Estimating velocity from noisy GPS data for investigating the temporal variability of slope movements

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Abstract

Detecting and monitoring of moving and potentially hazardous slopes requires reliable estimations of velocities. Separating any movement signal from measurement noise is crucial for understanding the temporal variability of slope movements and detecting changes in the movement regime, which may be important indicators of the process. Thus, methods capable of estimating velocity and its changes reliably are required. In this paper we develop and test a method for deriving velocities based on noisy GPS (Global Positioning System) data, suitable for various movement patterns and variable signal-to-noise-ratios (SNR). We tested this method on synthetic data, designed to mimic the characteristics of diverse processes, but where we have full knowledge of the underlying velocity patterns, before applying it to explore data collected.

Figures

  • Figure 1. Locations and field impressions of the GPS stations of pos27 and pos55. The small photo (bottom right) shows GPS station pos55 at the end of June 2012, by then the station is strongly tilted towards the slope. Each GPS station includes a GPS antenna and two inclinometers that are mounted on top of a mast. The energy to operate the devices is provided by a photovoltaic energy harvesting system and backed by a battery. (Photos: V. Wirz and R. Delaloye.) LK200 from the year 2008 (reproduced with permission of swisstopo BA14054).
  • Figure 2. GPS positions (E, N , h) and inclinometer measurements ( θ and its az) of positions pos55 and pos27 and their error range (± the standard deviation σ , in grey). The temporal resolution is 1 day. For better readability, the positions (E, N , h) are given relative to the position at the start of the measurements. Note, that both axes differ for pos55 and pos27. The vertical black lines indicate differing measurement devices (exchange of measurement device).
  • Figure 3. Schematic of differing slides and possible sources of rotation/translation (modified after Varnes, 1978): (a) translational slide with failure plane paralleling surface, (b) rotational slide with surface of rupture curved concavely upward, and (c) complex slide with various (unknown) types of slides involved and local rotation of a small volume below the GPS station.
  • Figure 4. Terms and conventions used: measurement setup with single-phase GPS receiver and two inclinometers. The tilt of the GPS mast is measured with two inclinometers installed perpendicular to the GPS antenna. This setup allows us to calculate θ and φ of the tilted GPS mast.
  • Table 1. Summary of the errors for the different methods: SNRT (with different thresholds: 5, 20, and 50), simple, spline, and lokern. Errors are defined as the mean of the absolute difference between estimated velocities and the reference velocity vtrue. The errors are given as 10−4 m d−1. Bold numbers indicate the smallest errors for each test-case (e.g. 0.81 for A-a).
  • Figure 5. Synthetic time series of positions following (A) linear displacement, (B) following sine function, and (C) linear displacement with short peak in velocity. For each time series three different periods with different noise levels are modelled (a: σnoise = vmin × 10; b: σnoise = vmin; c: σnoise = vmin × 10−1). The velocity of the displacement without noise (the “true” velocities) are plotted in dark grey with white dots. Velocities have been estimated with different methods (SNRT: blue, violet and dark red; simple: grey; spline: orange; and lokern: green). Periods with a SNR below the threshold t (SNRT 5, 20, or 50) are indicated with dashed lines.
  • Figure 6. Total displacement at pos55 and pos27 of the GPS position at the antenna, the inclinometer measurements and the position of the GPS foot (corrected for mast tilt). Data points with an error (in the original data) that is higher than the 95 % quantile are marked with grey circles. The uncertainty (σ ) of the cumulative distance (grey) is estimated using 2000 MCS (Sect. 4.1.2). Note that both axes differ for pos55 and pos27.
  • Figure 7. Distribution of the horizontal velocities (upper plots) and the direction of the movement (aziv, lower plot) calculated with SNRT applying different thresholds. Note that the y axes differ for pos55 and pos27.

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CITATION STYLE

APA

Wirz, V., Beutel, J., Gruber, S., Gubler, S., & Purves, R. S. (2014). Estimating velocity from noisy GPS data for investigating the temporal variability of slope movements. Natural Hazards and Earth System Sciences, 14(9), 2503–2520. https://doi.org/10.5194/nhess-14-2503-2014

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