Estimating Carrier’s Height by Accelerometer Signals of a Smartphone

The scope of our investigation includes two aspects of smartphones (mobile devices). First one is to search for possibilities of accelerometer signal analysis with a view to identification of biological or behavioral information (static or dynamic) of humans. For an example of this direction of studies where accelerometer signal is used among others (including positioning information) to recognize human behavior, refer to Pei et al. [1]. And there are quickly expanding number of medical and health care applications that utilize internal sensors of Apple iOS devices. Second one is related to the security issues of smartphones, that is, if a user takes his/her height or other information for private, and that information could be detectable by smartphone, it should be that the user is able to decide to or not to activate that functionality. Examples of unexpected or unattended privacy issues include extraction of speech from outside of soundproof glass by the use of video camera [2], or recovering text entered on keyboard by monitoring vibration via accelerometer of a smartphone placed on the desk [3].

Experimental setup. Participants went up the stairs in two conditions, (a) with a smartphone in the bag, or (b) in pants pocket. The small black bar is a smartphone.

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In our experiment, accelerometer signals were stored while the participants went up the stairs carrying a smartphone with them. We defined features based on the time course of the acceleration. As a result, we found out features that are highly correlated with height of participants.

In this section, we describe experimental procedures, specification of the smartphone and the accelerometer, definitions of the features, then we summarize the results.

Procedures. Thirteen participants were instructed to go up the stairs (twelve-step stairs) in their natural ways. They were also instructed to make the first step with their right foot. They did so four times, two times with carrying a bag (2 kg in weight) in their right hand (a smartphone was placed firmly in the bag), the rest two times with a smartphone in their right frontal pants pocket. Figure 1 illustrates the experimental situation.

Smartphone. The smartphone was HTC Desire SoftBank X06HT (60 mm \(\times \) 119 mm \(\times \) 12 mm, 135 g, OS: Android 2.2); sampling interval of acceleration was about 20 ms and the range was \(\pm 2\) g, where g is the earth’s gravity, \(9.8\,\mathrm {m}/\mathrm {s}^2\).

Data selection. In analyzing data, we have omitted the first step and the last two steps (12th and 13th step; note we need thirteen steps to go up twelve-step stairs). The reason why we omitted the first and the last step is that, in those steps, ascending motion is made only halfway. The reason of omission of the second last step was that we wanted to equalize the number of samples from the right and the left steps.

Definition of the Features. The features we adopted are categorized into two groups, group I and group II, with respect to in what way accelerometer signals are used. Group I features are defined directly by the profile of the vertical component of the signal. We thought the vertical component was effective in the bag condition since the bag’s—hence the smartphone’s—direction is approximately fixed and might well represent the participant’s vertical motion, which is expected to be more related to the participant’s bodily dimension than horizontal motion. Group II features are defined in such a way that they are usable in the situation where smartphone’s direction keeps changing in time (this applies to the pants pocket condition). Therefore the features are defined not by specific vector component of accelerometer signal but by the magnitude a(t) of accelerometer signal vector. Yet there remains a serious problem in using the magnitude of accelerometer signal. That is, there is always a bias due to the earth’s gravity. To do a workaround on this problem, we defined pseudo acceleration at time t, \(\tilde{a}(t)\), as \(\tilde{a}(t) = a(t) - g\) (see Fig. 2(a)). Then pseudo velocity is determined as

This \(\tilde{v}(t)\) determined from Fig. 2(a) is shown in (b). Again, there remains a problem in using pseudo velocity, that is, there is a drift attributable to the acceleration bias. To overcome this problem, again, we made another workaround. That is, for every single step of participant, right or left, we reset pseudo velocity to zero. We denote this new pseudo velocity as \(\tilde{v}_0(t)\). We defined the beginning of each step as the time at which pseudo velocity curve is minimized. Then we defined pseudo path length for ith step as

Note that, among thirteen steps in all, as mentioned above, we chose ten steps (\(i = 2, 3, \ldots , 11\)), where odd number belongs to the right steps and even number the left steps.

Example pseudo acceleration calculated from accelerometer signal and corresponding pseudo velocity for one participant’s in-pocket smartphone.

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Results. We have examined several possible features with respect to their correlation with height. As a result, for vertical acceleration profile in the bag condition, we found that mean minimum vertical acceleration is well related to height. To be specific, the ratio \(a_{\min }(\mathrm {left})/a_{\min }(\mathrm {right})\) is highly correlated with height (\(r = -0.745\); see Fig. 3(a)), where \(a_{\min }\) is mean minimum vertical accelerations, and “right” (“left”) stands for the steps with the right (left) foot.

Relationship between pseudo path length and height was examined for the bag and the pocket conditions. We found pseudo path length is highly correlated, in the pocket condition, with height. In the bag condition, however, correlation is not so high. To be specific, the right-step to left-step ratio of pseudo path length \(L(\mathrm {right})/L(\mathrm {left})\) is highly correlated with height (\(r = 0.801\); see Fig. 3(b)).

Feature values vs. height for the features highly correlated with carrier’s height. Correlation coefficients are calculated using average feature values of the first and the second trials.

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Correlations of the features with height are summarized in Table 1. For comparison’s sake, features’ correlations with the length of leg are given in the table. We defined the length of leg by the difference between height and sitting height, by assuming it approximates the sum of thigh length and lower leg length.

We have just made trial and error searching for features that might be correlated with height. We found that the ratio of left to right for mean minimum vertical acceleration is effective for the bag condition, and, for the pocket condition, the ratio of right to left for mean pseudo path length is effective.

Although we have found features that have fairly large correlation with height, certainly, estimation error by regression is rather large. One possible approach of reducing the error of estimation would be to use multiple features instead of single features. Also we need deeper understanding of why the particular features have higher correlations with height, preferably by analyzing bio-mechanical model of human walking.

It is interesting to note that the correlation of height with a particular feature derived from accelerometer signals is comparable to, or even larger than, the correlation obtained from anthropometric study, e.g. correlation of height with lower leg length is \(r = 0.776\) [4].

Finally we would like to comment on the features’ correlation with the length of leg. As can be seen from Table 1, correlations of the features are lower for the length of leg than height. This is a bit strange since the motion of going up the stairs may be thought to be determined mainly by the length of leg. By taking this result for sure, chances are that acceleration is influenced by whole-body motion, so that the length of leg is not the only determinant of acceleration profiles.