Analysis and development of an automatic eCall for motorcycles:a one-class cepstrum approach

Simone Gelmini∗, Giulio Panzani and Sergio Savaresi

Abstract— The automatic dial of an emergency call – eCall– in response to a road accident is a feature that is gaininginterest in the intelligent vehicle community. It indirectlyincreases the driving safety of road vehicles, but presents thetechnical challenge of developing an algorithm which triggersthe emergency call only when needed, a non-trivial task fortwo-wheeled vehicles due to their complex dynamics. In thepresent work, we propose an eCall algorithm that detects theseanomalies in the data time series, thanks to the cepstral analysis.The main advantage of the proposed approach is the directfocus on the data dynamics, solving the limits of approachesbased on the analysis of the instantaneous value of some signalscombination. The algorithm is calibrated and tested against realdriving data of ten different drivers, including seven real crashevents, and performance are compared with known methods.

I. INTRODUCTION

According to the most recent data, the number of roadtraffic deaths continues to climb reaching 1.35 million in2016, the 8th leading cause of death for people of all ages[1]. At least in Europe, this is partially due to the sharplyincreasing number of motorcycles – and, more generally,powered two-wheelers (PTW) [2] – with their 34-fold higherrisk of death in a crash than the other motor vehicles users[3]. Motorcyclist fatalities already account for almost 11%of the total in Europe [1].

One possible solution to the problem is the developmentof safety-related vehicle dynamics control. In spite of theeffort and the improved vehicles, there is still more to do forreducing this negative trend. To this end, as second pillar,regulatory agencies have started focusing on the improve-ment of the rescuing operations that follow an accident,because “the immediate transport to an appropriate traumacenter is one of the essential steps in the early treatment ofpolytraumatized patients” [4]. More specifically, the EU haspromoted an initiative, eCall, aiming to automatically dialan emergency call when a road accident happens, investingin a large project known as Infrastructure Harmonised eCallEuropean Pilot (i-Heero). The aim of the eCall is to detectpotentially dangerous events whose dynamics are compatibleto a crash, followed by a long enough time interval ofinaction, the most recurrent pattern in road accidents. Thisproject has already been transformed in a set of rules, leadingto the adoption of a standard equipment to be installed onall cars in EU since the end of 2018, [5], and an extensionfor motorcycles is under development. This work does notpresent the main results obtained in the i-Heero project, butit is a theoretical and research-oriented extension of suchresults.

The authors are with the Dipartimento di Elettronica, Informazione eBioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133Milan, Italy.∗Corresponding author: simone.gelmini@polimi.it.This research is partly supported by the EU-sponsored project i-Hero.

As far as crash detection is concerned, such event es-sentially takes place in the ground plane in four-wheeledvehicles. Thus, its detection can be obtained by monitoringabnormal longitudinal decelerations, see e.g., [6]. Instead, thecrash becomes more difficult to be defined in a unique waywhen moving to two-wheeled vehicles, since their motionis strongly affected by the roll angle dynamics. The fewworks found in literature on this topic can be clustered in twomain categories. The first one can be labelled as threshold-based: since PTW crashes are most often paired with thefall of the vehicles, static threshold methods like [7], [8],[9] aim to detect the occurrence of a crash monitoring whenthe motorcycles are suspiciously not upright. These methodsare usually the result of a significant analysis of the fallingdynamics, and the detection is generally obtained whensome post-processed signals exceed the given thresholds.The second approach is called statistical-based: as presentedin [10], [11], [12], these methods assume a crash to be ananomaly in the data distribution, and the detection is real-ized using statistical tools like outliers-detection algorithms.These methods are also capable of detecting crashes thathappen when the vehicles remain upright, events not detectedby threshold-based ones.

In all the published works, the dynamics of the recordedsignals – which are usually some inertial measurements ofthe vehicle – are not explicitly accounted. However, in theanalysis of dynamic systems like PTWs, the role of timeis central. In fact, the analysis of structured-time signalsallows to exploit the intrinsic correlations between them. Tothis purpose, a frequency-domain analysis is possible, whichallows inferring on the underlying physical phenomenonby inspecting the most discriminating harmonic ranges bymeans of efficient mathematical tools, like cepstrum [13].

In this paper we present a novel way to detect motorcyclecrash events through the dynamical analysis of the vehicle’smotion. To do this, recorded data are remapped in thecepstrum domain and then monitored, detecting an anomalywhen the driving dynamics differs significantly from itsregular trend. To our best knowledge, this is the first workwhere cepstrum-based signal processing is used for drivinganomaly detection.

II. PROBLEM STATEMENT AND EXPERIMENTAL SETUP

In this paper, an automatic eCall algorithm for two-wheeled vehicles is presented. The goal of the proposedcontribution is to analyze the underlying driving dynamicsand searching for patterns not compatible with the regularride of the vehicle, aiming to detect any event in whichdrivers need to be rescued (e.g., after falls or collisions). Dueto potentially impelling medical conditions, the detectionneeds to be performed shortly after the crash to provide a

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prompt assistance. Furthermore, the algorithm must detectall the anomalies while limiting the social and economicalcosts of triggering emergency calls unnecessarily.

In order to widespread the use even in outdated motorcy-cles, the algorithm is designed so to use a minimal sensorsetup. In contrast to the sophisticated sensor layouts likethose used in other contributions, e.g., [7], [12], the proposedeCall trigger is obtained only using data of a 5 degrees offreedom intertial measurement unit (IMU) – aligned withrespect to the standard reference frame, as depicted in Fig.1 – which embeds a triaxial accelerations vector and twoangular velocities, the roll-rate (ωx) and yaw-rate (ωz). Thisis the minimal sensor configuration already employed inrecent motorcycles for estimating the lean angle [14] andwhich could be easily replicated using the modern, flexible,cost-effective, and easy to install telematic e-Boxes [15]. In

Fig. 1: An overview of the standard reference frame.

the following, the available vehicle speed is presented onlyfor monitoring purposes and for testing one of the algorithmsalready presented in literature, but it is not used for theproposed approach.

The available data have been collected during an exper-imental campaign involving ten professional riders duringon-track tests, yielding more than eighty hours of recordings,including seven different crash events (listed in Table I).

TABLE I: Summary of the recorded crash types and theirduration.

Event Crash duration [s]

Front Lowside I 10Front Lowside II 8

Cornering Lowside 10Highside I 7Highside II 9

Sliding I 6Sliding II 14

III. RELATED WORKS

A. Threshold-based algorithmsThreshold-based algorithms aim to detect anomalous rid-

ing patterns by means of a combination of signal processingand static thresholds. These algorithms generally reflect theintuitive and simple idea of crashes, mainly related to themotorcycle impact and/or its fall to the ground, that resultin “extremely large” signals that overcome normal values.

For instance, the work discussed in [7] detects the oc-currence of a fall when the driver is close to experi-ence a nominal free-fall condition. Given the accelera-tion ‖a(t)‖ =

√ax(t)2 + ay(t)2 + az(t)2 and angular rate

‖ω(t)‖ =√ωx(t)2 + ωy(t)2 + ωz(t)2 norms, an emergency

call is fired when ‖a(t)‖ < γa = 0.5g, in which g =9.8056 m/s2 is gravity, and ‖ω(t)‖ > γω = 2 rad/s.

We test this intuitive and easy to replicate algorithmagainst our set of data. However, since the pitch-rate (ωy) isnot available in our setup, the angular rates norm is computedonly on axes x− z, ‖ω(t)‖x−z =

√ωx(t)2 + ωz(t)2.

Normal ride

Crash

Normal ride

Crash

Crash dynamics

Fig. 2: Analysis of the pattern of a falling motorcycle for theFront lowside I crash.

In Fig. 2 the dynamics of the Front lowside I is analyzed:during the fall, the angular rate norm grows and the acceler-ation one floats towards zero; at the impact, the two normsreach their peaks, with the vehicle bouncing on the grounduntil it settles. Even with a missing degree of freedom,the pattern still resembles the one discussed in the originalpaper. However, for a fair comparison, the algorithm has beenrecalibrated, ensuring the minimal tuning that guarantees thedetection of all the crashes, obtaining γa = 7.86 m/s2 andγω = 1.77 rad/s. Under this parametrization, the algorithmis yet able to detect the falls opportunely.

The main disadvantage of the threshold-based approachis that it results in a significant number of false-positive,triggering an eCall unnecessarily, as shown in Fig. 3: besidesthe correct crash trigger, several activations are visible duringthe normal driving scenario.

A better understanding is provided by Fig. 4, which depictsthe eCall triggering area (i.e., an emergency is detected if asample falls within the shadowed area): the normal drivingdata within the shadowed area are responsible for the falsepositive activations. The inspection of the same plot suggeststhat a different threshold tuning (e.g., increasing the angularacceleration norm threshold, portrayed in the illustration asFalse-positive-free γω) minimizes the number of incorrectactivations, since no normal riding data would fall in theeCall triggering one. This apparently positive result comeswith the unacceptable consequence of delayed or even missedcrash detections (false negative events), ignoring potentiallydangerous situations that must be detected.

As a result, static threshold methods do not seem aviable solution in real eCall applications since false positivescannot be systematically eliminated. A possible workaroundis to equip the motorcycle with an interface (e.g. a flashinglight button) which alerts the drivers when the algorithm istriggered, allowing them to interrupt the emergency call ifunnecessary. However, this solution might be still dangerous

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/s2]

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Fig. 3: An example in which the threshold-based algorithmgenerates many false positives before the actual Corneringlowside crash.

0 20 40 60 80 100

kak [m=s2]

0

1

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3

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5

k!k x!

z[rad

=s]

Normal rideCrash.!

.a

False-positive-free .!

Fig. 4: Analysis of the detected crash instances vs the regularriding distribution for the Cornering lowside crash.

as it would distract and annoy the motorcyclist, especially incase of frequently repeated false positives.

B. Statistical-based algorithms

Beside threshold-based algorithms, the scientific literatureproposes a different approach to the problem, based on statis-tical analysis. These algorithms, see, e.g., [10], [11], [16], as-sume that accidents are anomalies with respect to the nominaldata distribution, identifying them through outlier detectionmethods. In such framework, an accident is the samplethat does not statistically belong to the main cluster, fora certain significance level. Statistical-based crash detectionalgorithms can be considered an evolution of the threshold-based ones since the former analyzes the data through syn-thetic, independently distributed, features, whereas the latteranalyzes the data as a multivariate distribution, exploiting theintrinsic correlations not accounted previously.

In [16], Vlahogianni and authors propose to detect theanomalies (i.e., the accidents) by means of the Mahalanobisdistance, which provides a quantitative metric for assessinghow far a sample vector is from a given (possibly multivari-

ate) distribution. Denoting the sampled data at each timeinstant with l(t) ∈ Rp×1 (with p the number of signalsanalyzed), such distance is formulated as

dMah(t) =

√(l(t)− µ)

′S−1 (l(t)− µ), (1)

in which µ and S are the sampled mean and covariancematrix computed on the training dataset. A sampled datal(t) represents an anomaly if the Mahalanobis distance in (1)exceed a certain threshold, dMah(t) > γMah, triggering anemergency call. The advantage of using such an approachis twofold: on one side, the shape of the normal drivingdata distribution is taken into account; on the other, given astatistical significance level α (in this application, as in theoriginal paper, α = 0.05), the threshold γMah is learnedfrom data since the given Mahalanobis distance can beapproximated to an F−distributed variable

dMah ∼p(n− 1)(n+ 1)

n(n− p)Fp,n−p, (2)

in which n is the multivariate space dimension (i.e., thedataset’s number of sampled vectors). Moreover, limitedby the reduced sensor configuration of the present work,the benchmark results presented in the following refer tomodel C in [16], whose sample data include the vehiclespeed and all the available inertial measurements. Analogousresults are obtained for the smaller subset of sensors (i.e.,vehicle speed and longitudinal acceleration), accounted bymodel B in [16]. Figure 5 shows the detection results of

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ah[-]

Cautious-based training datasetAggressive-based training dataset

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Fig. 5: Performance analysis of the statistical-based approachtrained on two different driving styles datasets for the Cor-nering lowside crash.

the statistical-based method, on the same crash previouslypresented in Fig. 3. The analysis of the middle plot, wherethe computed Mahalanobis distance is depicted, highlightsthe high sensitivity of this approach with respect to thetraining datasets: as qualitatively shown in in Fig. 6, thetwo distributions are characterized by two different ridingstyles, which result in different sampled mean and covariancevalues, both part of the distance definition (1). The crash isdetected correctly in both the two situations, but the cautious-based trained algorithm results in a higher number of falsepositives.

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‖a‖ [m/s2]

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1.5

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2.5

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‖ω‖ x

−z[rad

/s]

Aggressive-based training dataset

Cautious-based training dataset

Fig. 6: The effects of the driving style on the data distributionfor the Cornering lowside crash: the shape and amplitudechange when considering cautious or aggressive drivers.

Although the statistical-based approach proves to be morerobust when the training distribution well approximates theunderlying one (in fact, no false positives are generated inthe aggressive-based case), it is not likely to be able to definea reference distribution for all the drivers. Besides, evenif a proper choice of the training dataset can significantlyreduce the number of false activations, statistical-based crashdetection approaches still suffer of another drawback, namelythe high variability of the resulting classification signal (i.e.,the frequent ON/OFF switches), which requires to post-process the output (e.g., through some debounce logic),ensuring the consistency of the detected events, eventuallydelaying or missing the detection. Furthermore, the methodcannot detect accidents whose dynamics lies within the maindistribution, implicitly assuming that a driver is always ableto control the vehicle under the same dynamic conditions.

These drawbacks are inherent of the nature of the twoapproaches, as they both classify each incoming data sampleindependently from its past values. This motivates the devel-opment of a different algorithm, capable of accounting forthe signal dynamics. Such approach is the main core of thepresent work and it is presented in the following section.

IV. ONE-CLASS CEPSTRUM CLASSIFICATION

A. Dynamical analysis

To improve the detection performance, the crash dynamicsis exploited. Data are analyzed in the frequency-domain, asillustrated in Fig. 7. Spectra are computed through a slidingwindow, before and during the crash event. As shown, themotorcycle does not significantly influence harmonics higherthan the vehicle dynamics range (i.e., greater than 10 Hz)during the normal ride. On the contrary, during the crashevent, the whole spectra are excited due to the sequence ofimpacts and rotations. Since all the harmonics are excited,a simple classification approach based on the intensity of ahigh-pass filtered version of the signals would not extractenough information to perform a robust detection. Thus, toproperly detect a crash, it is paramount to inspect all theinertial signals’ spectrum, searching for variations in thefrequency-domain which are not compatible with the regularride of the vehicle.

B. Cepstrum and related concepts

To capture anomalies analyzing the data dynamics, wepropose to use the power cepstrum, a mathematical toolintroduced in [17] as a better alternative of the autocorre-lation function. As analyzed in [18], cepstrum is an effectivetool for pattern recognition in time-structured problems asit has proved to have a higher discriminating power, thoughavoiding the curse of dimensionality.

The power cepstrum is defined as “the power spectrum ofthe logarithm of the power spectrum”. Assuming the inertialsignals measured from the vehicle to be second-order quasi-stationary during the normal ride [19], within a given windoweach logged signal can be considered a stationary stochasticprocess s(t) with spectrum Φs. The power cepstrum can becomputed as the inverse Fourier transform of the logarithmof the spectrum Φs [13], as

cs(k) =1

2π

∫ 2π

0

log(Φs(eiθ))eikθdθ. (3)

Furthermore, cepstrum is known to be a homomorphicsystem [13]: homomorphic systems are the ones in whichnonlinear relationships could be converted into linear in theirtransform domains. For this reason, the cepstrum computedon a stationary stochastic process v(t), obtained through theconvolution of two stationary stochastic processes v(t) =s1(t) ∗ s2(t) =

∫ +∞−∞ s1(τ)s2(t − τ)dτ , corresponds to the

sum of the cepstrum computed on s1(t) and s2(t) separately

cv(k) = F−1 (log (Φv))

= F−1 (log (Φs1)) + F−1 (log (Φs2))

= cs1(k) + cs2(k).

(4)

Thanks to the cepstrum’s homomorphic property, we pro-pose to extend the definition of the so-called Martin distance[20] – so far used for univariate time series clustering andclassification problems [21] – in order to account, in onemetric, multiple time series of the same operating mode (i.e.,same riding condition). Thus, assuming to record p signals intwo operating modes (e.g., ga and gb), the distance becomes

dcep(ga,gb) =

√√√√ ∞∑k=0

k

∣∣∣∣∣p∑j=1

cgaj(k)− cgbj (k)

∣∣∣∣∣2

, (5)

in which r(k) =∑pj=1 cgaj

(k) − cgbj (k) is the sum of thecepstral mismatch between the two operating modes, for allthe p features, for a given order k.

C. Detection algorithm

The proposed method automatically detects an accidentthrough the measured inertial signals, when the underlyingdynamics does not reflect the regular ride of the vehicle, bymeans of the homomorphic property of cepstrum. To thispurpose, at any time instant t, a stream of data s ∈ Rp×m isgiven, in which p is the number of signals recorded (e.g., inour case p = 5), while m = wfs is the size of a slidingwindow buffering the last m samples of each signal, inwhich w is the window size in seconds and fs the sampling

(a) Normal ride (b) Crash dynamics

Fig. 7: Comparison of the spectra in a window during the normal ride and the crash dynamics: most of the spectra harmonicsare highly excited during the crash event, compared to the normal ride of the vehicle.

frequency (in this work, fs = 100 Hz):

s(t) =

s1(t) s1(t− 1) . . . s1(t−m+ 1)...

......

...sp(t) sp(t− 1) . . . sp(t−m+ 1)

. (6)

The cepstrum of each signal sj (with j = 1, . . . , p) iscomputed as:• first, the spectra of each time series Φsj (t) = 1

m

∣∣Sj∣∣2is evaluated, where Sj is the periodogram computed onthe portion of signal sj(t−m, . . . , t), obtained by meansof the Fast Fourier Transform (FFT);

• then, the cepstrum coefficients of each signal sj (withj = 1, . . . , p) are evaluated with the Inverse Fast FourierTransform (IFFT) of the logarithm of the spectrum Φsj ,or csj (k) = IFFT

(log(Φsj (t)

)), with csj ∈ R1×m.

The overall process is summarized in the example in Fig. 8.

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Fig. 8: The process for calculating the cepstrum: the co-efficients are evaluated on the spectrum computed on thewindowed signal.

To detect the amplitude growth for all the signals’ spec-trum, the computed cepstrum is compared with a referencetime series, whose cepstrum coefficients o ∈ Rp×m areall set to zero, representing a stream of data composedof constant signals. The chosen reference time series is

independent from the driving style, making the analysisobjective and robust for different drivers. Thus, the measuredcepstrum coefficients s(t) are compared to the reference oneso thanks to the distance in (5):

dcep(s(t),o) =

√√√√ ∞∑k=0

k

∣∣∣∣∣p∑j=1

csj (k)− coj (k)

∣∣∣∣∣2

. (7)

An anomaly is detected when (7) exceeds a tuned thresholdγcep, meaning that the spectra have grown significantly withrespect to the standard driving condition.

V. EXPERIMENTAL RESULTS

In this section, preliminary results on data recorded duringan experimental campaign aiming to calibrate and validatethe proposed method are discussed. Test data include sevenreal crashes and more than eighty hours of standard driving,in which no accidents are reported. First of all, the size ofthe buffering window w is chosen such that the buffer issufficiently large so to capture the crash event almost entirely.As reported in Table I, except for one case, all the crashdynamics last less or equal ten seconds, thus the windowlength is set to w = 10 s.

To calibrate the threshold γcep, (7) is computed beforeand during the crash event for the seven datasets (Fig. 9):the maximum value of dcep reaches a peak of 0.027 duringthe normal ride; instead, in the crash dynamics, the peakdistance is always kept above 0.031. Setting γcep = 0.029makes possible to detect all the crashes: Fig. 10 and Fig.11 show two examples of cepstrum-based detection for theFront lowside I and Cornering lowside crashes, respectively.Beside the prompt crash detection, its consistency should

be appreciated: the eCall flag rises and keeps high for asignificant amount of time, which is indirectly linked tothe window length w, making the proposed cepstrum-basedcrash detection approach more appealing than the othermethods.

Finally, to assess the robustness of the method with respectto the false positive triggers, the algorithm is tested with theproposed tuning against more than eighty hours of tests, not

0 0.01 0.02 0.03 0.04

Peak dmM [-]

Front lowside I

Front lowside II

Cornering lowside

Highside I

Highside II

Sliding I

Sliding II

Crash

event

Crash dynamicsNormal riding

Fig. 9: Analysis of the maximum value of the modifiedMartin distance dcep for both the normal and crash dynamics.

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Fig. 10: An example of the cepstrum-based detection on theFront lowside I crash. The algorithm triggers the eCall in3.64 seconds after the suspected start of the crash dynamics.

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Fig. 11: An example of the cepstrum-based detection on theCornering lowside crash.

used in the calibration phase. The algorithm does not triggerany emergency call for the entire validation set, thoughdifferent driving styles are involved.

VI. CONCLUDING REMARKS

In the proposed contribution, a one-class, cepstrum-basedalgorithm was proposed to detect motorcycle accidents.Contrarily to the other works in literature, the algorithmtriggers an emergency call by exploiting the signals dynamicsthrough a multivariate cepstral analysis. Experimental resultson seven real crashes and more than eighty hours of testfavorably witnessed the effectiveness of the method.

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