The research behind Torq

1. Where the speed comes from

A GNSS receiver does not compute speed by subtracting one position from the next. It measures the Doppler shift of each satellite signal, which gives the velocity toward or away from that satellite directly, and solves for the receiver's velocity across all of them.[2] In dynamic conditions raw Doppler velocity is the most accurate of the GNSS velocity methods, at the 0.1 to 0.2 m/s level, and position-difference velocity is the worst.[1] iOS exposes the Doppler-derived speed on every fix with a course and a speed accuracy estimate.[32] Torq records all of them, once a second.

Every vehicle-motion quantity in Torq is derived from that speed series and the heading: acceleration and deceleration from the change in speed over time, lateral G from speed multiplied by the rate of heading change. The inertial sensors are reserved for the vertical axis and for confirming that a heading change is a real yaw. That choice removes phone-orientation error entirely; its cost is one-second time resolution, which is why the app's launch timer is honest about a few tenths of uncertainty and why dedicated performance loggers sample at 10 to 25 Hz.[31]

2. Cleaning the speed series

Smartphone GNSS is good under open sky and degrades about twofold in obscured environments, where errors are not white noise but heavy-tailed gross errors.[3] Speed estimates from phones carry an uncertainty that correlates with signal interruption.[4] A raw trace can read 60, 122, 58 km/h in three consecutive seconds. Simple thresholds and Kalman-based cleaning miss small and asymmetric outliers on low-rate trajectories, a result quantified on low-cost GPS data.[5]

Torq therefore runs a centered Hampel filter over the speed series: each sample is compared with the local median, using 1.4826 times the median absolute deviation as a robust scale, and flagged when it departs by more than a few of those units.[6] A physical plausibility gate follows: an acceleration no road car can produce, or a speed above 600 km/h, is rejected. Short runs of flagged samples are replaced by the local median; longer runs are left as a gap. The approach follows the trajectory-reconstruction literature, which treats vehicle dynamics as the basis for judging abnormal speed and acceleration and warns that differentiation amplifies position noise.[7][8] Rejecting outliers before the estimate rather than tolerating them afterwards is the principle the GNSS integrity literature argues for at the observation level.[10][11] A speed-dependent acceleration envelope, rather than one fixed threshold, is the documented next step.[9]

3. Smoothness

Smoothness is scored from jerk, the rate of change of acceleration. The speed series is smoothed with a three-point moving average, differentiated twice, and the 90th percentile of jerk is taken so that traffic-forced stops do not dominate. The scale is anchored to standards and studies: ISO 15622 limits adaptive-cruise longitudinal jerk to 2.5 m/s³,[12] comfortable maneuvers sit between 0.3 and 0.9 m/s³,[13] and passenger studies find discomfort rising past 0.42 m/s³ laterally.[14]

4. Cornering

A corner is a heading change of at least 22 degrees at a course rate above 12 degrees per second, at 12 km/h or more, lasting up to 35 seconds; the gyroscope confirms the yaw at low speed. Each corner records its entry speed, apex speed, exit speed and lateral G, where lateral G is the 90th percentile of the per-sample centripetal value so one noisy fix cannot inflate it. The performance score follows racing-line theory: half the score for holding speed to the apex, an asymmetric exit term that rewards leaving faster than the apex and penalizes leaving slower,[28][29] and a grip term for sustained lateral G, the friction-circle idea from motorsport data analysis.[30][31]

5. Speed control and efficiency

Speed control is the mean absolute rate of speed change while moving, a proxy for speed variability. Speed variability correlates with crash risk in fleet data,[15] and short-window volatility measures are among the strongest crash predictors.[16] Efficiency combines cruise ratio, idle ratio, hard accelerations and speed variation into an energy score, the additive bonus-and-penalty structure the eco-driving literature and commercial eco scores use,[18][21] with idles shorter than 45 seconds ignored so a red light is not a penalty.

6. Safety and harsh events

A brake event is a deceleration of 3.5 m/s² or more (about 0.36 g); a hard acceleration is 2.8 m/s² or more; an aggressive turn is a sustained lateral load past 0.4 g. The thresholds sit inside the range the telematics industry uses: Tesla's Safety Score counts hard braking at 0.3 g and aggressive turning at 0.4 g,[17] Damoov at 3.0 and 4.2 m/s²,[18] and fleet-telematics defaults near 0.36 g.[19] The safety grade normalizes events per 100 km so a long drive is not penalized for its length, in the spirit of multi-dimension weighted scores.[20]

7. Ride comfort

The vertical accelerometer channel, with gravity removed and stationary time excluded, is weighted with the ISO 2631-1 Wk curve, which emphasizes the 4 to 8 Hz band where the seated body is most sensitive, and its root-mean-square is graded on the zones the standard defines for seated passengers.[22] The weighting is implemented as a digital filter by bilinear transform.[23] Samples above 3.0 g are discarded as phone drops or mount slips.

8. Road quality

Road agencies rate pavement with the International Roughness Index, meters of suspension travel per kilometer, computed from a measured profile through the Golden Car quarter-car model.[24] A phone reads the road through tires, suspension, seat and mount, so Torq's value is an estimate: vertical RMS scaled by the square root of speed with an empirical factor, which is the simplified approximation the phone-based IRI literature starts from,[25] with calibration-free methods reaching about 8 percent accuracy as the documented upgrade path.[26] Grades use separate highway and urban thresholds, because a manhole cover on a city street is not a defect at 30 km/h.[27]

9. The overall score

The four components are weighted 30, 30, 25 and 15 percent for smoothness, cornering, speed control and efficiency, and any component under 40 applies an additional penalty so one weak dimension shows through rather than hiding behind three good ones. Weighted aggregation with a floor penalty is the pattern commercial driver scores converge on.[20]

10. What the app does not claim

• It is not an approved measuring instrument. GPS speed is informational; the accuracy page describes its failure modes.
• One-second sampling cannot resolve events shorter than about two seconds; a launch timer and a peak G reading carry that uncertainty.
• The road-quality index is relative to the car and the mount, not an agency measurement.
• The cornering and comfort analysis is calibrated for a car with the phone in a mount; on a leaning vehicle it does not transfer.
• No score here predicts collisions. It describes a drive to a set of formulas that are printed on this page.

References

1. Evaluation of the performance of GNSS-based velocity estimation algorithmsJi et al., Satellite Navigation, 2022. Raw Doppler velocity is the most accurate in dynamic conditions, at the 0.1 to 0.2 m/s level.
2. How does a GNSS receiver estimate velocity?Inside GNSS. Why receivers derive speed from Doppler shift rather than position differences.
3. Rigorous Performance Evaluation of Smartphone GNSS/IMU Sensors for ITS ApplicationsGikas and Perakis, Sensors, 2016. Smartphone GNSS degrades about twofold in obscured environments; 1 Hz limits vehicle-dynamics description.
4. Treating uncertainty in the estimation of speed from smartphone traffic probesGuido et al., Transportation Research Part C, 2014. Speed error correlates with signal interruption; estimates need an uncertainty.
5. Trend-Residual Dual Modeling for Detection of Outliers in Low-Cost GPS TrajectoriesChen et al., Sensors, 2016. Thresholding and Kalman cleaning miss small and asymmetric outliers on low-rate trajectories.
6. Quality assessment of daily GNSS coordinate time series from the SoftBank proprietary reference networkAichinger-Rosenberger et al., Earth, Planets and Space, 2025. The centered Hampel filter with a 1.4826 x MAD robust scale, and the dual-window variant.
7. Estimating Acceleration and Lane-Changing Dynamics Based on NGSIM Trajectory DataThiemann, Treiber and Kesting, 2008. Position noise is amplified by differentiation into speed and acceleration.
8. Vehicle Trajectory Reconstruction Using a Lagrange-Interpolation-Based FrameworkSun et al., Applied Sciences, 2024. Physical plausibility as a cleaning rule; accelerations beyond about 9 m/s² treated as implausible.
9. Adaptive physics-informed trajectory reconstruction exploiting driver behavior and car dynamicsMakridis et al., Scientific Reports, 2023. Speed-dependent acceleration envelopes rather than one fixed threshold.
10. Outlier Detection in GNSS Pseudo-Range/Doppler Measurements for Robust LocalizationZair, Le Hégarat-Mascle and Seignez, Sensors, 2016. Reject outliers before the estimate, not after.
11. Real-Time Detection and Correction of Abnormal Errors in GNSS Observations on SmartphonesMu et al., Remote Sensing, 2024. Residual-based gating of abnormal epochs on phones.
12. ISO 15622: Adaptive cruise control systemsThe 2.5 m/s³ longitudinal jerk ceiling that anchors the smoothness scale.
13. Comfort-related acceleration and jerk value ranges for common maneuversBae et al., 2020. Comfortable jerk between 0.3 and 0.9 m/s³.
14. Passenger discomfort in automated driving: lateral jerk and longitudinal acceleration thresholdsApplied Ergonomics, 2022. Lateral jerk above 0.42 m/s³ discomforts a fifth of passengers; 0.28 m/s² longitudinal is excellent, 1.23 m/s² the acceptable ceiling.
15. Speed variability and crash risk from 4,500 fleet vehiclesAccident Analysis and Prevention, 2022. Speed variation correlates with crashes; the basis of the speed-control component.
16. Driving volatility: coefficient of variation and MAD over short windowsOSTI, 2024. Three-second windows of speed volatility correlate most strongly with crash risk.
17. Tesla Safety ScoreHard braking at 0.3 g and aggressive turning at 0.4 g, folded into a predicted collision frequency.
18. Damoov Safety Score and Eco ScoreHarsh braking at 3.0 m/s² and harsh cornering at 4.2 m/s²; idle time, hard acceleration and cruise ratio for the eco score.
19. Defining thresholds for your fleetWex Telematics. Hard braking at 0.367 g and hard cornering at 0.357 g as fleet defaults.
20. FICO Safe Driving ScoreA multi-dimension weighted score; harsh acceleration weighted 20 percent and cornering 10 percent.
21. Eco-driving: a review of variables and methodsPMC, 2021. Acceleration and speed are the most used variables in eco-driving assessment.
22. ISO 2631-1: Mechanical vibration and shock, evaluation of human exposure to whole-body vibrationThe Wk frequency weighting and the comfort zones from under 0.315 m/s² to over 2.0 m/s².
23. Design of digital filters for frequency weightings required for risk assessments of workers exposed to vibrationRimell and Mansfield. Bilinear-transform implementation of the ISO 2631 weightings.
24. ASTM E1926: Standard practice for computing International Roughness Index of roads from longitudinal profile measurementsThe Golden Car quarter-car model behind IRI.
25. A framework for evaluating smartphone-based IRI estimationInternational Journal of Pavement Engineering, 2023. Systematic evaluation of phone-based roughness methods.
26. Calibration-free IRI estimation from random vibration theoryResults in Engineering, 2021. About 8 percent accuracy without suspension parameters.
27. IRI specifications around the worldCzech Republic approach: higher acceptable roughness on low-speed urban roads.
28. The racing line: four elements of a perfect cornerParadigm Shift Racing. Braking point, turn-in, apex, exit.
29. Exit speed is more important than entry speedDriver61. The asymmetry in Torq's exit term.
30. Cornering performance and the G-G diagramHP Academy. Trail-braking overlap as a marker of skill; the friction circle.
31. Total acceleration and total G from GPS dataDataMC. The resultant of lateral and longitudinal G as a grip-usage measure.
32. GPS accuracy in performance testingVBOX Automotive. Why 10 to 25 Hz loggers resolve launches that 1 Hz cannot.
33. CLLocationSpeedAccuracyApple Developer Documentation. The speed accuracy field iOS reports with each fix.