Abstract
We provide algorithms for inferring GPS (Global Positioning System) location and for quantifying the uncertainty of this estimate in real time. The algorithms are tested on GPS data from locations in the Southern Hemisphere at four significantly different latitudes. In order to rank the algorithms, we use the so-called log-score rule. The best algorithm uses an Ornstein–Uhlenbeck (OU) noise model and is built on an enhanced Kalman Filter (KF). The noise model is capable of capturing the observed autocorrelated process noise in the altitude, latitude and longitude recordings. This model outperforms a KF that assumes a Gaussian noise model, which under-reports the position uncertainties. We also found that the dilution-of-precision parameters, automatically reported by the GPS receiver at no additional cost, do not help significantly in the uncertainty quantification of the GPS positioning. A non-learning method using the actual position measurements and employing a constant uncertainty does not even converge to the correct position. Inference with the enhanced noise model is suitable for embedded computing and capable of achieving real-time position inference, can quantify uncertainty and be extended to incorporate complementary sensor recordings, e.g., from an accelerometer or from a magnetometer, in order to improve accuracy. The algorithm corresponding to the augmented-state unscented KF method suggests a computational cost of , where is the dimension of the augmented state-vector and is an adjustable, design-dependent parameter corresponding to the length of “past values” one wishes to keep for re-evaluation of the model from time to time. The provided algorithm assumes . Hence, the algorithm is likely to be suitable for sensor fusion applications.
Highlights
Global Positioning System receivers output a time-series of position measurements, but this signal suffers from errors due to many reasons, such as atmospheric and multipath effects [1,2,3] or insufficient coverage of satellite constellations
We found that the DOP parameters do not help in uncertainty quantification of the GPS positioning
The AUKF algorithm using an OU noise model provides an accurate series of posterior distributions for GPS position with improved uncertainty quantification compared to inference assuming iid Gaussian noise provided a large enough value is assumed for the OU noise variance
Summary
Global Positioning System receivers output a time-series of position measurements, but this signal suffers from errors due to many reasons, such as atmospheric and multipath effects [1,2,3] or insufficient coverage of satellite constellations. Sensors 2020, 20, 5913 algorithms that issue real-time position predictions with simultaneous uncertainty quantification and evaluate their performance. Embedding these algorithms in devices that use single frequency GPS will allow such devices to supply improved position estimates and real-time estimates of their uncertainty. Kalman filters [4] are commonly used to estimate the state of a system from a time-series of measurements corrupted with uncorrelated Gaussian noise. Such filters are promising candidates to infer position from GPS measurements and to characterise the uncertainty of the position estimates
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