Run time position estimation with basic sensors in real time SCADA applications

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 O(dx2dt), where dx is the dimension of the augmented state-vector and dt 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 dt=1. Hence, the algorithm is likely to be suitable for sensor fusion applications.

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An approach to real-time position estimation at zero and low speed for a PM motor based on saliency

IAS '96. Conference Record of the 1996 IEEE Industry Applications Conference Thirty-First IAS Annual Meeting ◽

10.1109/ias.1996.556993 ◽

2002 ◽

Cited By ~ 16

Author(s):

S. Ogasawara ◽

H. Akagi

Keyword(s):

Real Time ◽

Position Estimation ◽

Low Speed ◽

Time Position

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Current Trends in Random Walks on Random Lattices

Mathematics ◽

10.3390/math9101148 ◽

2021 ◽

Vol 9 (10) ◽

pp. 1148

Author(s):

Jewgeni H. Dshalalow ◽

Ryan T. White

Keyword(s):

Random Walk ◽

Random Walks ◽

Real Time ◽

Real Space ◽

Historical Background ◽

Escape Time ◽

The Real ◽

Current Trends ◽

One Step ◽

Time Position

In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location outside a bounded subset of the real space. In this case we target the virtual first passage (or escape) time. Thus, unlike standard random walk problems, rather than crossing the boundary, we deal with the walker’s escape location arbitrarily distant from the boundary. In this paper, we give a short historical background on random walk, discuss various directions in the development of random walk theory, and survey most of our results obtained in the last 25–30 years, including the very recent ones dated 2020–21. Among different applications of such random walks, we discuss stock markets, stochastic networks, games, and queueing.

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