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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/).

The paper presents a two-step technique for real-time track detection in single-track railway sidings using low-cost MEMS gyroscopes. The objective is to reliably know the path the train has taken in a switch, diverted or main road, immediately after the train head leaves the switch. The signal delivered by the gyroscope is first processed by an adaptive low-pass filter that rejects noise and converts the temporal turn rate data in degree/second units into spatial turn rate data in degree/meter. The conversion is based on the travelled distance taken from odometer data. The filter is implemented to achieve a speed-dependent cut-off frequency to maximize the signal-to-noise ratio. Although direct comparison of the filtered turn rate signal with a predetermined threshold is possible, the paper shows that better detection performance can be achieved by processing the turn rate signal with a filter matched to the rail switch curvature parameters. Implementation aspects of the track detector have been optimized for real-time operation. The detector has been tested with both simulated data and real data acquired in railway campaigns.

The availability of global satellite-based positioning systems provides an economically viable means to improve the safety of control in low-traffic single-track railway lines still relying on human operation, for which current standard trackside automated equipment would be too costly [^{®}, a railway management system developed by the authors. Railway navigation based on map matching of gyroscope signals was studied in [

BLOCKSAT^{®} is a satellite-based railway management system for single-track lines with low traffic density. The system allows upgrading the operations on secondary lines with optimal cost ^{®} system [

Present MEMS-based gyroscopes offer robust inertial self-contained measurements that do not depend on external signals. Commercially available MEMS gyroscopes measure turn rates with low noise standard deviations, which can deliver reliable turn detection even at slow train maneuver speeds. Simple threshold-based turn detection has been initially considered, giving under Gaussian noise assumption small false alarm and miss probabilities: 10^{−8} to 10^{−10}. However in case of trains maneuvering at very low speeds, turn-rate signals become weak and threshold-based detection is not sufficient for high reliability detection. For these reasons a more robust, near optimal detection method has been conceived. BLOCKSAT^{®} achieves track-change detection by processing MEMS gyroscope measurements with an adaptive system based on the matched filter principle, which yields very low false-alarm and miss probabilities even for very low velocities resulting in low amplitude of the gyroscope output.

The paper is organized as follows: in Section 2 the gyroscope-based turn rate signals are characterized in the turnout detection application. The main performance parameters applicable to the binary track detection are defined in Section 3. A first reference simple threshold detector is studied under the assumption of Gaussian noise, resulting in good performance from moderate train velocities but insufficient detector reliability at low maneuvering velocities (Section 4). An optimized detector based on matched filtering is then presented in Section 5; the theoretical analysis shows substantial improvement over the simple threshold detector. However the matched filter implementation is challenging because of time to space interpolation and adaptive preprocessing requirements. An efficient solution is presented in Section 6, which allows the matched-filter-based turnout optimum detection with small computation requirements. The improved track detector is characterized and tested by simulation and experiments in Section 7. The paper ends with the main conclusions derived from the presented work.

An example of simple siding geometry is shown in

A MEMS gyroscope provides a voltage signal that is proportional to the yaw turn rate. In this paper the gyroscope is assumed to be integrated in a navigation system installed in the train head. Using a common external direction of reference, in a first approximation, the heading angle of a railway vehicle can be assumed to be the angle of the track tangent at the vehicle position. However the measured turn rate differs from the tangent approximation because of the large typical distances between car bogies, which cannot be neglected with respect to the turnout length. For the geometry of

The resulting signal is increased, with respect the track tangent, by the distance between the train head bogies; this must be taken into account when characterizing the turnout yaw rate signature for the optimized detection systems, such as the one presented in Section 5, that require an accurate knowledge of the turn rate signal.

The experimental railway turn rate acquisitions with MEMS gyroscopes reveal the geometrical details of a real siding implementation consisting of a standard switch followed by a transition curve section to achieve a siding parallel track. The tests have shown a remarkable repeatability of the gyro turn rate measurements, which has been maintained for years, even when using different train heads, gyroscope models and acquisition equipment. As an example,

The detection of a turnout deriving a train to a parallel track siding from the main track can be obtained by processing the turn rate signal provided by a MEMS gyroscope. The turnout detection is a binary decision, similar to a single bit detection in telecommunications or target detection in radar [_{d}_{fa}_{m}_{d}_{m}_{d}

A simple yaw rate threshold comparator was used as a first reference detector as shown in ^{®} prototype system [

This gyro device has a typical yaw rate measurement range up to ±75 deg/s with a typical noise density of 0.04 deg/sec/√Hz at 25 °C. The sensor specifications [

The evaluation of the detection performance is based on the error characterization of the MEMS gyroscope. Neglecting the linear accelerations sensitivity and cross-axis coupling the measured yaw rate

A typical noise histogram provided by the gyroscope manufacturer suggests a Gaussian probability density function, which is a usual assumption for MEMS gyroscopes statistics based on physical considerations and experimental data [

In addition to the probability distribution, the stochastic process autocorrelation function is needed to describe how fast the gyroscope noise evolves with time. A white noise is often used as a physical error source model [_{w}_{g}^{2} is the noise variance at the gyroscope output. The time constant τ = RC sets the filter −3 dB Bandwidth

The resulting noise is a Gaussian process with an exponential autocorrelation function [

The noise variance can be obtained as ^{2} = _{0}_{N}_{0}_{N}

In many applications _{N}_{N}_{N}

In many cases of interest the train can stop immediately after being diverted into a siding track. For this reason the turnout detection will be based on the gyro yaw rate short term signal observation when the train head transits on the switch section of the track. A map-matching approach, which has been proposed in railway navigation [

Due to the short term observation of the gyro signal, the proposed siding detection requires an accurate train location on the track in order to carry out the detection at the peak of the yaw rate. In the BLOCKSAT^{®} system, this information is supplied by the navigation subsystem based on the position and velocity data supplied by an EGNOS enhanced GPS and a Doppler radar odometer (both duplicated). The train position on the track is specified to have a maximum error of 10 m. All sensors (gyroscope, odometer, GPS receiver), and processing and communication subsystems are duplicated to conform the system reliability and availability specifications.

The binary detection theory in the case of signals in additive Gaussian noise is well known in communications, radar and sonar applications and has been applied to the present case. Following the Neymann-Pearson Criterion [_{t}

In the hypothesis H0 the train head follows a straight trajectory, and assuming a well calibrated and temperature-compensated gyroscope, the probability of false alarm, at a given observation time, can be expressed as the probability that the Gaussian noise voltage equals or exceeds the threshold (see

Under the hypothesis H1 the detection probability can be calculated in a similar way (see also

To determine the detector threshold we need to estimate the gyro noise variance ^{2}. Since noise power is proportional to the sensor bandwidth it is convenient to reduce the gyro bandwidth to the minimum value compatible with the gyro turn signal of hypothesis H1. In the studied turnout the speed is limited to a maximum of 30 km/h; assuming a higher speed limit of 50 km/h, the gyro would eventually provide a signal that can be approximated by a sinusoidal cycle with a period _{trn}_{trn}

In this case the resulting noise variance at the gyro output is _{z}^{−3} deg/s. From

The threshold setting _{t}^{−9}, to assess the feasibility of a railway turnout detector based on low-cost MEMS gyroscopes. In the analyzed detector a required _{fa}^{−9} results in a threshold:

The probability of detection under hypothesis H1 will be conditioned by the train velocity. For a minimum velocity _{min}_{c}_{0}

The resulting miss probability is much higher than the 10^{−9} required limit. This implies that a high level of operation safety with both _{fa}_{m}^{−9} cannot be obtained with this simple detector at very low speeds. The peak signal-to-noise ratio is defined as the peak signal power at the instant of maximum amplitude _{m}

In the present case _{m})_{0}_{m}^{−9} corresponds to _{0}_{z}_{min} = 21.58 dB. This minimum

Correlation based signal detection in low signal-to-noise ratio situations is usual in communication systems [

In a first simplified analysis we assume that the velocity of the train is known and constant, and therefore the turnout yaw rate signal can be predicted from the track geometry. This allows to define the matched filter impulse response _{m}(t)

The deterministic component _{m}_{m}_{m}^{2}(_{m}_{0}

In the case of the Masquefa station turnout, the estimated average turnout yaw rate of ±0.277 deg/s at the minimum velocity of 5 km/h (see Section 4) is a worst case for turnout detection since the yaw rate signal is very small; however the turnout time in this case is _{tnt}

The matched filter provides a substantial increase of the peak signal-to-noise ratio (+16 dB) with respect to the simple detector. Due to the large margin achieved in signal-to-noise ratio there is a wide range of possible thresholds that would satisfy the requested probability of decision error, _{fa}_{m}^{−9}. Assuming the detection can be performed at the peak of matched filter response we can select the threshold _{t}

From _{t}_{m}_{fa}_{m}^{−9}. A remarkable safety margin is obtained even at the minimum manoeuvring velocity considered, which means the expected detection performance is robust in front of non-ideal subsystems performance like sensor degradation or matched-filter impulse response errors. At higher train velocities the yaw rate levels will increase proportionally, whereas the integration time provided by the matched filter will decrease. In any case the signal-to-noise ratio will always increase with higher train velocities from the baseline calculation of ^{2}) and proportional to the integration time (∝ 1/velocity).

The

The yaw rate signal delivered by the gyroscope is first amplified in order to adapt the expected output levels to the dynamic range of the 10 bit Analogue to Digital Converter (ADC). The amplifier response is low-pass with a frequency cut of 200 Hz in order to increase the rejection of a 14 kHz spurious signal which is the gyroscope mechanical resonance frequency [_{S}_{N}

Using the train odometer as travelled distance sensor, the yaw rate samples are processed by an adaptive accumulator (

For example, if the train velocity is reduced with respect to a reference value, the train head yaw rate in a curve decreases while the time scale of the signal is enlarged both in the same factor. In addition if we wish to process the yaw rate signal with a matched filter it would be convenient to spatially scale the signal in degrees/m in order to get an invariant geometric pattern with respect to the train velocity. This scaling is performed by the constant distance accumulator followed by an adaptive amplitude correction. The amplitude correction factor takes into account the number of accumulated

The combination of the scaling factors 1/_{S}_{S}_{S}

For this reason the adaptive 1/P and 1/v factors have been dropped in the final implementation of the distance sampler shown in ^{®} on-board navigation system. The spatial step of 2 m adopted for temporal-to-spatial yaw rate interpolation delivered by the accumulator provides a sufficient number of samples for the matched filter processing even for short turnouts. A Doppler radar-based odometer delivering digital measurements of velocity, traveled distance and pulse generation has been used avoiding wheel slippage errors.

To analyze the adaptive low-pass filtering function of the accumulator, it may be considered as equivalent to a Finite Impulse Response (FIR) filter with a variable order P dependent on the train velocity as depicted in

The power frequency response of the accumulator is:

The resulting noise-equivalent bandwidth is _{N}_{S}_{S}_{s}_{S}

Since the signal provided by the distance sampler is not affected by the vehicle velocity or accelerations, a simple spatial matched filter can be applied to the integrated gyro signal to obtain the optimal peak signal-to-noise ratio. The track decision is obtained by comparing the signal sample at the peak position of the matched filter output with an appropriate turn rate threshold. The resulting probabilities of detection and false alarm can be calculated with the approach described in Section 4.

With the proposed spatial sampling, the matched filter length is constant and sufficiently small for real-time operation. In the studied case the matched filter impulse response has a length of 35 samples corresponding to the 70 m long H1 turn rate signal of _{m}^{®} system Single Board Computer. The track detector operates locally, by real-time processing the gyro data, acquired during the train head passage through the switch. The spatial window of acquisition is dimensioned according to the switch length, the maximum position error, specified as 10 m, and an additional safety margin of 20 m.

The performance of the proposed processing chain has been simulated on MATLAB^{®}-Simulink at 5 km/h and 50 km/h, which are the minimum and maximum nominal velocities of operation in siding areas.

The horizontal axis of _{N}

A FFT analysis of the digitized noise-only signal shows a noise power spectrum very close to the theoretical values. Since no odometer has been included in the simulator, the accumulator performance has been assessed using a FIR filter and decimation equivalent model shown in

In the 5 km/h simulation, approximately 144 samples of the gyro signal are accumulated and delivered to the matched filter every 2 m. This results in a drastic sampling-rate reduction from _{S}_{S}

The Bottom-Left plot on

The noise spectrum and noise power evolution along the simulated sensor processing chain has been estimated when the yaw rate signal is absent (H0). Using a large signal power averaging in order to obtain statistically significant values, the standard deviation results are very close to theoretical predictions. This confirms the correct design of the multirate processing approach. In the 5 km/h velocity simulated case, the noise standard deviation obtained at the output of the ideal matched filter is σ_{y} = 91.02 mV and the signal peaks at 6.212 V, resulting in a simulated signal-to-noise ratio _{ideal} = 36.68 dB, which is very close the theoretical value _{rect} = 36.19 dB showing a degradation of about 0.5 dB with respect to the ideal filter

The simulation has also been carried out for the maximum velocity of 50 km/h, with results, shown in _{ideal} = 46.5 dB and _{rect} = 46.0 dB.

The proposed detector performance has been experimentally assessed using the gyroscope acquired data in the two available acquisition campaigns. ^{®} system. The typical train deceleration when arriving to the station has not been taken into account in the first acquisition campaign, because of the non-availability of the constant distance pulses, but has been accurately compensated in the validation campaign by the accumulator; this fact explains the spatial yaw rate discrepancies around the distance of 135 meters.

In absence of turnout (H0) the output of the accumulator has been assumed to be sensor noise only. The potential impact of train vibration on the gyroscope noise budget has been estimated from the gyroscope acceleration-rejection data [

The siding detection has been tested on the experimental data acquired in the validation campaign in December 2011 for both H0 (main) and H1 (siding) tracks using the simplified rectangular weight version of the matched filter.

The matched filter output in both cases H0 and H1 shows a very similar noise standard deviation, which is 0.052 deg/m in the H0 case. The signal peak in the H1 case is 6.028 volts, a value that includes the gyroscope yaw-rate sensitivity, accumulator scale factor and the unit weights and number of branches of the matched filter. This peak value is proportional to the yaw rate signal energy [

In the analysis the turn (D1) or no-turn (D0) decision has been assumed to occur close to the matched filter output peak. Since the train position will not be perfectly known in practice, some position tolerance should be accounted for by arming and disarming the threshold detector around the expected peak position. In order to maintain the intended probabilities of error, the length of the interval of detection should be established according to the position error statistics. In the BLOCKSAT^{®} case the specified maximum position error derived from duplicated Doppler radar odometers and differential GPS receivers is 10 m. This allows dimensioning the detection interval in the order of the correlation length of the matched filter output, which has been estimated as the inverse of the noise equivalent output signal bandwidth, or, in terms of travelled distance, _{c}

If larger decision intervals are required, the evaluation of false alarms must consider the effective number of independent decisions _{d}_{d}_{c}

After _{d}_{cfa}

In any case, with the proposed processing chain the detection errors are extremely improbable, since taking a threshold equal to the half peak value as was shown in Section 5, _{fa}_{m}^{−9}.

This paper presents an optimized processing chain and detection providing reliable decision on track occupancy in railway sidings based on yaw rate signals provided by MEMS gyroscopes. The binary detection problem has been stated for typical turnout geometries. It has been shown that a simple yaw rate threshold detector offer acceptable performance at moderate to high velocities, but does not provide the required probabilities of detection error at slow train maneuvering velocities.

An improved detector based on a two-stage multi-rate matched filter has been proposed, showing a remarkable improvement over simple threshold detectors. In this case the required error probabilities are achieved with a large signal-to-noise safety margin, even at the slowest operational velocities (5 km/h). The implementation aspects of the detector have been optimized for real-time operation in a recently developed BLOCKSAT^{®} blocking system that includes an accurate navigation subsystem. For optimum operation the detector filter must be matched to the gyroscope yaw rate signal expected in the turnout, dependent on the rail road geometry and train velocity, which cannot be assumed constant. For this reason the real-time velocity obtained from Doppler radar odometer combined with differential GPS is used to convert the acquired time-domain signal into spatial-domain yaw rate data. A digital accumulator implemented in the BLOCKSAT^{®} system FPGA provides the signal time-to-space scaling, amplitude compensation and adaptive low-pass filter, minimizing both the processed noise power and the spatial sampling. In this way, the spatial correlation of the matched filter can be obtained with a small amount of operations that can be further minimized for a constant weight approximate implementation.

The detector has been studied theoretically, by computer simulations and experimentally on a representative railway test case. The experimental results have confirmed the theoretical and simulated analysis, resulting in a reliable detection. In the proposed system, all the sensors and processing modules are duplicated for higher reliability and integrity. The gyroscopes and associated electronics can be periodically tested and calibrated on train stops and on straight and curved segments of the rail track. The gyroscope derived yaw rate patterns reveal small details of the track geometries and could be exploited for additional applications, like assessing track deformation and degradation of switch mechanisms. Present research is addressed to extend the proposed track detector to more general cases including sidings implemented on curved main tracks.

The authors gratefully acknowledge the support and railway facilities provided by Ferrocarrils de la Generalitat de Catalunya in the experimental campaigns. This research work has been funded by the Spanish Government, Ministerio de Ciencia e Innovación, Prog. Nac. Coop. Público-Privada. Subp. de Transporte e Infraestructuras. Proy. P18/08. BLOCKSAT^{®} is a registered mark of SENER Ingeniería y Sistemas, S.A.

Simplified geometry of a siding switch able to divert a train from the main track in black (H0) and siding track in red (H1).

Simplified turn rate signals for main track in black (H0) and siding track in red (H1).

Yaw rates of a turnout in the Masquefa station measured in two experimental campaigns with different hardware and software. (

Binary hypothesis of a real situation: H1: train diverted to siding, H0: train has remained on main track. Possible detector decisions: D1: turnout detected, D0: turnout not detected.

Simple threshold detector based on the comparison of a low-pass filtered turn rate _{t}_{t}_{t}

Probability of false alarm of a positive turnout detection D1|H0. The threshold value in deg/sec is _{t}

Probability of detection in a positive turnout D1|H1. The threshold value in deg/sec is _{t}_{0.}

Gyroscope processing for robust track occupancy detection.

Distance sampler accumulator including train velocity scaling factors.

Simplified Distance sampler accumulator.

The accumulator modeled as an adaptive P-order moving average low-pass filter, followed by a decimator.

MATLAB^{®}-Simulink model of gyroscope and proposed 2-stage optimal processing. The simulation parameters shown in the figure correspond to a 5 km/h test.

MATLAB^{®}-Simulink results of a 5 km/h simulation. Five signals are shown corresponding to the output ports 1 to 5 of the Simulink model. Top-left: port 1: actual yaw rate. Top-right: port 2: gyro output. Bottom-left: port 3: Accumulator output. Bottom-right: ports 4, 5: Blue is the ideal Matched Filter Output and Green is the Rectangular approximated Matched Filter.

MATLAB^{®}-Simulink results of a 50 km/h simulation. Five signals are shown corresponding to the output ports 1 to 5 of the Simulink model. Top-left: port 1: actual yaw rate. Top-right: port 2: gyro output. Bottom-left: port 3: Accumulator output. Bottom-right: ports 4, 5: Blue is the ideal Matched Filter output and Green is the rectangular approximated Matched Filter.

Absolute values of the normalized frequency transfer functions of the matched filter (constant coefficient version) and of the accumulator obtained at 5 km/h velocity. The black solid line corresponds to the matched filter; the blue dashed line is the accumulator fundamental response. The first accumulator aliases resulting from decimation are represented in red dot-dashed curve and magenta dot curve.

Spatial yaw rate signal obtained in Masquefa siding in the first acquisition and validation campaigns.

Output of the matched filter in the H0 and H1 trajectories obtained in the Validation 2011 campaign. The horizontal line shows the threshold proposed decision level.