human subjects on stage 2 of the half-gait-cycle. ject changes his walking speed for some tests, as the walking speed actually increase linearly with the cadence for these outliers. As tall people tend to have longer step lengths, we also give the heights of these five subjects in Table 1. The samples for subject C and E appear on a line with different slope in Figure 6 than those for subject A, B and D because they are taller and have longer step lengths than others. To understand the relationship between footstep length and height, we further run the footstep length estimation on a lar￾ger data set that contains 49 persons, using the product of torso speed and cycle time as the estimator of the step size. The Pearson correlation coefficient between the height and the footstep length of the subject is 0.405 and the p-value is 0.0039. This shows that there is actually a positive correla￾tion between the estimated footstep length and the height of the subject. Note that due to the variance in human behavior, there are subjects that varies footstep length significantly dur￾ing the test and some subject have non proportional step size to their heights. Nevertheless, the footstep length still can serve as a useful feature for gait based recognition. Spectrogram Signatures We propose a new set of features, called spectrogram signa￾tures, to further describe the gait patterns in detail. As hu￾mans may walk with similar speed and cadence, simply using the two metrics of gait cycle time and torso speed may not sufficiently recognize an individual among a large candidate set. The spectrogram in Figure 3 actually provides more in￾formation than the gait cycle time and torso speed. For ex￾ample, the small green downward spikes appeared in almost every cycle, e.g., at 1.7 and 2.3 seconds, are possibly caused by the lower leg or the foot of the supporting leg that has lower speed than the torso [27]. Such detailed information enables us to characterize human gait patterns. To capture human gait patterns from spectrograms, we use the distribu￾tion of reflected energy on predetermined frequency points to serve as “signatures” of the spectrogram. These energy dis￾tributions give an overview on how different body parts are moving at a given stage of walking. Thus, they help to cap￾ture the detailed walking patterns of a human subject. In other words, the energy distribution can serve as the “signature” for a human gait pattern. We extract the spectrogram signature as follows. First, we use the cycle time measured in the previous section to help us to find peaks on the torso contour curve. We then cut the spec￾trograms into half-gait-cycles using these peaks. Each half￾gait-cycle contains the process of swinging one leg, which could be the left or the right leg. We further divide the half￾gait-cycle into 4 stages with equal length in time, which rep￾resent the different stages for leg swinging. On each stage, we calculate the normalized energy on 40 frequency points by averaging the FFT magnitudes during the stage. The shape of energy change in the frequency domain serves as the spectro￾gram signature for the subject. The spectrogram signature can serve as a fingerprint of the gait pattern. Figure 7 plots signatures on stage 2 for five sub￾jects. For each subject, we plot the signature curve for 50 walking samples on the same graph. We observe that the sig￾nature curves for the same subject are clustered together so that they appear to be a “thick” curve, while different subjects have very different signatures. These signatures are determ￾ined by the gait patterns and other complex factors such as the height and size of the person. Therefore, they can serve as unique characters for a human. In WifiU, we extract a set of 170 features for each walking sample, including gait cycle length, estimated footstep length, the maximum, minimum, average, and variance for torso and leg speeds during the gait cycle, and spectrogram signatures for the 4 stages in the half-gait-cycle on 40 frequency points. TRAINING AND CLASSIFICATION In this section, based on the features that we extract from WiFi signals, we use machine learning techniques to build a gait recognition system. The first step for human recog￾nition is enrollment. In this step, we collect gait instances of the target human subject, which will be used as training data. Our experimental results show that the number of gait instances that WifiU needs is around 40. Although the target human subject needs to walk for a distance of 5∼6 meters for 40 times in the enrollment phase, we can collect training data when the individual is using traditional identification mech￾anisms (such as access tokens) to identify himself to reduce the data collection effort. Using the data gathered in enrollment phase, WifiU trains a gait model for the target human subject, which can be either used for single user identification or multiple user recogni￾tion applications. The single user identification application answers the question whether the subject is the target person or a stranger and the multiple user recognition application an￾swers the question who the subject is among the given set of users. We use the LibSVM tool [5] with the Radial Basis Function (RBF) kernel in the training. The optimal values for parameters ν and γ for the RBF kernel are selected through grid search. To train a gait model for single user identification, we build a classifier that can classify gait instances into two classes, one