On the Use of Magnetic Field Disturbances as
Features for Activity Recognition with on Body
Sensors
Gernot Bahle, Kai Kunze, and Paul Lukowicz
Embedded Systems Lab
University Passau, Passau, Germany
first.lastname@uni-passau.de

Abstract. We investigate the use of magnetic ﬁeld disturbances asfeatures for motion based, wearable activity recognition systems. Such
disturbances are mostly caused by large metallic objects and electricalappliances, both of which are often involved in human activities. We
propose to detect them by subtracting angular velocity values computedfrom the changes in the magnetic ﬁeld vector from gyroscope signals. We
argue that for activities that are associated with speciﬁc objects or devices such features increase system robustness against motion variations,sensor displacement and inter user diﬀerences. On a previously publisheddata set of 8 gym exercises we demonstrate that our approach can improve the recognition by up to 31% over gyroscope only and up to 17%
over a combination of a gyroscope and 3D accelerometer. Improvementsof 9.5% are also demonstrated for user independent training as well as
for the case of displaced sensors.
A particularly interesting result is the fact that adding the magnetic
disturbance features signiﬁcantly improves recognition based on the vector norm of accelerometers and gyroscopes. The norm is often used when
the orientation of the sensor is not known. This is common when usinga mobile phone or other consumer appliance as a sensor.

1

Introduction

Gyroscopes and magnetic ﬁeld sensors are often used modalities in activity recognition ( [7,4,17,15]). In general, magnetic sensors are used to determine orientation (possibly together with an accelerometer) while the gyroscope helps ﬁlter
out distortions due to disturbances in the magnetic ﬁeld.
In this paper, we investigate a diﬀerent way of using the information from amagnetic sensor. Rather than try to ﬁlter out the disturbances we speciﬁcally use
them as features. This approach is aimed at activities that are related to motionsin the proximity of ﬁxed metallic objects with each activity being associated witha diﬀerent object. The example considered in this paper are exercises on gym
machines. Such machines are mostly metallic and diﬀer signiﬁcantly in the shapeof metallic parts which users hands come close to.
P. Lukowitz, G. Kortuem, and K. Kunze (Eds.): EuroSSC 2010, LNCS 6446, pp. 71–81, 2010.
c Springer-Verlag Berlin Heidelberg 2010


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G. Bahle, K. Kunze, and P. Lukowicz

Metallic objects disturb the earth magnetic ﬁeld in a way determined bytheir shape and composition. This means that while the absolute value of themagnetic ﬁeld signal is predominantly given by position and the speciﬁc motionthat the user has been performing, the disturbances are more dependent on theobject itself (although position and motion also play a role). As will be shown in
the paper this reduces the dependence of the recognition performance on sensor
placement and motion variations that occur when looking at diﬀerent users.
We demonstrate this on a data set recorded from gym exercises on diﬀerent
machines that we have previously used to study the eﬀect of sensor placement
variations on activity recognition [9].
1.1

Related WorkIn general, gyroscopes are used together with magnetic ﬁeld sensors to ﬁlter out
magnetic disturbances. Levi et. al. present a patent describing how to improvethe magnetic heading information using a gyroscope [12]. Ladetto et. al improvea dead-reckoning system fusing the gyro and compass information [10]. Young etal. use the magnetic ﬁeld as source of orientation data in motion capturing applications ( [16]). The application scenarios for magnetic ﬁeld sensors range fromlife recording, over music performances to novel interface designs ( [7,3,14,5]).
Still the use is as described above.
Merging compass and rotation data for activity recognition is also quite common( [11,6,2,1]). Lester et. al. use a combination of accelerometer, sound, gyroand magnetic ﬁeld sensors embedded in a mobile phone size device [11]. Junker
et. al. describe how to combine inertial sensors to spot sporadic user gestures ina data stream [6].
Complementary to the work presented in this paper, Minnen et. al. describe
a way to detect unsupervised “Motifs” in sensor data [13]. This might be used
to detect “interesting” disturbances in the magnetic ﬁeld automatically without
training.
In previous work, we have shown how to estimate the angular velocity form
magnetic ﬁeld sensor data only [8].
While all of the above research deals with magnetic sensing in activity recognition, our work is fundamentally diﬀerent as it aims to use magnetic disturbancesrather then the pure magnetic signal caused by user motion. As such it is complementary to previous work. Features derived using our method can thus be usedand can be applied in situations where magnetic ﬁeld signals were previously of
little use.

2

Approach

To isolate the magnetic disturbances we compare the angular velocity given by
the gyroscopes with the value computed from the magnetic ﬁeld data. To this end
we use the approximation of angular velocity from 3D magnetic sensor data described in [8]. It is based on the fact that the three ﬁeld strength components that

On the Use of Magnetic Field Disturbances

73

a 3D magnetic ﬁeld sensor outputs represent a vector B that is tangential to themagnetic ﬁeld line at sensor location. This vector is given in the local coordinate
system of the sensor with the vector length representing the scalar ﬁeld strength(norm of the ﬁeld vector at the location). Thus, if we orient the sensor in such a
way that one sensor axis (e.g. x-axis) points in the direction of the magnetic ﬁeld
(is tangential to the ﬁeld line) then the sensor reading will be B(t) = (b, 0, 0)with b = B(t) being the magnetic ﬁeld strength at the location. If we orient
the sensor with the (x, y) plane being tangential to the ﬁeld line than the output
will be (b ∗ cos(ϕ), b ∗ (sin(ϕ), 0). Generalizing to arbitrary orientations of thesensor with respect to the ﬁeld line we have:1 Bi (t) = B(t) · cos(ϕi ) The angle ϕi (B(t)) between the i-th axis and the magnetic ﬁeld strength vector B(t)Bi (t)
where Bi (t) is themeasured at time t is then given by ϕi (B(t)) = arccos B(t)
i-th component of B(t). Angular velocity then equals the ﬁrst derivative of theangle.
2.1

Analyzing the Distortion

Obviously, the presence of metallic objects and artiﬁcial magnetic ﬁelds (e.g.
caused by electric appliances) has signiﬁcant inﬂuence on the quality of theapproximation. Figure 1 shows an example comparing the magnitude of gyrodata and the magnitude of estimated angular velocity based on magnetic data.
The third graph in 1 highlights the principle we exploit in this work: whenangular velocity measured by the gyro and angular velocity estimated by useof the magnetic sensor are equal, their diﬀerence is zero. When they diverge,
however, the diﬀerence takes on non zero values, signifying a disturbance in themagnetic ﬁeld. In previous work we have tried to ﬁlter out this inﬂuence andfocus on applications where it is negligible. In this paper we do the opposite: we
explicitly try to analyze the distortions and use them as a source of information.
We focus on scenarios where the user wears a combination of a magnetic ﬁeld
sensor and a gyroscope while performing activities in the proximity of metallic
objects and other sources of magnetic disturbance.
As described in [8], the distortion depends on many factors and is not easily
described in exact terms. However, in most cases the nature of the source ofmagnetic distortion is a more signiﬁcant inﬂuence then ﬁne variation in the
motions associated with the activity. Thus, in activity recognition tasks where
the classes are associated with diﬀerent objects or devices (=diﬀerent sourcesof magnetic ﬁeld disturbance), the use of magnetic disturbance as a feature canincrease the robustness of the system in comparison to purely motion analysis
based approaches. This is because the sources of disturbance often remain largely
unchanged, whereas the speciﬁc motion signals associated with the activities cansigniﬁcantly vary. Such variations are particularly relevant when looking at user
independent recognition, but can also be non negligible for a single user. In
1

This assumes the magnetic sensor delivers data in a standard basis coordinate system; it is, however, possible to perform a basis transformation if that is not the casefor a given device.

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G. Bahle, K. Kunze, and P. Lukowicz

Fig. 1. Magnitudes of (estimated) angular velocities from gyro and magnetic data anddiﬀerence thereof

addition, as was shown in [9], recognition rates drop dramatically if training
data is recorded from a diﬀerent sensor location than testing data (e.g. becauseof the sensor being loosely attached and slipping). In all of the above cases using
features gained from diﬀerence of estimated and real angular velocity, recognition
rates can be improved.
2.2

Problems and Limits

The main problem we encountered was that the approximation of angular velocities using magnetic data on individual axes was not good enough to yielduseful information when subtracted from the three individual gyroscope signals.
As [8] states, the estimate depends on the basis vectors chosen for the projections of the magnetic ﬁeld strength vector. Calculating the magnitude over all
three estimated axes skirts this diﬃculty, as the magnitude is not dependent on
the exact distribution of the velocities between the three axes. Unfortunately, italso destroys potentially useful direction speciﬁc information. At the moment,
this boils down to using the total amount of distortion as a feature instead ofthe distortion on each axis. In the future, we will try to further reﬁne the approximation technique to allow for individual axis estimates good enough to use
in the way described in this paper.

On the Use of Magnetic Field Disturbances

3

Evaluation and Results

3.1

DataSet75

We evaluated our approach on part of the gym data set previously published in[9]. This data set consists of 8 gym exercises (lat machine, butterﬂy, shoulderpress, upper back, arm extension, arm curl, pull down, chest press). The exercises
are performed by two subjects with 10 to 15 repetitions on each machine (totalof around 200 instances), taking about 5 minutes for each set.
The data set is recorded with XSENSE MTX inertial sensor modules containing both a gyroscope and a magnetic ﬁeld sensor, as well as an accelerometer.
For both test subjects, ﬁve modules have been used to record the entire training
session; we exploit this to demonstrate our approach for displaced sensors (using
data of one sensor for training and then testing on the other 4).

Fig. 2. Sensor placement for gym dataset for subject 1 and 2; blue rectangles represent
the rigid bodies (upper / lower arm), yellow boxes the placement of the sensors

The sensors were split into two groups of three and two sensors respectively.
Figure 2 shows the positions of the modules).
It is noteworthy that during the recording of subject two, one of the sensors
attached to the upper arm shifted position, resulting in a new position between
both upper and lower arm sensor groups.
3.2

Evaluation

We calculated features in a sliding window one second long with 0.5 seconds
overlap. The features used were mean, var, amplitude, rms, centre of mass
and ﬂuctuation of spectrum and the ﬁrst ﬁve cepstrum coeﬃcients as deﬁned
by ift(log(abs(ﬀt(signal)))).
All features were calculated on the magnitude of acceleration, gyroscope andmagnetic 3D data vectors. As stated above, the magnetic ﬁeld based approximation of angular velocity is not yet sophisticated enough to work on individual
axes. Furthermore, using the individual axes for classiﬁcation performs significantly better only as long as there is no sensor displacement (for reference,

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G. Bahle, K. Kunze, and P. Lukowicz

we did include the 3D data in the case of non displaced sensors). Once sensor
displacement happens, the opposite is actually the case. As translations androtations change the distribution of force to individual axes far more than theoverall amount of force measured by the sensor, using features based on magnitudes of sensor signals is far more robust under displacement. E.g., using gyro
and acceleration data, recognition rates are as good as 96.8% using 3 axes but
drop down to 24% when the sensor is displaced. On the other hand, resorting to
the magnitude features only yields 69.2% without displacement, but only drops
to 56.5% in a diﬀerent sensor location.
A note on computational complexity: All the calculations required for ourapproach are quite simple; both the estimation of angular velocity from magnetic data and the features used do not require extensive computational power;
while we used an already available data set for this work and performed ouranalysis oﬄine on a workstation running Matlab, it is computationally feasible
to implement it in an online setting, e.g. on a mobile device.
For the classiﬁcation itself, we tested diﬀerent frame-by-frame classiﬁers (C4.5
decision tree, kNN, NaiveBayes). Results from these classiﬁers were within 1%of one another, so without loss of generality, the numbers we present are derived
from the NaiveBayes classiﬁer. Training data consisted of half a set (obtained by
a 50% percentage split) of full data for non displaced sensors and of a full set ofany one sensor in the case of displaced sensors. Testing data likewise was either
the other half in the single sensor case or the full data of the remaining four
sensors in the displaced case. In all evaluations safe the last one, both training
and testing was done on a per subject basis. The results were then averaged.
While user independence is a desirable quality in activity recognition, it is also
diﬃcult to achieve; in the gym setting, e.g., diﬀerent users perform motions
slightly diﬀerently. We address this topic in the last part of the evaluation.
In order to determine whether the diﬀerence of gyro signal and magnetic estimated angular velocities contained useful information, in a ﬁrst step we compared two sets of features. The ﬁrst set contained only features derived fromthe individual gyro and magnetic data vectors; the second set was expanded byadding features calculated from the diﬀerence of gyro and estimated magnetic
angular velocities.
As outlined above, it is not a good idea to use raw magnetic data for activity recognition. In our data set, rotating the sensors (or, just as bad) thegym machines would result in completely diﬀerent magnetic sensor readings. We
therefore performed two more evaluation steps.
In a second evaluation, we compared two sets of data; one set only containing
features derived from the gyro readings, with the second set once again including
the gyro and magnetic velocity diﬀerence features.
In a third step, we added the acceleration data, comparing one set of features
calculated on magnitudes of acceleration and gyro data to a set containing thoseand additionally the information derived from diﬀerences in gyro and magnetic
angular velocity.

On the Use of Magnetic Field Disturbances77

As a ﬁnal evaluation step, we have tested how well the additional featuresderived from the angular velocity comparison perform when training data andtest data do not originate from the same person. To that end, we used sensor
data from subject 1 for training and data from subject 2 for testing; afterwards,
we switched persons and repeated the process, averaging over the results.
3.3

Results

Carrying out the evaluation strategy outlined above, we achieved the results
shown in Figure 3. The details of each evaluation step are described in thecorresponding subsection below.
Comparison: gyro + magnetic data to same + diﬀerence in angularvelocities. In the case of no sensor displacement, classifying the gym data set
with features calculated from gyroscope and magnetic sensor data yields average
recognition rates of 90.0% using individual axis data and 74.6% using magnitudeof axes data. Extending the feature set by features derived from the diﬀerenceof gyro angular velocities and estimated magnetic angular velocities can boost
these rates to 93.0% in the 3D case and 83.9% in the magnitude case; the gainsof 3.0% and 9.3% respectively prove that the features stemming from angularvelocity comparison of gyro and magnetic data do contain additional information

Fig. 3. Overview of base recognition rates and gains for various cases

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G. Bahle, K. Kunze, and P. Lukowicz

that can be used to further improve recognition rates. The lower gain in the 3D
case is partly due to the much higher base recognition rates, which limit theroom for improvement.
In the case of displaced sensors, adding the diﬀerence features boosts average
recognition rates from 52.4% to 59.7%, resulting in an average gain of 7.3%.
Individual gains between each pair of sensors were uniformly distributed evenbetween the diﬀerent sensor groups of upper and lower arm; this implies that- at the very least - the additional features are less sensor location dependent
than e.g. raw gyro or magnetic data. Looking at the individual axis data underdisplacement underscores the arguments for using the magnitude of sensor data
made above, with recognition rates dropping to about 30%. There is, however,still an average gain of 3.7% when adding the additional features.
In conclusion, the results of the ﬁrst evaluation step show that both in caseswith and without sensor displacement, using the magnetic/gyro diﬀerence features improves recognition rates. Table 1 summarizes these results.
Table 1. Comparison of recognition rates w/o and with angular velocity comparison
features for gyroscope and magnetic data
Modality
3D, undisplaced
magnitude,
undisplaced
magnitude, displaced

Recognition Rate w/o ang. vel.
comp. features
90.0%
74.6%

Recognition Rate w. ang. vel.
comp. features
93.0%
83.9%

Gain

52.5%

59.7%

7.3%

3.0%
9.3%

Comparison: gyro data to gyro + diﬀerence in angular velocities. Classifying the gym dataset with features derived solely from gyroscope sensor data
yields an average recognition rate of 80.1% in the 3D case and 48.5% in the magnitude case as long as the sensor has not been displaced. In both cases, adding thefeatures resulting from our diﬀerence of angular velocities approach net improvements: average recognition rates rise to 90.4% in the 3D case, a gain of 10.3%.
Adding the additional features to features calculated from the magnitude gyrosignal vector, recognition can be boosted to 79.9%, showing a tremendous gainof 31.4%. This suggests that adding the new features manages to recoup at least
part of the information lost by switching from 3D data to magnitude of data. In
the case of displaced sensors, recognition rates using only gyroscope data dropby 11.8% to 36.7% using the features calculated on the magnitude of the signal.
Once again, adding the information resulting form our comparison of gyro angular velocity and the estimated magnetic one yields signiﬁcant improvements,
raising average recognition rates amongst the four diﬀerent groups of displaced
sensors to 53.1%, a gain of 16.4%.
Table 2 summarizes these results.
Comparison: gyro + acceleration data to same + diﬀerence in angular velocities. In the third section of the evaluation, we combined gyroscope
and acceleration data for the feature set; these modalities provide a realistic

On the Use of Magnetic Field Disturbances

79

Table 2. Comparison of recognition rates w/o and with angular velocity comparison
features for gyro data
Modality
3D, not displaced
magnitude, notdisplacedmagnitude, displaced

Recognition Rate w/o ang. vel.
comp. features
80.1%
48.5%

Recognition Rate w. ang. vel.
comp. features
90.4%
79.9%

Gain
10.3%
31.4%

36.7%

53.1%

16.4%

scenario for activity recognition. In the case of a single, non displaced sensor,
recognition rates are very good, especially when using the 3D signal for feature
calculation. Averaged over the 5 diﬀerent sensors and both test persons yields a
recognition of 95.7%. This is very close to perfect already and leaves little room
for improvement. Even so, however, adding the features derived from the angular velocity comparison raises accuracy slightly to 96.8%, a gain of 1.1%. Using
the magnitude of acceleration and gyroscope as basis for feature calculation expectedly drops recognition rates to 70.0% when there is no sensor displacement.
Adding the information derived from our approach manages to increase accuracy
signiﬁcantly again to 87.6%, a gain of 17.6%.
Finally, in the case of displaced sensors, recognition rates drop down to an
average of 52.0% over all 4 groups of sensors, using just acceleration and gyroscope data. Adding in the gyroscope - magnetic comparison features manages toimprove accuracy by 5.6% to 57.6%.
Overall, as in the other cases presented in our evaluation, there is measurable information contained in the features derived from comparing actual andapproximated angular velocity. Table 3 summarizes these results.
Table 3. Comparison of recognition rates w/o and with angular velocity comparison
features for combined gyro and acceleration data
Modality
3D, not displaced
magnitude, notdisplacedmagnitude, displaced

Recognition Rate w/o ang. vel.
comp. features
95.7%
70.0%

Recognition Rate w. ang. vel.
comp. features
96.8%
87.6%

Gain
1.1%
17.6%

52.0%

57.6%

5.6%

Comparison: gyro + acceleration data with and without angular velocity diﬀerence between subjects one and two. In activity recognition,an added diﬃculty may present itself: when classiﬁers trained on data obtained
from one person are used to classify activities performed by a diﬀerent person,
recognition accuracy usually drops, sometimes severely. Thus, while user independence is of course a desirable quality of any recognition system, it is usually
hard to achieve. E.g., diﬀerent users may perform activities slightly diﬀerently
and sensor placement may diverge slightly. In theory, magnetic distortions should
be quite person independent, as they depend mostly on the environment. To
test this hypothesis, we trained with acceleration and gyroscope data from subject one and tested on data from subject two and vice versa. We obtained these

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G. Bahle, K. Kunze, and P. Lukowicz

results: Training with upper arm data without our magnetic distortion features
resulted in a recognition rate of 40.05%, while lower arm data performed slightly
better at 46.51%. On average, recognition accuracy was 43.28%. Adding thefeatures calculated from angular velocity comparison resulted in noticeable gains;
upper arm accuracy increased to 46.86%, a gain of 6.81%; lower arm recognition
was boosted to 56.08%, an increase of 9.57%; ﬁnally, on average, recognition roseto 51.47%, an improvement of 8.19%. Table 4 summarizes these results.
Table 4. Comparison of recognition rates w/o and with angular velocity comparison
features between diﬀerent subjects
Modality
upper arm
lower arm
both

Recognition Rate w/o ang. vel.
comp. features
40.05%
46.51%
43.28%

Recognition Rate w. ang. vel.
comp. features
46.86%
56.08%
51.47%

Gain
6.81%
9.57%
8.19%

Since sensor placement on subject one was diﬀerent from sensor placement on
subject two, it is not possible to divide total gains from the additional features
into gains from displacement resistance and gains from person independence.
Overall, while recognition expectedly performs worse than in the case of same
subject training and testing (51.47% compared to 57.6%), the gain from themagnetic distortion features is actually 46% higher (8.19% compared to 5.6%).
This indicates that our initial supposition of the added value for achieving ameasure of subject independence is correct.

4

Conclusion

The results presented in the previous section are a strong indication that magnetic ﬁeld disturbances computed from the diﬀerence between gyro signals andangular velocity derived from magnetic ﬁeld vector changes are useful for wearable activity recognition. The inclusion of the corresponding features has leadto an improvement of performance in all experiments. This included cases ofshifted sensors and person independent recognition.
Despite the promising results, our evaluation, however, should only be considered a starting point for further work. The technique presented here shouldbe tested on a wider range of datasets. It would also be interesting to apply it todata gathered from mobile devices like the iPhone 4. Another aspect deservingof more research is further reﬁning the estimation approach itself in order tobe able to apply it to individual axes with suﬃcient precision. It would thenbe possible to characterize distortions along three individual dimensions insteadof just their magnitude, possibly making the technique even more valuable. Inthat context, it might also be worth exploring how much sensor displacement isnecessary before the gains from the greater invariance to displacement outweighthe accuracy penalties in case of little displacement when switching from 3D
signal data to magnitude of signal data.

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81

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