APPLICATION CHALLENGE 

RTK GPS

Precise Rail Track Surveying

All photos courtesy of terra international ltd

This article describes the Swiss Trolley, a multisensor measurement system incorporating real-time kinematic (RTK) GPS, and its use to survey sections of railroad track in the United Kingdom. ince May 2003, large track renewal projects have taken place within the West Coast Route Modernization Program (WCRM), demanding a major effort from the United Kingdom rail industry. Survey companies play a key role in this program by providing spatial information for the designers of through alignment, tunnels, platforms, drainage, and overhead lines — in other words, for the whole of the rail system’s infrastructural assets.

S

The survey companies support several aspects of required measurement activities during construction — such as monitoring progress of build-up of ballast and to check passing and structural clearances — that bring the new track and other systems to within their

RALPH GLAUS holds a degree in geodesy and has more than 10 years experience working in the domain of surveying engineering. He is employed by the Institute of Geodesy and Photogrammetry of the Swiss Federal Institute of Technology, Zurich (ETH). GERARD PEELS has a degree in civil engineering. He has worked as a consultant in the international rail

industry for more than 14 years and is employed by terra international surveys ltd., Zurich, Switzerland. URS MÜLLER is a managing director of terra international surveys ltd. ALAIN GEIGER received his diploma in physics from Swiss Federal Institute of Technology, Zurich (ETH). He holds a Ph.D. in engineering sciences also from ETH. Presently, he lectures in satellite geodesy and navigation at the Institute of Geodesy and Photogrammetry (ETH) and serves as president of the Swiss Institute of Navigation. 12

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 FIGURE 1 The West Coast Route Modernization Program www.gpsworld.com

design specifications in the track corridor. The scope of work for Route Section 12, covering about 80 kilometres (Colwich Junction to Cheadle Hulme, Figure 1) was the first in a series of track renewal projects that was crowded with activities coming from different disciplines and departments. As the project got under way, survey companies were soon stretched to their limits using the traditional relative techniques of datum rails and measuring offsets, simply because the construction program allowed for “floating” roads. These relative measurement methods are common practice within UK surveying companies. Offsets are measured and marked up against spatial, fixed objects (pegs, nails, permanent ground markers, datum rails). For instance, the six-foot distances between up and down line tracks are measured back to back, or as running edge to running edge of the railheads. These measurements are marked up (with chalk or other more The Swiss Trolley with total station (background) sustainable paints, adding or subtracting both the re- struction efforts of the other track. This works as long quired horizontal shift and required lift as per design) as the so-called datum rail is not touched, moved by on that rail, which is intended to stay during the con- tamping operations or rail stressing, or in the worst

Glossary Ballast: Angularly shaped crushed stone used to support sleepers, timbers, and bearers, both laterally and vertically.

1500 mm Cant

Cant (or super elevation): The amount by which a rail, usually the outside rail of a curved track, rises above the lower rail on the same piece of track.The cant is referred to a nominal base (for example, 1.500 meters). See accompanying figure.

0 - 14 mm

Track axis

Chaining: Path length. Gauge: Smallest distance between the rails measured 0–14 millimeters below the rail top edge.A nominal measure is, for example, 1.435 meters. See accompanying figure. Gradient: Longitudinal inclination of a railway track. Lift: Vertical displacement of the actual railway track from the nominal track. Passing and Structural Clearances: Passing clearance allows trains to pass on two parallel tracks without hitting each other. Structural clearance is the clearance required for trains passing structures such as tunnels, bridges, platforms, and signal posts. www.gpsworld.com

717.5 mm .

Track gauge

Slew: Horizontal displacement of the actual railway track from the nominal track. Through Alignment: Expression used for an alignment that covers a project from start to end.The three components of alignment are horizontal, vertical and cant, regardless of the typical cross sections encountered. Track Axis: Line parallel to the reference rail at the distance of the half nominal gauge. See accompanying figure. Twist: Cant rate.

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RTK GPS

case taken out. terra international surveys ltd. of Zurich, Switzerland was invited by NetworkRail to demonstrate its real-time kinematic (RTK) track-measuring device, called Swiss Trolley, which incorporates optical kinematic total stations and RTK GPS receivers. Soon it became evident that this absolute way of surveying was the solution required to provide accurate, dense and multi-parameter information. This article features the Swiss Trolley and describes the performance and limitations of GPS-based track surveying that we encountered.

System Design

PPS

Incremental Encoder (Odometer 1)

Incremental Encoder (Odometer 2)

Angular Transducer (dGauge Left) Serial Port RS232 Angular Transducer (dGauge Right)

Data Acquisiton Card

Serial Port RS232 PT100 (Ambient Temperature)

Gradient tiltmeter

Inclinometer (Superelevation)

Odometers (cen terline path)

Inclinometer (Gradient)

Transducer left

Sensorbox Total Station (XPrism )

Transducer right

Integrity tests and blunder detection

Cant tiltmeter

PT100 (Box Temperature)

Corrected gradients

Track gauge

Results (Steering file for tamping machines, charts, and so forth)

GPS (XAPC)

Forward / backward filter and smoother

PosData / PPS

Synchronization, reduction to reference rail and comparison with nominal geometry

Swiss Trolley

The University of Applied Sciences Burgdorf developed the trolley in collaboration with terra international surveys, Switzerland, as part of a project financed by the Commission for Technology and Innovation by the Swiss Office for Professional Education and Technology. The trolley originally was designed for kinematic applications with subcentimeter accuracy. However, Grunder Ingenieure AG of Burgdorf, Switzerland, another project partner, successfully applied it in combination with high-precision optical total stations for the alignment of 18 kilometers of slab track in the Zurich-Thalwil-tunnel of the Swiss Federal Railways. Alignment of the slab track required millimeter-level accuracies. Apart from GPS/RTK and total stations, further sensors are needed to completely measure track geometry. Two tiltmeters, a track gauge measuring system, and odometers enable the assessment of the key parameters: cant, gradient, track gauge, and chaining. (See Glossary on page 13.) The modular design of the trolley allows for the use of further sensors such as laser scanners or ground pen-

GPS/RTK

 FIGURE 2 Block diagram of track surveying trolley 14

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 FIGURE 3 Post-processing concept www.gpsworld.com

etrating radars (GPR). The operation of the trolley in a stand-alone mode also can provide “path”-“twist” and “path”-“track gauge” charts showing twist and track gauge as a function of the covered chaining. Standalone surveys represent a quick method for track monitoring during construction.

Use of Sensors Cants and gradients are measured by two fluid damped inclination sensors. Typical precisions in the static mode reach about 0.2 mrad. Biases are checked at the beginning of a survey. This is done by means of inclination measurements in two faces over a reference plane. The track gauge is determined by a function of the angular position of two dragging mechanical scanners. Angular transducers measure the deflection of the scanners. Calibration is accomplished by comparing the track gauge reading with a measuring rod reading. The precision of the track gauge measuring system reaches about 0.5 millimeters. Two odometers provide path measurements of the parallel rails, which in turn can generate differential odometer readings for dead reckoning. The average of the left and right odometer represents the path length of the centerline. Systematic errors may arise from an inappropriate scale factor (diameter). This parameter can be calibrated by comparing the odometer path against the true path length, using total station data and nominal track data. If the odometer data are free from slippage, precision can reach a level of up to 50 ppm. Figure 2 gives an overview of the sensors incorporated into the Swiss Trolley system.

Data Processing In order to benefit from the “past” and “future” correlations of adjacent measurements, data are postprocessed. Kinematic data postprocessing uses a cascading filter concept. In contrast to a tightly coupled filter, we preprocess parameters such as tangential accelerations that have minor effect on the final results. This produces a simpler and more stable filter formulation. The cascading data processing is divided into these steps:  blunder detection / data reduction I  synchronization / data reduction II  filter / smoother Figure 3 illustrates the cascading postprocessing concept. Blunder Detection, Data Reduction I. Data processing includes integrity checks and blunder detection for each data channel. The reasons for blunders are manifold. For example, welding seams on the rails can cause nuisance accelerations that mainly www.gpsworld.com

Track surveying trolleys in use

affect the tiltmeter readings. The blunder-free data allow for a first reduction step. As previously mentioned, tangential accelerations are removed from the gradient tiltmeter readings during the preprocessing stage. We can derive accelerations and velocities from the path measurements by means of fitting polynomials and the corresponding derivatives. Cubic parabolas provide good fits with a moderate noise gain. Centripetal accelerations are ignored in the data processing, which is considered acceptable because of the low operation speed and the large track radii. The angular transducer data are used for the assessment of the track gauge and to determine the trolley wobble between the rails. Wobble rates are smooth due to the inertia of the trolley. Synchronization, Data Reduction II. Synchronization of the trolley data with the positioning sensor data only must be done if no pulse per second (PPS) signal is available from the GPS receiver. In contrast to use of a GPS-RTK with PPS, optical total station data are not synchronized with the trolley data during data acquisition. For the GPS case, the 20 Hz trolley data are downsampled to the typically used 1 Hz GPS data. A rate of 1 Hz is effective to accurately record all track patterns. NMEA sentences sent to the serial port contain the GPS-RTK solutions that use carrier phase integer ambiguity resolution methods. The postprocessing software allows for a refinement of the geoid undulations and use of a separate geoid model along a railway track MAY 2004

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being measured. Within the UK project, we refined the existing geoid model by comparing the leveling and GPS data along the tracks. In order to compare the measurements with nominal data, the GPS antenna phase center coordinates have to be reduced to the cen-

 FIGURE 4 Influence of the tiltmeter on the lift parameter

 FIGURE 5 Slew of a forward and a backward run

 FIGURE 6 Lift of a forward and a backward run 16

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RTK GPS

terline of the track. The centerline in general does not correspond to the actual track axis, because the track gauge can deviate from its nominal value (for example, 1.435 meters). However, reducing to the track axis would result in a discontinuous curve disturbing the subsequent filter step. Therefore, corrections due to deviations from the nominal gauge are applied after filtering. For track renewal projects, a nominal geometry describing the track as a series of analytical functions — straight lines, circles, or clothoids — is available. In this pre-filter step, residual displacements of the nominal trajectory are evaluated and submitted to the filter. Filter and Smoothing. An 11-state Kalman filter estimates the track parameters. The filter states include displacements from the nominal track, the cant, and the track gauge. The model assumes a non-accelerated motion, incorporates rates for the horizontal and vertical displacements as well as the cant, and introduces additional adaptive parameters for the odometer scale and the gradient tiltmeter bias. The latter two parameters can be fixed if they remain constant for a single survey, which allows a more reliable filter formulation. For the filter update, seven observations are used per time batch. The measured horizontal and vertical displacements from the nominal track, path, cant, track gauge, gradient, and odometer path can be submitted to the Kalman filter. The postprocessing allows for filtering in forward and backward directions and smoothing. This reduces the variance of a forward-only filtered solution and minimizes lags caused by a forward-only filtered series. The filtered data are represented on charts that show relevant parameters for track renewals as horizontal and vertical displacements (“slew” and “lift”), cant, twist and track gauge. The postprocessing software generates steering files for machine guidance systems of tampers. By using the slew and lift parameters, the tampers can correct the track to the desired position. If no nominal track data is available, as sometimes occurs with older railway lines, an absolute trajectory is estimated. The filter states in this case include position, velocity, azimuth, curvature, cant, gradient, track gauge, odometer scale, and gradient tiltmeter bias. The filtered data are a basis for track regressions in which analytical functions have to be fitted through the trajectory. The typical work flow contains several track runs with overlapping sections. To improve accuracy, a track is normally surveyed in both directions. A further tool within the postprocessing software allows for merging data from all runs and takes into consideration the eventual remaining biases. The merge process takes into www.gpsworld.com

account the covariance matrix of the single filtered solutions. Sections with poor GPS reception or with GPS outages (tunnels, bridges) are supplemented by total station measurements in combination with the trolley. The total station data are tied to the GPS reference frame.

tion of track. The twist describes the cant rate. Cant rates acquired by the trolley are almost bias-free. However, the noise gain can be considerable due to the derivation of the (noisy) cant measurements. By means of the postprocessing, smooth estimates for the twist

Survey Example The performance of the Swiss Trolley was evaluated by comparing a forward and a backward run on a 250meter-long section of track as part of the UK project. The survey was done at walking speed of 1.2 meters/second, with all GPS phase ambiguities solved for both runs. Apart from an accuracy assessment, forward and backward runs allow for a determination of most sensor biases and for a boresight calibration. We processed the data according to the previously described scheme and computed displacements with respect to a nominal geometry. Figure 4 shows the influence of the gradient tiltmeter measurements on the GPS heights. Tiltmeter measurements smooth a pure GPS solution with a consequent improvement in accuracy by a factor of up to 1.5 compared to the GPS-only solution. In the given example, an a priori standard deviation of 20 millimeters was chosen for the GPS heights, while the gradient a priori standard deviation was set to 3 mrad. However, gradients have to be weighed carefully, since residual nuisance accelerations can result in local trajectory tilts. Table 1 summarizes the differences between the forward and backward run in slew, lift, cant, track gauge, gradient, and twist, showing very small mean values as the result of first removing the remaining biases. For the comparison, backward points were interpolated on the corresponding forward chaining. The covariance information of smoothed solutions was used for the evaluation of the differences. Figure 5 shows the progression of the slew parameter. A standard deviation better than 4 millimeters results for the differences. Figure 6, which shows the tiltmeter-smoothed GPS heights, reflects the ballast tracks’ typical cyclic patterns. Most of these cycles can be assigned to previous relative track alignments. The area below the curve with respect to the cross section gives an idea of the missing ballast. If lift parameters reach such high magnitudes, we might well consider a local adaptation of the nominal geometry. Apart from the slew and lift charts, cant and track gauge parameters are also generally of interest in a track survey (Figures 7 and 8). A crucial parameter concerning safety aspects of a track is the twist. Allowable tolerances for twist mainly depend on the foreseen operation speed of trains traversing the secwww.gpsworld.com

 FIGURE 7 Track gauge of a forward and a backward run

 FIGURE 8 Cant of a forward and a backward run

 FIGURE 9 Twist of a forward and a backward run MAY 2004

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RTK GPS

meter-long section of double track, repeated runs using Mean Std Min Max Units the trolleys produced more Slew 0.1 3.9 -9.9 9.4 mm than 135 kilometers of meaLift 0.6 8.1 -22.6 19.8 mm surements. Often and whenCant 0.0 0.3 -0.9 1.0 mm ever possible, measuring was Track gauge -0.4 0.3 -1.1 0.6 mm done with two trolleys on both tracks simultaneously, Gradient 0.0 1.8 -4.8 8.0 mrad thus minimizing interference Twist 0.0 0.1 -0.5 0.4 mm/m with other construction acThe mean, standard deviation (std), minimum and maximum in track parameters between the forward and tivities and traffic on the the backward run.The cant is referred to a 1.5-meter base. track. The dense and accurate track information, captured on the last measurement run, enabled terra international surveys to guarantee a precise description of the actual physical track position. Subsequent applied regression analysis techniques resulted in a new geometrical description of the two lines, which can now be used to mark up the track and maintain it to this new definition. Moreover, any wave patterns or irregularities were corrected. As a result of their involvement in these projects in the UK, terra international surveys has become more aware of the extreme demand for additional, highly accurate spatial data of the environment both above and under the track. More research and development has Sensor box with two tiltmeters been put into finding a solution for combining and are obtained as seen in Figure 9. The data shown from registering more parameters together, such as ground the forward and backward runs has already been penetration data and laser scans, in order to achieve a smoothed separately. complete three-dimensional zone around the track.  The accuracies demonstrated here fulfill most track alignment requirements. Long periodic track position Acknowledgments errors, such as the ones induced by relative chord tech- The authors would like to thank CTI of the Swiss Ofniques, do not occur using a GPS reference frame. fice for Professional Education and Technology for Thanks to the GPS-based approach, homogenous ac- providing the opportunity to develop the track surcuracies are obtained along a railway track. An accu- veying trolley. A special thanks also is extended to Netracy-limiting factor using GPS for track surveying has work Rail, who gave us the opportunity to gain vast exmultipath effects. New antennas with “stealth” ground perience in optimizing interaction with construction planes will be used in the near future and are expected workflows for the UK market. to produce significant reductions in multipath. TABLE 1

Manufacturers Conclusion Following completion of the Route 12 project described earlier, another WCRM Project, Route Section 2, has been finished. In contrast to the Route 12 project, terra international surveys was able to install a first-order GPS network. The daily track measurement quantities increased considerably as data could now be captured more flexibly at walking speed using the Swiss Trolley in GPS mode, regardless of day- or night-time working hours. By using the coordinated second-order fixedpoint network (studs in every second stanchion) and the Swiss Trolley in optical total station mode, GPS-obscured areas were efficiently covered. On this 27-kilo18

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This project used Trimble (Sunnyvale, California). GPS RTK receivers 5700/5800 and the Zephyr antenna, Trimble optical total stations ATS600, and a Swiss Trolley by terra international surveys ltd. (Zurich, Switzerland).

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