Stochastic Analysis and Behavior Modeling of Errors associated with Global Positioning Sensor

Abstract

The aim of this work is to analyze the behavior of errors associated with a commercial grade Global Positioning Sensor (GPS receiver) and thereafter, to characterize the error pattern of the sensor based on a mathematical analytic model. The measurement errors associated with a GPS receiver are generally perceived to be random. Thus for manual decision-making purposes, the inferences are drawn qualitatively by human operator with respect to a relative quality factor referred to as Dilution of Precision (DOP) as per NMEA 0183 standard. However with an appropriate mathematical modeling it can be inferred that these positioning errors behave in a definable way. The current work encompasses comparative testing of two commercial grade GPS receivers as per National Standard for Spatial Data Accuracy (NSSDA, Part 3 of FGDC-STD-007.3-1998) with Standard Positioning Service (non-differential, horizontal positioning with Selective Addressability off). The error patterns associated with these receivers are then statistically analyzed with standard statistical tools e.g. mean & standard deviation. Thereafter the Cumulative Distribution Function (CDF) and Probability Density Function (PDF) of these experimental data are compared with those of theoretical stochastic models. The corresponding stochastic models are selected which fits best with the experimental results and thus the error patterns are identified mathematically. This characterization helps in analyzing the spatial accuracy of a positioning sensor by obtaining the parameters like Circular Error Probability and R95. This characterization will further help in fusing the position information with other similar sensors and thereby increasing the confidence of position estimate. The methodology for stochastic error characterization suggested in this paper can be applied to any measurement sensor for improving the decision-making capabilities of an automated system.