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Contents lists available at ScienceDirect

Sensors & Actuators: B. Chemicaljournal homepage: www.elsevier.com

Feature Extraction for Transient Chemical Sensor Signals in Response to TurbulentPlumes: Application to Chemical Source Distance PredictionJavier Burgués a, b, ⁎, Santiago Marco a, b

a Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology, Baldiri Reixac 10-12, 08028, Barcelona, Spainb Department of Electronics and Biomedical Engineering, Universitat de Barcelona, Marti i Franqués 1, 08028, Barcelona, Spain

A R T I C L E I N F O

Keywords:Gas sensorsDifferentiatorLow pass filterMetal oxide semiconductorMOX sensorsSignal processingFeature extractionGas source localizationRobotics

A B S T R A C T

This paper describes the design of a low-pass differentiator filter with linear phase and finite impulse response(FIR) for extracting transient features of gas sensor signals (the so-called “bouts”) which are relevant for accu-rately estimating the source-receptor distance in a turbulent plume. Our current proposal addresses the short-comings of previous ‘bout’ estimation methods, namely: (i) they were based in non-causal digital filters pre-cluding real time operation, (ii) they used non-linear phase filters leading to waveform distortions and (iii) thesmoothing action was achieved by two filters in cascade, precluding an easy tuning of filter performance. Thepresented filter preserves the signal waveform in the bandpass region for maximum reliability concerning bothbout detection and amplitude estimation. Thanks to its FIR design, the filter can be implemented with nonrecur-sive structures, thus being inherently stable and allowing an easy algorithmic implementation and optimization.As a case study, we apply the proposed filter to predict the source-receptor distance from recordings obtainedwith a metal oxide (MOX) gas sensor in a wind tunnel. We demonstrate that proper tuning of the proposed filtercan reduce the prediction error to 8cm (in a distance range of 1.45m) improving previously reported perfor-mances in the same dataset by a factor of 2.5. The performance of bout-based features are also benchmarkedagainst traditional source-receptor distance estimators such as the mean, variance and maximum of the response.We also study how the length of the measurement window affects the performance of different signal featuresand how to tune the filter parameters to make the predictive models insensitive to wind speed. A MATLAB im-plementation of the proposed filter and all analysis code used in this study is provided.

1. Introduction

While the spatial distribution of a time-averaged chemical plume isoften described by a Gaussian model [1], the instantaneous dynamicsof chemical concentration in a turbulent plume are complex. A turbu-lent plume occurs when a chemical substance is dispersed by a carrierfluid (e.g., wind) which flow presents turbulent characteristics, such asvortices and intermittency. Close to the chemical source, the instanta-neous concentration fluctuations depart strongly from Gaussianity andare characterized by strong bursts and intermittent periods of near-zeroconcentration. Yee et al. described that the concentration distribution ofa turbulent plume fits well a Clipped-Gamma probability density func-tion [2]. In the frequency domain, chemical plumes are wide-band ran-dom signals with substantial power spectral density (PSD) up to sev-eral KHz [3]. While it is accepted that insects are able to find hid-den information from these complex signals for odor navigation pur-poses [4], the sub-Hz bandwidth of chemical sensor signals largely lim

its the efficacy of information retrieval, hindering the application of mo-bile robots for chemical source localization (CSL) tasks [5].

One path to follow is to improve the dynamics of the sensor responseby signal processing methods. While it is possible to model the direct dy-namic behavior of chemical multisensory systems [6–8], for the purposeof real-time signal processing it is more convenient to use non-lineardynamic inverse filters [9–11]. In a very interesting approach, Di Lelloet al. modeled the sensor dynamics as an Augmented Switching LinearDynamical System [12] and use the Expectation Correction InferenceMethod [13] to estimate the ground truth gas concentration. However,many of these attempts have been tested in laboratory conditions wherethe presence of a sensor chamber masks the underlying sensor dynam-ics. In few cases, inverse modelling has been used to compensate nakedgas sensors for robotics applications [14]. However, currently there isa lack of consensus on the best procedure to extract information fromslow-response chemical sensors for CSL purposes.

⁎ Corresponding author at: Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology, Baldiri Reixac 10-12, 08028, Barcelona, Spain.Email address: jburgues@ibecbarcelona.eu (J. Burgués)

https://doi.org/10.1016/j.snb.2020.128235Received 15 April 2019; Received in revised form 23 March 2020; Accepted 30 April 2020Available online xxx0925-4005/ © 2020.

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Instead of pursuing the ambitious goal of improving the dynamic re-sponse of chemical sensors, a workaround is to extract dynamic featureswhich are informative of the distance between the sensor and the chem-ical source, i.e. the source-receptor distance. A source distance estimateis important for CSL in applications such as environmental monitoring[15] or mobile robotic olfaction [16–19]. In the latter case, a source dis-tance estimate can be used by a mobile agent to navigate towards thechemical source [18,19] or to declare that the source has been found[16,17]. These dynamic features often appear related to the intermit-tent contact between the sensor and chemical filaments or patches inthe plume. Lilienthal et al. [16] found that the standard deviation of thesignals of a metal oxide (MOX) sensor placed at different distances (0.5– 1.45m) to a naturally evaporating gas source was more correlated tothe source-receptor distance than the average sensor response (both fea-tures were computed during 90s). Ferri et al. [18] derived an empiricalformula to assess the proximity to a chemical source based on the meanintensity and number of peaks of the MOX sensor signals, assuming astrong unidirectional airflow. Such formula was used in real-time by amobile robot to navigate towards a gas source in a small indoor envi-ronment (3×2 m2).

More recently, Schmuker et al. [19] proposed an algorithm to ex-tract short time-scale features from the first derivative of the responseof MOX sensors, the so-called “bouts”, which were exploited to predictthe source-receptor distance (range 0.25 – 1.45m) using MOX sensorsin wind tunnel experiments. Before going into algorithmic details, it isenough to understand that the bouts are simply the rising edges of the“clean” derivative of the sensor response, and they appear when the sen-sor gets in contact with a chemical patch (Fig. 1). The advantage of us-ing the derivative is that it is an approximation to the inverse dynamicresponse of a MOX sensor, which is often modelled as a leaky integratorof the concentration [20]. It has been show empirically that the deriva-tive combined with low-pass filtering can increase the bandwidth of theMOX sensor by a factor of four [21]. Thus, the derivative will show fea-tures associated to fast fluctuations of the chemical concentration thatwould otherwise be masked in the raw sensor response due to the lowbandwidth of the sensor (Fig. 1). A second advantage of the derivative isthat it is insensitive to changes in background concentration, providinga source distance estimate that is independent from slowly time-varyingconcentration fields. Background issues can be encountered, for exam-ple, in confined environments such as wind tunnels or indoor areas dueto gas accumulation.

Under certain simplifying conditions, such as unidirectional and con-stant air flow, constant release rate and long measurement window, thenumber of bouts detected by a MOX sensor in the centerline of thechemical plume monotonically increases with proximity to the source,enabling accurate source distance predictions [19]. In the wind tun-nel mentioned before, a linear model relating the number of bouts de-tected in three minutes and the distance to the source (distance range25 – 145cm) achieved a cross-validation error of only 18cm. How-ever, since these results were not benchmarked against previously pro-posed source distance estimators, such as the mean [22], maximum [23]or variance [16,17,24] of the response—which may also perform wellconsidering the long measurement window—it is hard to say if the re

sults are good or bad. Also, the wind speed has a strong effect in thenumber of detected bouts, which could notably increase the predictionerror if the wind conditions during operation of the algorithm deviatefrom those of training [25]. Another factor that could degrade the al-gorithm performance is the size of the measurement window, which insome applications (e.g., mobile robots) must be certainly lower thanthree minutes.

Working with the derivative has also some practical inconveniences,as differentiation is a risky signal processing operation that often leadsto amplification of high-frequency noise. Differentiation of noisy signalsis a well-known signal processing problem [26] widely used across sev-eral disciplines, e.g., in biomedical signal processing for the detection ofQRS complexes in ECG signals [27]. To prevent signal to noise degrada-tion, differentiation must be combined with low-pass filtering matchedto the signal bandwidth. The standard approach is to use a low pass dif-ferentiator (LPD), also known as linear-phase FIR differentiator, whichcan be designed from the selected specifications in the frequency do-main using the Remez algorithm [28]. A linear-phase filter delays allfrequency components by the same amount, preserving the waveform ofthe input signal (assumed bandlimited and contained in the filter band-pass). Preserving the waveform is of utmost importance for the properoperation of the bout detector (in terms of signal-detection theory) be-cause a thresholding decision must be made on the amplitude of thedetected bouts to distinguish between “genuine” bouts produced by theplume and “false positive” bouts caused by noise. Bout detection errorswill degrade the performance of posterior bout-based estimators.

Instead of following the standard approach, Schmuker’s algorithmcomputes the low-pass derivative using a rather arbitrary cascading ofdigital filters with nonlinear phase, introducing unnecessary complex-ity into the algorithm and distorting the waveform of the output sig-nal. Specifically, the raw sensor response is first smoothed with a Gauss-ian filter, the resulting signal is differentiated, and the derivative issmoothed again using a first order infinite impulse response (IIR) filter[29]. Gaussian filters are ideal time response filters since they show thefastest step response under the condition of no overshooting [30]. Theyare mostly used in image processing, but seldomly in signal processingsince they are non-causal and physically unrealizable. Beyond simpletruncation, more sophisticated approaches to Gaussian filter approxima-tion have been proposed for both IIR [31] and Finite Impulse Response(FIR) [32] filters. In any case, the intended advantages of the Gaussianfilter are lost when in cascade with an IIR filter. The disadvantage of IIRfilters is the signal distortion due to nonlinear phase in the pass band. Afurther disadvantage of using two low-pass filters instead of one is that,for a desired filter response, two coupled parameters (the standard de-viation σ of the Gaussian filter and the time constant τ of the IIR filter)with non-intuitive interpretation must be tuned.

Probably due to this non-optimal low-pass filtering, Schmuker et al.found that low-amplitude bouts may appear in the baseline response ofthe sensor (Fig. 1), i.e. in signals recorded in the absence of gas that,by definition, should not contain any bout. In order to filter out thesefalse positives, Schmuker’s algorithm discards all bouts with amplitudelower than a certain threshold, defined as the mean plus three stan-dard deviations of the amplitude of all bouts detected in the sensor base

Fig. 1. Schematic representation of the raw sensor response, its “clean” derivative and the detected “bouts” when the sensor is exposed to a chemical plume. The figure illustrates that thedynamics of the derivative are much faster than those of the raw response.

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line. This statistical rule, known as the three-sigma rule, states that fora normal distribution 99.73% of the samples will fall within three stan-dard deviations of the mean. It is empirically used by Schmuker et al.to treat 99.73% probability as near certainty that no bout in the sen-sor baseline will exceed the threshold, assuming that the distribution ofbout amplitudes in clean air follows a normal distribution. However, werecently found empirically that this assumption is not necessarily true[33], mainly because the bout amplitude is bounded by zero (i.e., it isstrictly positive). Two questions that immediately arise are: (1) is thethree-sigma rule an optimal threshold? and (2) are these low-amplitudebouts a consequence of non-optimal low-pass filtering?

In this paper, we propose a method to predict the distance to a gassource from the transient response of MOX sensor signals, inspired bythe bout detection algorithm presented by Schmuker et al. The proposedalgorithm uses an LPD filter with a single and intuitive parameter (band-pass frequency) followed by a thresholding decision on the amplitudeof the resulting bouts, reducing the number of parameters of the algo-rithm from three to two (bandpass frequency and amplitude threshold).Instead of a heuristic selection of the algorithm parameters (as was donein the original work by Schmuker et al.), we propose in this contribu-tion a systematic optimization aiming to extract the maximum predic-tive power from the sensor signals. As a case study, we use recordingsfrom MOX sensors in a wind tunnel (same dataset used by Schmukeret al.). First, we optimize the algorithm parameters and the regressionmodel (linear and non-linear) in cross-validation samples, and then as-sess its performance in external validation samples, i.e. unseen duringmodel fitting. The results are benchmarked against Schmuker’s algo-rithm and traditional source distance estimators such as the mean, vari-ance and maximum of the response. We demonstrate that the proposedalgorithm can largely improve the prediction performance of the origi-nal bout detection algorithm and make the predictive models more ro-bust against changes in wind speed. We also study how the length of themeasurement window affects the performance of the different estima-tors. The last (but not least) contribution is a MATLAB implementationof the proposed algorithm and the scripts used to generate the resultsand figures of this paper.

2. Signal Processing Methods

Section 2.1 provides a general overview of the signal processingpipeline required to compute the bouts of a signal and how to usethem to predict the source-receptor distance. The algorithmic details ofSchmuker’s implementation and the one proposed in this paper are de-scribed in Sections 2.2 and 2.3, respectively.

2.1. Bout detection and source-receptor distance prediction

The goal of the bout computation algorithm is to detect and countthe number of bouts from a raw sensor signal. Fig. 2 illustrates the gen-eral signal processing pipeline to do that. First, the low-pass derivative

of the raw signal x is computed. The bouts, which are the risingedges of , are segmented by looking for two consecutive zero-cross-ings of the positive derivative of this signal, i.e. . The amplitudeof a bout is defined as at the end of the respective bout segment mi-nus at the start of the same bout segment. Due to sensor noise or in-sufficient smoothing, bouts with very low amplitude are usually inter

leaved with larger bouts produced by the plume. It is of practical inter-est to filter out bouts produced by noise, as they deteriorate the relation-ship between bout count and source distance. For that, a threshold isapplied to the amplitude of the detected bouts and only bouts with am-plitude larger than the threshold are considered for the final bout count.

By repeating the above process with signals captured at different dis-tances to a chemical source (Fig. 3A), the functional relationship be-tween the bout count and the source-receptor distance can be estab-lished (Fig. 3B). Once a good calibration model has been obtained, thesource-receptor distance of new (unseen) sensor signals can be predictedby projecting the bout count of the unseen signal into the regressionmodel (Fig. 3C). However, it should be clear that this model is local tothe experimental conditions used in the calibration phase.

2.2. Schmuker’s algorithm

2.2.1. Schmuker’s (SMK) low-pass differentiating filterTo compute the low-pass derivative of a signal, Schmuker’s algo-

rithm implements a rather cumbersome digital filter, named in this pa-per SMK filter, resulting from the cascading of a Gaussian filter and aemaα digital filter (Fig. 4). The choice of the Gaussian filter is rather ar-bitrary and introduces undesirable effects such as non-causality and in-troduces an extra parameter (the standard deviation σ ) that needs to beoptimized. Another problem of the Gaussian filter is that different val-ues of σ may change the gain of the filter (see Fig. 11D in [19]) leadingto potential misinterpretations of the effect of σ on the filtered signal.Additional issues of this implementation are described in detail in theAppendix A.

The emaα digital filter, originally proposed by Muezzinoglu et al.[20] to improve the response time of a MOX sensor, is a rough approx-imation for a linear inverse filter of the dynamics of the MOX sensorresponse. It is used by Schmuker et al. to compute the low-pass deriv-ative of a signal that has been already smoothed. This filter is basedon the exponentially weighted moving average (EWMA) filter [34], alsoknown as exponential moving average (EMA) filter. EWMA is a first-or-der IIR filter commonly used to smooth temporal series, which givesmore importance to recent data by discounting older data in an expo-nential manner (Equation (1)). At time t = nTs, (being Ts the samplinginterval) the smoothed value y[n] is found by computing

(1)where x[n] is the observation at time t = nTS, y[n - 1] is the previousoutput of the filter and the smoothing factor α (0 < α ≤ 1) controls thespeed at which older responses are dampened. Values of α close to zeroplace most of the weight on past values of the signal, whereas α closeto 1 give most importance to the current value, quickly forgetting oldvalues. By expanding Equation 1, we can derive the output of the filteras a convolution of the input with the unit impulse response

(2)

which illustrates the exponential behavior since the weights, (1 - α)kdecrease geometrically. A meaningful way to specify α is by the half-lifetime (s), τ, of the exponential decay, which is the time at which the ex-ponential weight (1 - α)k decays by one half

Fig. 2. Signal processing pipeline to detect and compute the bouts from a raw sensor signal.

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Fig. 3. Signal processing pipeline to detect and compute the bouts from a raw sensor signal.

Fig. 4. Block diagram of the low-pass differentiation of a signal using Schmuker’s (SMK) filter. The meaning of each symbol is given in the text.

(3)

where fs is the sampling frequency of x (Hz).The output of the emaα digital filter at time t = nTs is

(4)

where the variables have the same meaning than in Equation 1. Theemaα operator is a connection in cascade of two linear time-invari-ant systems: first, taking the derivative of the input signal, i.e.

; second, smoothing the derivative using an EWMA fil-ter (Equation 1). The derivative of the response is the simplest inversefilter of a MOX sensor, which due to the slow chemical reactions hap-pening on the sensor surface acts as an integrator of the input stimuli[19]. Smoothing is necessary because differentiation degrades the sig

nal to noise ratio (SNR). As α approaches 1, the closer is the filtered sig-nal to the derivative and the faster is the response. However, being closeto the derivative means also higher noise. Thus, α governs a trade-offbetween response time and SNR. By embedding the computation of thederivative into the EWMA filter and naming Equation 4 the emaα opera-tor, Muezzinoglu et al. introduced a slight confusion in the terminologybecause Equation 1 is also known in the literature as the EMA filter.

2.2.2. The three-sigma thresholdBy definition, bouts must be caused by the plume, so Schmuker et al.

intelligently use the amplitude of the bouts detected in the baseline ofthe sensor as an indicator of the level of noise that is still present in thesignals. Assuming that the distribution of bout amplitudes in the sensorbaseline follows a normal pattern, Schmuker et al. use a fixed amplitudethreshold, bthr, defined by the three-sigma rule

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(5)where μ and σ are the mean and standard deviation, respectively, of thedistribution of amplitudes of the bouts detected in the sensor baseline(i.e. in clean air). This threshold guarantees a 99.73% specificity or truenegative rate (TNR) if the underlying distribution is Gaussian. The ad-vantage of this threshold is that it can be straightforwardly applied inpractice, since it only requires exposing the sensor to clean air duringseveral minutes. However, it is not an optimal threshold for several rea-sons. First of all, we recently found empirically that the normality as-sumption in which it is based is not necessarily true [33]. This meansthat the 99.73% specificity cannot be guaranteed. The threshold is alsonon-optimal from a signal-detection theory point of view, since it im-plicitly assumes that high specificity (i.e., low false positive rate) is moreimportant than high sensitivity (i.e., low false negative rate). However,the latter one is very important far from the source where signals arevery weak and bouts so infrequent that the threshold of the detectormust be set as close as possible to the noise level to detect low-ampli-tude bouts produced by the plume. Finally, the threshold also assumesthat the measurement noise is additive, i.e., the noise characteristics areindependent of the magnitude of the signal. In the case of chemical sen-sors, electronic noise can be additive but other sources of noise that alsoaffect the sensor signal (e.g., chemo-transduction noise) usually dependon the chemical concentration [35]. This means that the noise level inthe sensor baseline may not be representative of the noise level duringgas exposure.

2.2.3. Linear regression modelSchmuker’s algorithm only considers a linear regression model for

fitting the relationship between bout count and source-receptor dis-tance, despite the experimental data they measured was slightly non-lin-ear. They argue that linear models are simpler and can prevent overfit-ting when the true relationship between both variables is unknown.

2.2.4. Parameter optimizationSchmuker’s algorithm requires two parameters to be optimized: the

standard deviation σ of the Gaussian filter and the time constant τ of theIIR filter. The bout amplitude threshold is also a parameter of the algo-rithm but is automatically estimated from the baseline signals. The orig-inal paper does not describe how these two parameters should be op-timized but instead provide a heuristic selection of values for the windtunnel dataset, i.e., σ = 0.4 s and τ = 0.3 s.

2.3. Proposed algorithm

The implementation proposed in this paper uses a linear-phase FIRdifferentiator to compute the low-pass derivative of the raw signal, atunable amplitude threshold and a non-linear regression model.

2.3.1. Low pass differentiator (LPD) filterA linear-phase FIR differentiator or low pass differentiator (LPD) fil-

ter differentiates the input signal at low frequencies and, at the sametime, removes high frequency components from the signal. Operatingwith such a differentiator results in a constant non-zero group delay,which means that all frequency components are delayed by the sameamount, preventing signal distortion. The design specifications of anLPD filter include the pass-band frequency (fp), stop-band or cut-off fre-quency ( fc), amplitude in pass-band ( Ap ), amplitude in stop-band (As ) and the maximum allowable deviation or ripples between the fre-quency response and the desired amplitude of the output filter for eachband (Fig. 5). Given some filter specifications, the Parks-McClellan al-gorithm [28,36] provide filters with an optimal fit between the desiredand actual frequency responses, and minimum order. For FIR differ-entiators, which have an amplitude characteristic proportional to fre

Fig. 5. Frequency response specifications of a low-pass differentiator (LPD) filter. Themeaning of each symbol is given in the text.

quency, the algorithm uses a special weighting technique so that the er-ror at low frequencies is much smaller than at high frequencies. Reason-able values for Ap and As are Ap = 1,As = 0 and a maximum deviationin both bands of -60dB. In order to minimize the number of tunableparameters, we also fix the size of the transition band (i.e., fc - fp) to0.1Hz. In this way, the filter has only one parameter to be tuned: thecut-off frequency fc.

2.3.2. Tunable bout amplitude thresholdTo improve the predictive performance of the bout detector, we

use a tunable amplitude threshold, bthr, to discard low-amplitude bouts.Similarly to the SMK filter, the LPD filter will also produce some boutsin the baseline response, depending on the selected cut-off frequency(see Supplementary Material). Instead of fixing the threshold in ad-vance, i.e., as the three-sigma threshold, in our implementation thethreshold is a free parameter of the algorithm that must be optimizedjointly with the cut-off frequency of the LPD filter in order to extract themaximum information from the signals.

2.3.3. Linear and non-linear regression modelsIn order to increase the predictive performance when the measured

data deviates from linearity, the proposed algorithm considers both lin-ear and non-linear models, such as polynomials, power laws, exponen-tials and logarithmic models.

2.3.4. Parameter optimizationThe proposed algorithm has three parameters that must be opti-

mized: the cut-off frequency of the LPD filter ( , the bout amplitudethreshold ( bthr ) and the type of regression model (linear, exponential,etc). These parameters must be jointly optimized because they are in-terrelated, i.e., the amount of smoothing of the derivative will influencethe amplitude of the resulting bouts. For example, if fc is lower than thesignal bandwidth, the filtered derivative will be noisy and bthr wouldhave to be high to ignore many low-amplitude bouts caused by noise.On the other hand, if fc is higher than the signal bandwidth to ensurethat most noise is removed, bthr can be lower as the filtered derivativewill be cleaner. To optimize the three parameters simultaneously, wepropose a grid search procedure in combination with cross-validation.The idea behind grid-search is to define, for each parameter, a range ofvalues that will be explored. Then, the cross-validation procedure willsplit the experimental data into multiple train and test partitions to as-sess which combination of values achieves the best performance, mea-sured in terms of root mean squared error (RMSE)

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(6)

where is the source-receptor distance (m) predicted by the model, yiis the true source-receptor distance (m) and n is the number of test sam-ples. Specific details on the values used for each parameter, number ofpartitions, size of each partition, etc. are given in Section 3.2 and 3.3.

3. Experimental

The goal of the experiments is to optimize the proposed algorithmand evaluate its performance for predicting the source-receptor distancein real data. For that, we use the wind tunnel dataset used by Schmukeret al. In this section, we provide an overview of the dataset and explainhow we optimized the algorithm and analyzed the data.

3.1. Wind tunnel dataset

The wind tunnel dataset [37] contains recordings from nine gassensor arrays inside a small wind tunnel where turbulent gas plumesof single compounds from ten possible chemicals (e.g., Acetaldehyde,Toluene, Carbon Monoxide) were created by injecting pressurized gasinto one end of the tunnel and dragging it with an exhaust fan from theother end of the tunnel (Fig. 6). The gas source is a flexible nozzle thatreleases the selected gas at a constant flow rate of 320sccm. The noz-zle is connected to the outlet of three mass flow controllers (MFCs) thatproduce a certain concentration from pressurized gas stored in cylin-ders. The nine sensing boards were always positioned along a line per-pendicular to the wind direction, acquiring simultaneous measurementscross-wind. Depending on the experiment, the whole line of sensors wasplaced at a different distance to the gas source (range 0.25 - 1.45m).In this way, the concentration within the wind tunnel was measured in54 locations (9×6 grid). Each sensor array integrates eight MOX sen-sors (Several TGS 26XX models, Figaro Engineering Inc.) operated atthe same, constant heater voltage (range 4.0-6.0V). The sensor responsewas measured with a voltage divider (10 kΩ load resistor) and sampledwith a 12-bit ADC. A total of 900 distinct experiments were performedby varying the distance to source (6 possible), gas (10 possible), sensortemperature (5 possible) and wind speed (3 possible). Each experimentwas repeated 20 times. Different wind speeds (range 10-34cm/s) werecreated by varying the rotational speed of the exhaust fan.

In each experiment the following sequential procedure was per-formed: (i) Measure the baseline response of the sensors for 20 s in theabsence of gas, (ii) Release the selected gas for 3minutes, (iii) Circulateclean air for 1minute to record the sensor recovery and (iv) Purge thewind tunnel by setting the fan at maximum speed (signals not recorded).Despite gas is released at t = 20 s, it does not arrive immediately to thesensors. The recorded signals show a transient behavior from t = 20 sto t = [80,110] s corresponding to the propagation and stabilization ofthe gas within the wind tunnel. The duration of the transient dependson the distance to the source (i.e., sensors closer to the source stabi-lize faster) and the wind speed (i.e., signals stabilize faster at high windspeeds). A common time frame where all signals are stable regardless ofthe distance and wind speed is from t = 110 s to t = 200 s. We denotethis time frame (of length 90s) as the “stable gas release” period.

3.2. Data analysis

We use the following data from the wind tunnel dataset: board #5(located in the plume centerline), sensor #4 (TGS 2600), heater voltageof 6V and Acetaldehyde gas. For this configuration, sensor recordingsare available at 3 wind speeds, 6 distances to the source and 20 trials perdistance/wind combination (360 experiments). The recordings capturedat d = 1.40 m present some artifacts due to an imperfection of the windtunnel (this was already pointed out by Vergara et al. and Schmuker etal.) so we excluded them from the analysis. Thus, the dataset that weuse contains 300 experiments (3 wind speed x 5 distances x 20 trials).From each recording, we extract the region corresponding to the sta-ble gas release period and compute four descriptors of the signals: themean, variance, maximum response and bout frequency.

Regarding the computation of the bout frequency, we compare dif-ferent filters and bout amplitude thresholds. Specifically, we useSchmuker’s filter (Section 2.3) with default smoothing parameters (i.e.,σ = 0.3 s and τ = 0.4 s) and 20 LPD filters (Section 2.4) with differ-ent pass-band frequencies ( fpass ) spanning the range [0.1, 2.0] Hz insteps of 0.1Hz. For each of these filters, we extract the bouts accord-ing to the procedure described in Section 2.5 and, instead of applyingthe μ + 3σ threshold (Eq. 5), we compute the bout frequency using 500thresholds (bthr) spanning the range [10 - 4, 101 ] MS/s (S stands forSiemens) in logarithmic steps. The bout frequency (bouts/min) is thenumber of above-threshold bouts divided by the length (in minutes)of the measurement window. The bout frequency associated to eachcombination of fpass and bthr is considered a different signal feature.

Fig. 6. Schematic representation of the wind tunnel. The six measuring distances are coded in a gray scale and labelled P1 to P6. The inset on the bottom right corner shows a board with8 MOX sensors (Several TGS models: 2600 (2x), 2602 (1x), 2610 (1x), 2611 (1x), 2612 (1x), 2620 (2x), Figaro Engineering Inc.). Adapted from [19].

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Thus, we have 10,500 bout-based features (500 thresholds x [20 LPDfilters + 1 SMK filter]).

Using the bout-based features and the three statistical descriptors(mean, variance and maximum) we build a feature matrix X containing300 rows (1 per experiment) and 10,503 columns (1 per feature). Thematrix X is then split into 3 subsets X1, X2, X3, each one correspondingto a different wind speed. Each Xi is composed of 100 rows (5 distancesx 20 trials) and 10,503 columns.

3.3. Fitting, selection and validation of predictive models

For each signal feature y (dependent variable) in Xi, we want to findthe model f that best fits the relationship , where x is the dis-tance to the source (independent variable). Due to the limited numberof levels (5) of the independent variable, we are forced to use simpleempirical models with few degrees of freedom, such as linear, quadraticand cubic polynomials, one-term exponential and one-term power se-ries. To find which of these models achieves the best prediction accu-racy for each signal feature, we performed a combination of hold-out(external validation) and cross-validation (CV) (internal validation) pro-cedure (Fig. 7).

The hold-out procedure is initially applied to split the dataset Xi intoa ‘train’ and ‘test’ subsets using the first 14 trials (70% of the data) fortraining and the remaining 6 trials (30% of the data) for testing. Thetraining set is used to find a suitable model for the data, and the test setis used to assess how well the selected model performs on unseen data.To find a suitable model for the data, we apply 5-fold CV in the ‘train’subset which consists on breaking the data up into 5 partitions and then,5 times in turn, using one partition for testing and the remaining onesfor fitting each of the models. Then, we compute the RMSE (Eq. 6) ofeach model in each test partition and select the model that minimizesthe average RMSE over the 5 folds. This model is refit using all train-ing samples and validated against the hold-out test set by computing theRMSE in prediction (RMSEP). To assess the performance of the predic-tive models under non-matching train and test wind speeds, the RMSEPis computed on hold-out partitions (i.e., last 6 trials) from datasets Djwith i≠j.

3.4. Distance prediction using shorter measurement windows

We also studied the impact of using shorter measurement windowsof 60, 30 and 10s. Since the window is shorter than the length of

Fig. 7. Model selection and validation by a combination of hold-out and 5-fold cross-val-idation (CV). The dataset is split into ‘test’ (30%) and ‘train’ (70%) partitions. The ‘train’partition is used to evaluate the performance of different models by 5-fold CV. In eachfold, different models are fit using 80% of the data and validated against the remaining20% of the data. The model with minimum average RMSE across the 5 folds is refit usingall training samples and validated against the hold-out subset.

the available signal (90 s) we need to select a chunk of the signal of thedesired length. To minimize sampling bias, we randomly sample (withreplacement) N segments of the desired length from the stable gas re-lease period of the 300 available signals. We used values of N of 5, 10and 20 for the window sizes of 60, 30 and 10s, respectively. Then, foreach wind speed, signal feature, window size and segment, we followthe procedure described in Section 3.3 to fit, select and validate a pre-dictive model. The only difference is that now we have N RMSEP valuesassociated to a given feature (one per segment), so we take the averageRMSEP across all segments.

3.5. Spectral analysis

The power spectral density (Syy) of the signal x will be approximatedby the Periodogram [38].

3.6. Software and reproducibility

Data analysis was performed using MATLAB (version R2018b) andthe following toolboxes: signal processing, and statistics and machinelearning toolbox. Spectral analysis was performed using the functionfft. LPD filters were designed using firpmord and firpm functions with‘differentiator’ argument. Schmuker filter was implemented in the timedomain using the convolution of two impulse responses: a truncatedGaussian filter G, implemented using the function gausswin(N, α) withN = 10σs and α = 5, and a first order FIR differentiator D of the form[1, -1]. The output of this filter was the input of the EWMA filter E. Con-volution was performed using function conv. The resulting filters wereapplied to new data using function filter. Curve fitting was performedusing polyfit and evaluated on new data using polyeval.

All analysis code used in this study is freely available under an opensource license at https://github.com/jburgues/DistPredMOX. The codeallows the reader to reproduce the entire analysis, including recreationof most figures.

4. Results and Discussion

4.1. Raw signals

We analyzed the signals recorded by a MOX sensor in the plume cen-terline at several downwind distances and three wind speeds (Fig. 8).Regardless of the wind speed and source-receptor distance, the signalsare characterized by a plateau of stable mean value (produced by theaccumulation of gas within the wind tunnel) modulated by some fluc-tuations due to turbulence. The source-receptor distance and the windspeed have a strong influence on the mean intensity and the fluctuationsof the signals: with increasing distance or wind speed, the intensity andvariability of the signals decrease. Higher wind speeds dilute faster thereleased chemicals, resulting in lower average concentrations. While atlower wind speeds the mean, maximum and variance of the responsesseem to be correlated with the distance to the gas source, as the windspeed increases such correlation becomes unclear.

4.2. Source-receptor distance prediction using the mean, maximum andstandard deviation of the response

Fig. 9 shows the relationship between common statistical descrip-tors of the raw signal and the source distance at different wind speeds.The average response was best fit with logarithmic models at low windspeeds and with power models at high wind speed (Fig. 6a). The RM-SEP degrades from 21cm to 28cm as wind speed increases, due to adecrease in sensitivity far from the source. The RMSEP is inflated bythe abnormally low concentration measured at d = 50 cm, which doesnot agree with previously reported empirical models [39] describingthe relationship between mean concentration and source distance, x,

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Fig. 8. Responses of a TGS2600 sensor at four downwind distances (coded by the line transparency; see labels on the left-most plot) and three wind speeds (coded by the line color; seelabels on top of each plot). Data corresponds to trial #1 and sensor #4.

Fig. 9. (a) mean, (b) variance and (c) maximum response vs. source-receptor distance at different wind speeds in one of the folds of 5-fold cross-validation (CV). The fit and test samplesfor this fold are represented by solid circles and crosses, respectively. The solid lines represent the models with minimum over 5 folds.

as a power law of the form 1/x. A potential cause for the anomalousmeasurements at d = 50 cm is the high variance in wind direction mea-sured by Vergara et al. at that sampling location (c.f. Fig. 3b in [37]),probably owing to the geometry of the wind tunnel.

The standard deviation of the response (Fig. 6b) is highly scatteredin different trials, leading to a high RMSEP of around 26cm regard-less of the wind speed. The high scattering observed at the lowestwind speed may be a consequence of the low-energy turbulent mix-ing characteristic of environments with weak airflow [18]. The opti-mum model switches from linear to logarithmic to power with increas-ing wind speed.

Finally, the maximum of the response (Fig. 6c) has a similar behav-ior than the mean response but with lower RMSEP (20-25cm), resultingthe best estimator at all wind speeds.

4.3. Source-receptor distance prediction using bouts

We now explore if bout-based features can improve the previousresults. The spectral analysis of the raw signals (Fig. 10a) indicatethat the power content of the signal decays exponentially with increas-ing frequency. The recordings at lower wind speeds or closer to thesource contain more power in higher frequencies than the recordings athigher wind speed or longer distances. Thus, the range of frequenciesin which the derivative can be applied with reasonable signal-to-noiseratio (SNR) depends on the wind speed and the distance to the source.From visual inspection, it seems that cut-off frequencies of 5 and 10Hz

could be appropriate for wind speeds of 34 and 10cm/s, respectively.However, in practice these values are too high since computing thebouts requires taking the second derivative of the signals, which is ex-tremely sensitive to noise. Thus, we limited the maximum pass-band fre-quency of our LPD filters to 2Hz.

Fig. 10b compares the frequency response of two SMK filters and twoLPD filters with different specifications. SMK filters are characterizedby a narrow pass-band region where the response of the filter approxi-mates the ideal differentiator, and a wide transition band were neitherthe derivative is computed, nor the noise is fully rejected. Resultingly,the filtered signal will deviate from the ideal derivative in all frequencycomponents corresponding to the transition band. Another disadvantageof SMK filter is that the design parameters σ and τ have no clear rela-tionship to the standard filter design parameters such as the pass- andstop-band frequencies or the attenuation in the stop band. For exam-ple, the filter SMK0.3s, 0.4s (i.e., σ = 0.3 s and τ = 0.4 s) has pass- andstop-band frequencies of around 0.25 and 0.7Hz, respectively, whereasin the filter SMK0.2s, 0.2s these frequencies are around 0.4 and 1.5Hz.Considering that the power spectral density (PSD) of the recorded sig-nals beyond 0.5Hz is not negligible (especially at wind speed of 10cm/s), the SMK0.3s, 0.4s filter is probably filtering out useful information con-tained in the signals.

In contrast, LPD filters maximize the region in which the derivativeis computed and can provide narrow transition bands, resulting in sig-nals with higher SNR. Comparing the LPD0.7Hz filter (i.e., fc = 0.7Hz) with the SMK0.3s, 0.4s filter, it can be seen that, with a similar stop-

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Fig. 10. (a) Power spectral density (PSD) of the raw signals at different distances to the source and wind speeds. Each trace represents the average of 20 trials. The noise threshold isestimated from the PSD of the baseline responses; (b) Frequency response of two Schmuker filters ( and two low pass differentiator filters (LPDf) with different cut-off frequency.The signals of panel (a) are drawn in the background for visual reference. The ideal differentiator is depicted as a black dashed line.

Fig. 11. Filtered MOX-sensor signals at d = 0.98 m and wind speed of 34cm/s using SMK filter ( σ = 0.3 s and τ = 0.4 s) and LPD filter ( fc = 0.8 Hz). LPD-filtered signal has been shifteddownwards by 0.01 MS/s for visualization purposes. “Bouts” in both signals are highlighted in black and red, respectively. The number in parenthesis in the legend indicates the numberof detected bouts.

band frequency, the former one computes the derivative up to 0.7Hzwhereas the latter only up to 0.25Hz. As an illustrative example, Fig. 11shows the output of both filters for a signal captured at d = 0.98 m andwind speed of 34cm/s. Compared to the filtering produced by the SMKfilter, the LPD produces a sharper signal with a similar level of noise andas twice more bouts (19 versus 38 bouts).

To evaluate if the higher number of bouts is advantageous forpredicting the source distance, Fig. 12 shows the regression betweenbout frequency and source distance for the two filters. When all de

Fig. 12. Bout frequency for 20 trials vs. distance from source using LPD filter ( fc = 0.8Hz, bthr = 0) and SMK filter ( σ = 0.3 s and τ = 0.4 s) with different amplitude thresholds.The wind speed is 34cm/s and the window size is 90s.

tected bouts are used for regression (i.e., bthr = 0) the bout frequencydecreases with proximity to the source, indicating that the noise (i.e.low-amplitude bouts) decreases with proximity to the source. In thiscase, both filters provide similar RMSEP values of around 20cm, whichis already 5cm lower than the best error (25cm) achieved for this windspeed with statistical descriptors of the signal. By increasing the boutamplitude threshold, bthr, the slope of the regression changes from neg-ative to positive, the scattering among trials decrease and the RMSEPdecreases. For example, using bthr = μ + 3σ = 0.06 MS/s leads to a lin-ear decay between bout frequency and source distance, yielding an RM-SEP of 17cm. Further increasing the threshold to 0.15 MS/s changes thefunctional relationship from linear to a power law and the RMSEP de-creases to 14cm. Since the threshold seems to have a clear impact intothe prediction error, we will try to optimize it to achieve the minimumpossible RMSEP.

Fig. 13 shows the RMSEP associated to different values of fc and bthr,for two different wind speeds. If bthr is low or no threshold is used at all,fc has a big impact on the RMSEP, varying in the range 16-40cm. Filterswith high fc (i.e., 1.6-2.0Hz) are optimal at low wind speed (Fig. 13a),whereas filters with fc of 0.7-1.0Hz are optimal at higher wind speeds(Fig. 13b), which matches our visual analysis of Fig. 10b. By increasingbthr, the RMSEP of certain filters can be reduced below 15cm. For exam-ple, at low wind speed the threshold region 0.3-1.0 MS/s is optimum forall filters, and those with fc > 0.2 Hz achieve RMSEP < 15 cm in thisregion. The absolute minimum RMSEP (7cm) is obtained with fc = 1.9Hz and bthr = 0.53 MS/s. In contrast, the RMSEP of the SMK filter isalways higher than 15cm regardless of the value of bthr. The μ + 3σthreshold (0.06 MS/s ), located outside of the optimum threshold band,achieves an RMSEP of 23cm.

As fc increases (this is, the signal is less low-pass filtered) the RM-SEP in the optimum region becomes more sensitive to bthr. Lookingat the reddish traces in Fig. 13a, we can observe that a small devia-tion from the optimum threshold produces a fast increase in RMSEP.The sensitivity to the threshold is reduced at low fc (bluish traces)

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Fig. 13. RMSEP of the bout frequency as a function of the bout amplitude threshold (log scale) and the cut-off frequency of the LPD filter, for two wind speeds: (a) 10cm/s and (b) 34cm/s. For comparison purposes, the RMSEP of SMK filter with default parameters is depicted as a black trace (the μ + 3σ threshold is indicated by a red dot).

where RMSEPs below 15cm are obtained in nearly one decade aroundthe optimum threshold value.

As wind speed increases, the optimum threshold band shifts towardssmaller thresholds (Fig. 13b). At wind speed of 34cm/s, the optimumthreshold band 0.05-0.20 MS/s leads to RMSEP values below 15cmfor filters with fc < 0.7 Hz. The minimum RMSEP (13cm) is obtainedwith fc = 0.4 Hz and bthr = 0.13 MS/s. Despite the μ + 3σ thresholdis located within the optimum threshold band, the SMK filter operatedwith this threshold provides a higher RMSEP of 18cm. Low fc values(bluish traces) which might appear as the worst choice if no thresholdis used, provide the minimum RMSEP values if combined with an op-timum threshold. This illustrates the coupling between these two para-meters and suggests that simultaneous tuning of both parameters is theway to achieve the best performance.

The observed shift in the optimum threshold band as the wind speedincreases can be explained by the histogram of bout amplitudes at dif-ferent source-receptor distances (Fig. 14). At low wind speed, the over-lapping between the distributions of baseline amplitudes (noise) andplume-induced amplitudes (signal) is low, so a high threshold canseparate the noise from the signal. At higher wind speed, the his

tograms of bout amplitudes during gas exposure shift to the left whilethe baseline histogram remains fixed. Therefore, the threshold must“follow” the histogram shift to keep sufficient sensitivity far from thesource. The optimum threshold lies as far to the right as possible in thebaseline distribution while still capturing enough density of bouts at thefurthest source-receptor distances. Since the three-sigma threshold is de-termined solely from the baseline distribution, it cannot adapt to thedifferent level of overlapping produced by the various wind speeds, de-grading its performance as the wind speed drecreases.

Since the baseline distribution does not resemble a normal pat-tern—instead it can be better approximated by a Beta function— theμ + 3σ threshold does not capture the expected 99.97% of the data,but a lower value (97.81%). In other words, approximately 2.2% (in-stead of 0.13%) of the bouts detected in clean air will be declared as“true bouts”. This means that 2.2% of the detected bouts correspondto noise, increasing the scattering among different trials. This can beseen in Fig. 8, by comparing the regression of the SMK filter withbthr = 0.06 MS/s ( μ + 3σ ) and bthr = 0.15 MS/s (optimum for 34cm/s). The higher threshold not only produces less scattering of the data butalso produces a smoother increase in bout frequency as the distance to

Fig. 14. Histogram of bout amplitudes at various source-receptor distances and wind speeds. The width of the bins in the x-axis is distributed logarithmically. The y-axis represents therelative probability of each bin, computed as the number of elements in the bin divided by the number of samples. Both axes are displayed in logarithmic scale. The μ+3σ and optimumthresholds for each wind speed are depicted with vertical lines.

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the source decreases, allowing a polynomial model to accurately fit thedata even at d = 0.5 m.

The optimum predictive model for each combination of fc and bthr, as determined in cross-validation, is shown in Fig. 15. The optimummodels can be roughly clustered in three main regions: power and log-arithmic models in the upper left corner (high fc and low bthr), expo-nential models in the region 0.5MS/s < bthr < 5 MS/s, and linear mod-els elsewhere. This explains why Schmuker et al. found that their filter,which has an approximate cut-off frequency of 0.6Hz and a thresholdof 0.06 MS/s, was best approximated by a linear model. However, ifone considers the entire space of combinations, more complex modelsshould be used for optimum performance. The best model for each fc al-ways lies in the leftmost edge of the exponential region, where quadraticmodels are chosen at low fc and exponential models dominate at high fc. A summary of the optimum filter parameters and predictive model foreach wind speed is provided in Table 1.

4.4. Source-receptor distance prediction using shorter measurementwindows

Fig. 16 shows the RMSEP curves of the LPD1.9Hz filter for differentsizes of the measurement window ( W ). As it was expected, the RM-SEP degrades with shorter measurement windows. Surprisingly, reduc-ing the window size only produces a shift of the RMSEP curve with-out affecting its waveform, resulting in an optimum threshold that is al-most independent of W. Also, the RMSEP degrades non-linearly with W; e.g., reducing W from 30 to 10s (difference of 20 s) has a stronger im-pact to the RMSEP than reducing W from 90 to 30s (difference of 60 s).Specifically, the relationship between the minimum RMSEP and W canbe approximated by a power law of the form RMSEP = 80∙W - 0.26 - 17(see inset). We observed similar trends at other cut-off frequencies andwind speeds, and for the SMK filter. This confirms that the optimumvalue of fc is independent of W and mostly depends on the wind speed.

Fig. 17 compares the minimum RMSEP of different signal featuresas a function of W. As can be seen, the mean and maximum re

Fig. 15. Optimum models, as found in cross-validation, as a function of the cut-off fre-quency (fc) and the bout amplitude threshold (bthr). The window size is 90s and the windspeed 10cm/s. The threshold that achieves the minimum RMSEP at each cut-off frequencyis indicated by a red dot.

sponse are nearly insensitive to W, probably due to the slow dynam-ics of the wind tunnel facility which produced a stable plateau of meanconcentration (Fig. 8). The RMSEP of the standard deviation feature de-grades at a linear rate of 1cm for every 10s of increase of W. Finally,the bout frequency is the most sensitive to W, exhibiting a power lawdependency. Resultingly, at small window sizes the bout frequency pro-vides worse performance than simpler statistical descriptors such as themean or maximum response. In this dataset, the bout frequency is ad-vantageous only for window sizes larger than 15 s.

4.5. Source-receptor distance prediction under non-matching train and testwind speed

So far, the predictive models have been validated using trainingand test data captured at the same wind speed. If the train ( wtrain) and test wind speed ( wtest) differ, the optimum predictive modelswhen wtrain = wtest produce high RMSEP values when wtrain≠wtest. Thiscan be observed in Fig. 18 , which plots the RMSEP of the SMK fil-ter as a function of bthr and wtest whenwtrain = 21 cm/s. The optimumthreshold for this wtrain (which produces an RMSEP of 15cm whenwtest = wtrain = 21 cm/s) leads to an average RMSEP across all possi-ble wind speeds of 37cm. Similarly, the μ + 3σ threshold produces er-rors as high as 62cm if wtest = 34 cm/s. There is an optimum thresholdregion (0.019 – 0.033 MS/s) in which the prediction error at differentwind speeds is balanced, providing average RMSEPs of around 30cm.In the LPD filter, the same cut-off frequency (0.6Hz) is optimum for allwtrain, and the optimum threshold region ranges from 0.035 to 0.050MS/s. Table 2 summarizes the optimum filter values for each filter andwtrain.

5. Conclusions

We have experimentally demonstrated that, in the wind tunnel facil-ity and assuming the same constant emission rate during training andtest, the proposed algorithm can exploit transient features of gas sensorsignals to predict the gas source distance with high accuracy. This algo-rithm significantly reduces the prediction error, as compared to previ-ously reported algorithms, over a wide range of amplitude thresholds.The main finding of the study is that the cut-off frequency ( fc ) of thelow-pass differentiator filter and the bout amplitude threshold ( bthr )are coupled parameters, which means that both must be tuned simul-taneously to find the global optimum . The optimum values of fc andbthr strongly depend on the wind speed, with low fc and bthr being suit-able for scenarios with high wind speed and vice-versa. Intuitively, thissays that the cut-off frequency of the filter should match the bandwidthof the signal. If the cut-off frequency is too high, the derivative will benoisier and the detected bouts will be smaller in amplitude. Interest-ingly, low-amplitude bouts resulting from too high fc do not necessar-ily degrade the prediction error if a suitable bthr is used. Expressing thelow-pass differentiator filter with a single parameter ( fc ) was a key stepfor reducing the complexity of the optimization problem and simplify-ing the visualization of the results.

A second question addressed by this work is whether the opti-mized bout frequency outperforms traditionalsignal features such as

Table 1Optimum filter parameters for different wind speeds. Wind speed in train is the same than in test.

Wind(cm/s) LPD [optimum] SMK [optimum] SMK [μ + 3σ]

fcut(Hz)

bthr(MS/s) Model

RMSEP(cm)

bthr(MS/s) Model

RMSEP(cm)

bthr(MS/s) Model

RMSEP(cm)

10 1.9 0.51 Exp 7 0.44 Linear 13 0.06 Log 2221 1.0 0.21 Poly2 9 0.30 Exp 14 0.06 Log 2234 0.7 0.11 Exp 10 0.15 Poly2 14 0.06 Linear 18

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Fig. 16. RMSEP of the bout frequency computed with the LPD1.9Hz filter, as a functionof the bout amplitude threshold (log scale) and the window size ( W). The inset shows apower series fit to the relationship between minimum RMSEP and W. The wind speed is10cm/s.

Fig. 17. RMSEP of different signal features as a function of the window size. The windspeed is 10cm/s.

the mean, maximum or variance of the response. We found that if themeasurement window is larger than 30s, the bout frequency alwaysprovides lower prediction errors. However, the mean and maximum ofthe signal are more accurate if the measurement window is as short as10 s. This raises the question as to what extent the bout frequency pro-vides any advantage over these simpler estimators in applications suchas gas source localization by mobile robots, where rapid response time iscritical. The variance of the sensor response—which some authors con

Fig. 18. Sensitivity of the RMSEP vs. threshold curve to the test wind speed, for the boutfrequency estimator computed with the SMK filter ( σ = 0.3 s and τ = 0.4 s). The windowsize is 90s, training wind speed is 21cm/s and each line represents a different test windspeed (black line is the average of the other three lines).

sider a reliable estimator of source proximity—did not work well in thisdataset. The reason for the good performance of the bout frequency (as-suming a long enough measurement window) is the consistency of itsvalue among different trials, probably owing to the insensitivity of thederivative to changes in background concentration.

It should be noted that the optimum values of the algorithm para-meters found in this study are specific to the wind tunnel dataset. Un-fortunately, the locality of results to the experimental conditions is acommon factor in most works dealing with turbulent propagation ofchemicals, due to the complexity of such processes and the large num-ber of degrees of freedom involved. This is even complicated furtherwhen using chemical sensors, as they are cross-sensitive to external fac-tors such as variations in ambient temperature, relative humidity, at-mospheric pressure, air flow, background chemicals, etc. To confirmthat the algorithm works properly in more realistic environments, spe-cific experiments would have to be performed in such scenarios. Theoptimization methodology proposed in this paper, based on a cross-val-idation procedure, is general enough to be applied to a new scenarioincluding those that do not satisfy the assumptions of constant emis-sion rate or non-matching train and test emission rates. Indeed, weused the methodology to find optimum values in a challenging situa-tion in which the train and test wind speed do not match. In the likelycase that the test wind conditions are unknown, our results suggest thatlower prediction errors will be obtained if fc and bthr are small andthe models are trained at medium wind speed. We also optimized thealgorithm for different sizes of the measuring window, and we foundthat the optimum values of both parameters do not change substantiallybut the minimum possible error increases as a power law of the win

Table 2Optimum filter parameters when the train and test wind speed are different. The train wind speed is indicated in the first column. The other columns are optimum values considering theaverage of all possible test wind speeds. The window size is 90s.

Wind(cm/s) LPD [optimum] SMK [optimum] SMK [3 sigma]

fcut(Hz)

bthr(MS/s) Model

RMSEP(cm)

bthr(MS/s) Model

RMSEP(cm)

bthr(MS/s) Model

RMSEP(cm)

10 0.6 0.035 Linear 31 0.19 Log 33 0.06 Log 5621 0.6 0.050 Linear 29 0.33 Linear 28 0.06 Exp 4034 0.6 0.041 Linear 30 0.21 Linear 30 0.06 Linear 36

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dow size. These results encourage us to think that the same procedurecan be applied, for example, to optimize the algorithm for the case ofnon-constant emission rate.

The current work focused on source-receptor distance predictionsfrom sensors placed in the plume centerline. An obvious and interest-ing future line of work is to build predictive models that can predict thesource distance also from locations outside of the plume centerline, de-spite we anticipate higher prediction errors due to the lower bout fre-quency at those locations. Using the proposed methodology, the pub-lished code and the dataset, it would be possible for anyone interestedin this topic to continue this line of work.

Funding

This research was funded by Spanish MINECO, grant numbersBES-2015-071698 (Severo-Ochoa) and TEC2014-59229-R (SIGVOL).CERCA Programme / Generalitat de CatalunyaCRediT authorship contribution statementJavier Burgués: Conceptualization, Methodology, Software,Validation, Formal analysis, Investigation, Data curation, Writing -original draft, Writing - review & editing, Visualization. SantiagoMarco: Resources, Writing - review & editing, Supervision, Projectadministration, Funding acquisition.

Declaration of Competing Interest

The authors declare no conflict of interest.

Acknowledgments

We would like to acknowledge, the Departament d’’Universitats, Re-cerca i Societat de la Informació de la Generalitat de Catalunya (ex-pedient 2017 SGR 1721); the Comissionat per a Universitats i Recercadel DIUE de la Generalitat de Catalunya; and the European Social Fund(ESF). Additional financial support has been provided by the Institut deBioenginyeria de Catalunya (IBEC). IBEC is a member of the CERCA Pro-gramme/Generalitat de Catalunya.

Appendix A.

The description of Schmuker’s filter in the original paper (i.e., Eqs.1–4 in [19]) contains two typos that hinder the implementation of thealgorithm by other authors. First, the smoothed response (xs) is differ-entiated before applying the emaα transformation (Eq. 2 in [19]) (thisstep has been omitted in the diagram shown in Fig. 2), which is unnec-essary because the emaα transformation already differentiates the inputsignal. This extra derivative was probably included by error, due to theambiguous terminology used by Muezzinoglu et al. [20] to define theemaα operator. The source code published by Schmuker et al. is howevernot affected by this error because they apply the emaα operator by call-ing the Python function ewma, which provides the functionality of theEWMA filter only (i.e. it does not differentiate the input signal). Simi-larly, the definition of α as a function of τhalf in Schmuker’s paper (Eq.4 in [19]) contains a typo (compare it to the correct formulation, i.e.Eq. (3) of the current paper). Despite the source code published by theauthors is not affected by this error (because such definition is imple-mented by the Python function pandas.ewma) this typo has difficultedreplication of the algorithm by other authors [40].

Appendix B. Supplementary data

Supplementary material related to this article can be found, in theonline version, at doi: https://doi.org/10.1016/j.snb.2020.128235.

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Dr. Javier Burgués is a postdoctoral student in the Signal and Infor-mation Processing for Sensing Systems Lab at the Institute for Bioengi

neering of Catalonia (IBEC). Since 2014 he is working under the ad-visement of Dr. Santiago Marco at IBEC. Javier received his PhD de-gree in Engineering and Applied Sciences by the University of Barcelonain 2019, a master’s degree in Computer Science from the Universityof Southern California in 2013 and a bachelor’s degree in Telecom-munication Engineering from the University Autónoma of Madrid in2010. His main research interests are the application of signal process-ing and pattern recognition techniques to chemical sensor data, integra-tion of chemical sensors into robotic platforms and the development ofbioinspired flight algorithms for localization and mapping of chemicalsources.

Dr. Santiago Marco completed his university degree in Applied Physicsin 1988 and received a Ph.D. in Microsystem Technology from the Uni-versity of Barcelona in 1993. He held a European Human Capital Mo-bility grant for a postdoctoral position at the Department of ElectronicEngineering at the University of Rome “Tor Vergata”. Since 1995, heis associate professor of Electronic Instrumentation at the Departmentof Electronics at the University of Barcelona. In 2004 he had a sabbat-ical leave at EADS Corporate Research, Munich, working on Ion Mobil-ity Spectrometry. In 2008 he was appointed leader of the Signal andInformation Processing for Sensing Systems Lab at the Institute of Bio-engineering of Catalonia. His research concerns the development of sig-nal/data processing algorithmic solutions for smart chemical sensingbased in sensor arrays or microspectrometers integrated typically us-ing Microsystems Technologies (more at http://www.ibecbarcelona.eu/signalinfo).

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