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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Determination of (in)activity periods when monitoring human body motion is a mandatory preprocessing step in all human inertial navigation and position analysis applications. Distinction of (in)activity needs to be established in order to allow the system to recompute the calibration parameters of the inertial sensors as well as the Zero Velocity Updates (ZUPT) of inertial navigation. The periodical recomputation of these parameters allows the application to maintain a constant degree of precision. This work presents a comparative study among different well known inertial magnitude-based detectors and proposes a new approach by applying spectrum-based detectors and memory-based detectors. A robust statistical comparison is carried out by the use of an accelerometer and angular rate signal synthesizer that mimics the output of accelerometers and gyroscopes when subjects are performing basic activities of daily life. Theoretical results are verified by testing the algorithms over signals gathered using an Inertial Measurement Unit (IMU). Detection accuracy rates of up to 97% are achieved.

Large amounts of works related with Ubiquitous Computing and Ambient Intelligence (AmI) are appearing in the literature within the past years [

Detection of human body movement and inactivity periods is a critical step for human body monitoring applications. When body movement is being monitored using inertial or MARG (Magnetic, Angular Rate and Gravity) sensors, their output signals can be used to discriminate periods where the subject being monitored is static from those where he is moving. This distinction is imperative for sensor calibration and different motion monitoring applications like inertial navigation and human activity classifiers.

Most sensors present random time variations in the parameters of their mathematical model, such as the scale factors or biases [

Inertial navigation applications also need to reset the offset parameters and perform corrections during static periods in order to help avoid erroneous drift in the trajectory of the subject [

Detecting static periods is, thus, a mandatory step in most inertial sensors applications.

Detection algorithms can be classified according to the sensor they use as an input. The Acceleration Moving Variance Detector (AMVD) proposed in [

A comparative study among some of the aforementioned algorithms is also presented in [

The goal of the present work is to complete the comparative study among the previously mentioned methods over a large range of signals, in order to ensure statistical robustness. Due to the infeasibility of obtaining many signals gathered from different subjects performing a set of predetermined activities and hand labeling the start and end points of each activity/inactivity period, we have developed an acceleration and angular velocity signal synthesizer. This synthesizer will allow us to perform Monte Carlo tests over a large number of signals, making the study statistically representative.

In addition to using a larger data set, we have also completed the comparative study by implementing and testing four more detection methods. The first two are based on the computation of the spectrum (Fourier transform) of the input signals. We will use the Long Term Spectral Detector (LTSD) presented in [

This paper is organized as follows. Section 2 briefly presents the different detection methods that will be tested in the comparative study. Section 3 shows both the simulations and the application of the algorithms on real signals. Section 4 analyzes both results from theoretical and real experiments and compares our results to with those obtained in previous studies. Section 5 draws the conclusions and future evolution of the research.

As said in the introduction, we will be testing nine different methods. These methods can be grouped in three different sets: those based on the magnitude of the acceleration and/or the angular rate (AMVD, AMD, ARED, SHOD and FRD); those based on the spectrum of the acceleration and the angular rate (LTSD and FSD); those based on abrupt changes in data distributions (MBGTD and MBCD). The following subsections present the mathematical core of each of the detectors that is essential to program them,

The following methods use the magnitude of the acceleration, the magnitude of the angular velocity or a linear combination of both as the input signal. All the computations are carried out in the time domain of the signals.

The AMVD exclusively uses the acceleration signals to carry out the distinction of (in)activity periods. A sliding window is applied over the signal in which the variance of the acceleration is computed. The figure of merit of the detection algorithm is computed as follows,
_{k}_{n}

The AMD is also solely based on the acceleration signals. The magnitude of the gravity acceleration vector is subtracted from the magnitude of the acceleration vector which is computed at every instant. The figure of merit used as the input of the classifier can be computed as
^{2}) and

On the other hand, the ARED, uses only the angular rate signals as the input. The squared magnitude of the angular rate vector at each instant is compared with a predefined threshold. This can be expressed in the following way
_{k}

The SHOD uses both acceleration and angular rate signals. Its goal is to increase the precision of the previous detectors by taking into consideration that there might be instants where human body movement presents angular rate but no acceleration and

The FRD was developed by Veltink [

Instead of using the time domain to detect possible transitions from inactivity to activity and

The LTSD computes the Long Term Spectral Envelope (LTSE) of the signal. Let _{FFT}_{FFT}

The FSD is similar to the LTSD, but instead of computing the Long Term Spectral Envelope, it uses the spectrum of each frame in which the input signal is divided. Its expression is as follows
_{FFT}

The MBGT algorithm is based on computing the distance between two distributions, which are indirectly specified by means of two sample sets. Consider that we have a buffer which is filled with the last _{ij}_{−1} and _{j,N}_{a,b}_{a},x_{b}_{k,l}

The overall figure of merit of the detection algorithm is the maximum _{i,j}

Further information about the algorithm and about how to implement it so its complexity is suitable for practical applications can be found in [

The Memory-Based Cumulative Sum Detector is a variation of the well-known Cumulative Sum (CUSUM) algorithm first proposed in [_{θ}_{0}(_{i}_{θ}_{1}(_{i}_{k}

However, the CUSUM algorithm can only be applied when both the distributions (_{θ}_{0}(_{i}_{θ}_{1}(_{i}

Once we know how to estimate the distributions of each one of the sub-windows, we can proceed to compute the log-likelihood ratio as follows
_{l,k}_{l}, x_{k}

The general figure of merit of the algorithm is

Further information about the algorithm and how to reduce its computational complexity can also be found in [

All the presented algorithms have been implemented following the structure which is explained by the steps mentioned below.

Set input parameters of the algorithm.

Algorithm starts a swipe, using a sliding window, through the input signal.

For every signal frame, compute the resultant value of the figure of merit by applying

Compare figures of merit obtained for each one of the aforementioned methods with the predefined threshold. For every instant

Finally, the following list clarifies the corresponding inputs and outputs of every presented algorithm:

Input:

Signal to be analyzed:

Acceleration (X, Y and Z axes): AMVD and AMD.

Angular Rate (X, Y and Z axes): ARED.

Acceleration and Angular rate (X, Y and Z axes): SHOD.

Flexible input: FRD, LTSD, FSD, MBGTD and MBCD.

Window length (size of sliding window): AMVD, AMD, ARED, SHOD, LTSD, FSD, MBGTD and MBCD

Threshold (empirically predefined): AMVD, AMD, ARED, SHOD, FRD, LTSD, FSD, MBGTD and MBCD.

Shift (sliding window overlapping): LTSD and FSD.

Output:

Figure of merit.

Binary activity marker (computed by comparing the figure of merit with the predefined threshold).

Once the detectors are implemented we need to design a comparative study that computes different statistic parameters to determine the performance of each algorithm. Such a comparative study is divided in two parts. The first part includes simulations derived from the application of the detectors on a large set of synthesized signals, and the second part aims to complete the study by applying the algorithms on real datasets gathered from inertial sensors.

The main goal of the theoretical simulations is to apply the algorithm over a very large set of signals, since this will alow the computed performance parameters to have statistic significance. Specifically, we will be calculating the Accuracy and Correlation coefficient of the resultant activity marker with respect to the actual activity marker. The actual markers are obtained by visually inspecting each one of the gathered acceleration and angular rate signals and hand labeling the starting and ending points of each activity period. This is done by averaging the observed starting and ending points. Due to the cumbersomeness and almost impracticality of carrying out such a procedure over a large set of signals, we decided to design a synthesizer that is able to mimic signals coming out of an accelerometer and a gyroscopic sensor. The synthesizer is designed not only to avoid the hand-labeling procedure but to be able to generate large data sets as gathering many real signals is very time consuming. Therefore, the synthesizer will also generate the marker with the actual starting and ending points of each activity period so we do not have to label them manually.

At the start of the simulations we need to generate the synthetic signals and to that purpose we use the signal synthesizer. The signal synthesizer has been built to generate acceleration-like and angular rate-like signals coming from five different basic activities: walking, sitting on a chair and standing up, laying on a bed and standing up, running and jumping. Two more general activities have been implemented. The first one includes no acceleration and shows a constant angular rate and the second one includes no angular rate and shows a constant acceleration period. Although this may look like an unrealistic activity, there exist instants of time where this may happen. Thus, we have included them to ensure that the detector is as much robust as possible. The intensity of each activity,

Once the signal synthesizer is set, a Monte Carlo simulation of

Spectrum-based and memory-based methods can be computed using different combinations of sensor inputs. We have used four different combinations: the magnitude of the acceleration; the magnitude of the angular rate; and the sum and product of both acceleration and angular rate magnitudes. Proceeding this way, we will be able to determine which of the sensor combinations offers the best performance.

In order to check the theoretical results obtained in the simulations we have gathered a set of signals using two Wagyromag Inertial Measurement Units (IMUs), that we previously designed [

An Analog Devices MEMS ADXL335 triaxial accelerometer [

Two ST Microelectronics MEMS Coriolis vibratory gyroscopes are employed to sense angular velocity: LPR550AL [

A Honeywell HMC5843 triaxial magneto-resistive sensor [

A Microchip MCP9700A analog temperature sensor [

Three male healthy subjects (179.33±4.04 cm, 72.33±7.09 kg, 25±1 years) wearing two Wagyromag units placed at the hip and the ankle respectively performed twice a circuit composed of the following activities: walk 20 m, stop, sit down-stand up, stop, run 20 m, stop, jump 5 times, stop, and lay downstand up. A total of 96 signals were gathered (3 acceleration axes + 3 angular rate axes)×2 IMUs×4 subjects× 2 runs) and used as the input for all detection algorithms.

The (in)activity markers were set manually by visually inspecting the gathered signals.

Like in the theoretical simulations, an analogous optimization procedure was carried out using the real dataset in order to obtain the average maximum Accuracy and Correlation coefficient values and their associated algorithm configuration parameters. By doing this we aimed to verify those results previously obtained from the theoretical simulation and check for possible differences.

We now proceed to discuss the results obtained in the experiments we carried out. In the first part of the section we will analyze and compare all the tested algorithms between them. Additionally, in the second part, we compare our results to those obtained in other works present in the literature.

When analyzing the results thrown by the theoretical simulations using magnitude-based methods (

On the other hand, the performance of the spectrum methods is somewhere between the performance of the AMVD and the ARED. Amongst them, FSD using the product of the acceleration and the angular rate magnitudes as the input does the best in terms of accuracy. This is due to the fact that the product of the magnitudes will increase the resultant amplitude of activity periods leading to values much higher than the threshold,

Memory-based methods are thought for detecting any abrupt change in signals. This means they also detect changes during active periods. For example, if the subject starts to run faster, the resultant inertial signals will have a larger amplitude and frequency and the figure of merit of the detector will have a higher output. This can be a drawback because if the intensity change during an activity period is very radical, which is similar to a change from inactivity to activity, the detector may wrongly detect the change as a transition from activity to inactivity.

In addition to the Accuracy and the Correlation coefficient, we have also computed the ROC curves and Area Under Curve (AUC) values to follow the standards used to compare detectors and to ease the performance classification of all tested methods.

In terms of parameter configuration, we would prefer a shorter window length if we are monitoring movement in real time. Most methods have an optimal window size of around 10 samples which is an adequate latency for real time applications. Only AMD has a latency of 80 samples until it is able to start the detection procedure. This translates to a continuous delay of almost two seconds during the whole monitoring session when we use an IMU having a sampling frequency of 50 Hz like the one we used in the present work.

Now, if we look at the results when real signals are used, we can see that the effectiveness of the spectrum and memory-based methods has improved. LTSD using just the acceleration magnitude as input has the best accuracy of all tested methods (0.9711 ± 0.0072). Acceleration signals gathered using the IMU showed a slightly larger noise than the synthesized signals. This may have caused the performance increase of spectrum methods. Both MBGTD and MBCD present a raise of 3% in the accuracy rate, as the subjects did not perform abrupt changes of intensity while running or walking, which decreased the rate of false changes from activity to inactivity. Alternatively, the raise in the general performance of spectrum and memory-based methods could also be a result of the lower number of real signals that were used to run the tests compared to the number of synthesized signals.

AMD presents a lower performance when monitoring real signals as the zero-crossing-rate was higher than in the theoretical case. Its poorer performance is caused by the high amount of instants where the acceleration crosses the zero level. After computing the magnitude of the acceleration, the values corresponding to zero-crossing instants will still be zero or close to zero; they will be below the threshold and the instant will be erroneously classified as “static”. AMVD does better as the transitions from states in real signals are smoother than in synthesized signals.

Computation times of both memory-based and spectrum-based methods are larger than magnitude based methods when executed in a regular computer. Difference in computation time can be much higher if the algorithms are implemented in processors embedded in mobile devices or IMUs. This may lead to unacceptable delays in real time monitoring applications. However, this is not a problem if signals are being processed both online or offline in a regular computer. Implementation of magnitude-based methods such as SHOD should be considered when using devices that have low computation power.

Our main contribution in this work is the proposal of new algorithms to detection of human body (in)activity periods using inertial sensors, as well as other existing detection algorithms that had not been applied to this field yet. We have also extended the work in [

We have obtained similar results for the methods tested in [

Not all works presenting detection methods contain an explicit performance study, as in most cases the algorithms were developed as a part of a more complex system with different goals (activity classification, human body positioning algorithms, inertial navigation,

In summary, average maximum accuracy rates and correlation coefficients between the actual activity markers and the markers computed by the algorithms have been presented, together with the optimal configuration parameters, in

The main motivation of the presented work was to help readers wishing to implement an (in)activity detector for human body movement monitoring (and also other applications such as inertial navigation) to choose and appropriate algorithm. To do so, we have carried out a rigorous and complete comparative study between different algorithms that have been applied in recent literature to detect (in)activity periods in human body motion by means of inertial sensors. To extend the study, we have proposed and tested other methods that are being applied to detect abrupt changes in signals in different applications (industrial processes, voice detection,

Discrimination of (in)activity periods is of critical importance in inertial navigation algorithms so the Zero Velocity Updates (ZUPT) can be computed. It is also a very important preprocessing step for inertial-based human activity classifiers since it helps to divide the signals into periods that are later analyzed.

Along the paper, we have presented a comparative study among different magnitude-based algorithms provided in literature, such as the Acceleration Moving Variance Detector (AMVD), the Acceleration Magnitude Detector (AMD), the Angular Rate Energy Detector (ARED), the Stance Hypothesis Optimal Detector (SHOD), and the Filtered Rectifier Detector (FRD). The study presented in [

The use of SHOD is strongly recommended when the system has a reduced computation power and/or when lower delay is preferred over higher precision. Alternatively, LTSD is the best option if movement is being analyzed using a powerful computer and/or in an offline way.

Future work will focus on improving the quality of the signal synthesizer by increasing the resemblance between the synthesized signals and the real ones as well as including other activities of daily life in its repertoire. Other existent abrupt change detection algorithms will also be tested over a larger set of real signals to increase the statistical significance of the obtained results.

This work was partly supported by the MICINN under the TEC2008-02113/TEC project and the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía, Spain) under the Excellence Projects P07-TIC-02566, P09-TIC-4530 and P11-TIC-7103.

General diagram of positioning angles computation system based on inertial sensors. (In)activity detection is applied before position computation to allow correction of drifting parameters.

Acceleration, angular rate synthesized signals and activity marker. Activity sequence: walking, laying-standing up, walking, sitting-standing up, running, no angular rate, jumping, walking, laying-standing up, no acceleration.

Theoretical simulation diagram. A Monte Carlo simulation is performed to ensure statistical robustness.

Parameter optimization. Sweep of window length and threshold values to find maximum accuracy (MBGTD).

Internal (left and center) and external (right) appearance of Wagyromag, the employed IMU to gather inertial data.

Parameter optimization. Sweep of window length and threshold values to find maximum accuracy (MBGTD). Real signals.

Input (product of acceleration and angular rate magnitude) and output (vector of characteristics and marker) of the LTSD. Real signals.

Input and output (vector of characteristics and marker) of the AMVD. Real signals.

ROC curves computed for the eight best methods. Synthesized signals. Complete curves (up), zoomed curves (down).

ROC curves computed for the eight best methods. Real signals. Complete curves (up), zoomed curves (down).

Results of the Monte Carlo simulation (

Accuracy | 0.8741 ± 0.0181 | 0.9641 ± 0.0087 | 0.9431 ± 0.0136 | |

Correlation coeff. | 0.7137 ± 0.0360 | 0.9205 ± 0.0175 | 0.8752 ± 0.0270 | |

Window length | 26.065 ± 1.1011 | 96.9560 ± 9.8260 | 21.9300 ± 1.5849 | 10.7556 ± 1.3007 |

Threshold | 0.0188 ± 0.0049 | 0.0008 ± 0.0002 | 2.3712 ± 2.1621 | 1.3426 ± 0.2898 |

Results of the Monte Carlo simulation (

Accuracy | 0.9395 ± 0.0155 | 0.9344 ± 0.0153 | 0.9330 ± 0.0351 | |

Correlation coeff. | 0.8639 ± 0.0331 | 0.8534 ± 0.0311 | 0.8520 ± 0.058906 | |

Window length | 18.0836 ± 1.8278 | 17.3496 ± 1.8112 | 13.0636 ± 0.9983 | 9.5292 ± 1.7607 |

Threshold | 2.6441 ± 0.6272 | 13.8640 ± 3.0741 | 10.4764 ± 2.6726 | 8.3344 ± 2.8890 |

Shift | 15.1304 ± 2.2318 | 16.9824 ± 0.9055 | 13.1048 ± 0.4916 | 7.2364 ± 2.9423 |

Results of the Monte Carlo simulation (

Accuracy | 0.9252 ± 0.0179 | 0.9150 ± 0.0926 | 0.9318 ± 0.0884 | |

Correlation coeff. | 0.8328 ± 0.0388 | 0.8209 ± 0.15256 | 0.8585 ± 0.1266 | |

Window length | 14.6012 ± 0.7580 | 5.2376 ± 0.8156 | 3.3848 ± 0.2816 | 11.3200 ± 0.3639 |

Threshold | 4.9140 ± 1.7976 | 17.3252 ± 3.0170 | 16.1172 ± 3.6251 | 8.7112 ± 1.7633 |

Shift | 1.6348 ± 0.7648 | 1.3936 ± 0.5699 | 1.2744 ± 0.5312 | 1.7776 ± 0.7616 |

Results of the Monte Carlo simulation (

Accuracy | 0.9243 ± 0.0139 | 0.9114 ± 0.0179 | 0.9115 ± 0.0179 | |

Correlation coeff. | 0.8295 ± 0.02813 | 0.8040 ± 0.0345 | 0.8041 ± 0.0345 | |

Window length | 12.8088 ± 3.4643 | 5.9932 ± 3.4687 | 5.9900 ± 3.4701 | 9.7260 ± 3.7743 |

Threshold | 1.1286 ± 0.7215 | 84.9760 ± 79.7386 | 84.8680 ± 79.275 | 151.8720 ± 81.4212 |

Results of the Monte Carlo simulation (

Accuracy | 0.9257 ± 0.0145 | 0.9098 ± 0.0180 | 0.9100 ± 0.0180 | |

Correlation coeff. | 0.8339 ± 0.0289 | 0.80002 ± 0.034774 | 0.80066 ± 0.034845 | |

Window length | 8.4584 ± 3.1602 | 7.6108 ± 2.4729 | 6.0644 ± 2.1265 | 11.1192 ± 3.2323 |

Threshold | 1.749e−6 ± 5.389e−7 | 0.1117 ± 0.0179 | 0.0925 ± 0.0182 | 0.1068 ± 0.0267 |

Results of the Monte Carlo simulation (

Accuracy | 0.7921 ± 0.0178 | 0.7608 ± 0.0207 | 0.7610 ± 0.0207 | |

Correlation coeff. | 0.5228 ± 0.0389 | 0.4823 ± 0.0464 | 0.4825 ± 0.0463 | |

Threshold | 0.0100 ± 0.0070 | 0.1720 ± 0.2862 | 0.1780 ± 0.2990 | 0.1680 ± 0.2777 |

Algorithms applied to real signals. Average Accuracy, Correlation coefficient and associated parameters (Magnitude methods without flexible input).

Accuracy | 0.8875 ± 0.0196 | 0.9418 ± 0.0185 | 0.9447 ± 0.0236 | |

Correlation coeff. | 0.7610 ± 0.0411 | 0.8678 ± 0.0381 | 0.8730 ± 0.0473 | |

Window length | 16.7333 ± 2.3851 | 86.2000 ± 36.2165 | 8.5167 ± 6.5721 | 19.6167 ± 9.2617 |

Threshold | 0.0173 ± 0.0106 | 0.0011 ± 0.0006 | 38.3250 ± 26.9008 | 2.3995 ± 1.1856 |

Algorithms applied to real signals. Average Accuracy, Correlation coefficient and associated parameters (Framed Spectrum Detector).

Accuracy | 0.9533 ± 0.0194 | 0.9479 ± 0.0151 | 0.9515 ± 0.0162 | |

Correlation coeff. | 0.8918 ± 0.0420 | 0.8804 ± 0.0359 | 0.8886 ± 0.0385 | |

Window length | 20.2000 ± 9.2214 | 16.4500 ± 4.8910 | 13.5167 ± 2.5943 | 14.3000 ± 6.3390 |

Threshold | 3.2433 ± 1.3441 | 5.0667 ± 2.3935 | 5.0583 ± 2.72227 | 5.2917 ± 2.6446 |

Shift | 18.6667 ± 7.0711 | 15.9667 ± 2.6592 | 9.4667 ± 1.4477 | 9.5667 ± 2.5293 |

Algorithms applied to real signals. Average Accuracy, Correlation coefficient and associated parameters (Long Term Spectral Detector).

Accuracy | 0.9682 ± 0.0096 | 0.9523 ± 0.0591 | 0.9670 ± 0.0122 | |

Correlation coeff. | 0.9261 ± 0.0228 | 0.9165 ± 0.0428 | 0.9264 ± 0.0225 | |

Window length | 13.8500 ± 6.4327 | 5.1167 ± 2.4056 | 4.6833 ± 0.8023 | 10.7500 ± 2.5498 |

Threshold | 5.4167 ± 1.9185 | 8.9167 ± 3.0781 | 8.7083 ± 2.3045 | 9.0500 ± 2.9711 |

Shift | 2.4500 ± 0.6390 | 2.2333 ± 0.8628 | 1.9167 ± 0.6640 | 2.5833 ± 1.1134 |

Algorithms applied to real signals. Average Accuracy, Correlation coefficient and associated parameters (Memory Based Graph Theoretic Detector).

Accuracy | 0.9452 ± 0.0120 | 0.9452 ± 0.0121 | 0.9468 ± 0.0109 | |

Correlation coeff. | 0.8632 ± 0.0383 | 0.8634 ± 0.0384 | 0.8670 ± 0.0359 | |

Window length | 13.1833 ± 4.5759 | 13.6833 ± 5.0705 | 13.6167 ± 5.0182 | 13.6500 ± 5.0040 |

Threshold | 1.5467 ± 0.7218 | 454.0000 ± 285.2036 | 447.333 ± 279.4448 | 453.5000 ± 280.7149 |

Algorithms applied to real signals. Average Accuracy, Correlation coefficient and associated parameters (Memory Based CUSUM Detector).

Accuracy | 0.9414 ± 0.0164 | 0.9414 ± 0.0165 | 0.9434 ± 0.0154 | |

Correlation coeff. | 0.8588 ± 0.0465 | 0.8583 ± 0.0469 | 0.8635 ± 0.0429 | |

Window length | 12.6167 ± 4.1869 | 15.2500 ± 6.4345 | 15.0500 ± 6.8720 | 14.5167 ± 6.6832 |

Threshold | 3.468e-6 ± 2.049e-6 | 0.3588 ± 0.1731 | 0.3551 ± 0.1746 | 0.4346 ± 0.1690 |

Algorithms applied to real signals. Average Accuracy, Correlation coefficient and associated parameters (Filtered Rectifier Detector (FRD)).

Accuracy | 0.8136 ± 0.0282 | 0.8414 ± 0.0218 | 0.8248 ± 0.0305 | |

Correlation coeff. | 0.5754 ± 0.0616 | 0.6313 ± 0.0653 | 0.5878 ± 0.0703 | |

Threshold | 0.0055 ± 0.0077 | 0.1508 ± 0.0928 | 0.1566 ± 0.0899 | 0.1558 ± 0.0903 |

Area Under Curve (AUC) computed out of ROC curves obtained from application of algorithms on synthesized signals. Number in brackets indicates overall position in performance comparison.

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Area Under Curve (AUC) computed out of ROC curves obtained from application of algorithms on real signals. Number in brackets indicates overall position in performance comparison.

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