Vertical ionospheric delay estimation for single-receiver operation

Abstract

An apparent delay is occurred in GPS signal due to both refraction and diffraction caused by the atmosphere. The second region of the atmosphere is the ionosphere. The ionosphere is significantly related to GPS and the refraction it causes in GPS signal is considered one of the main source of errors which must be eliminated to determine accurate positions. GPS receiver networks have been used for monitoring the ionosphere for a long time. The ionospheric delay is the most predominant of all the error sources. This delay is a function of the total electron content (TEC). Because of the dispersive nature of the ionosphere, one can estimate the ionospheric delay using the dual frequency GPS. In the current research our primary goal is applying Precise Point Positioning (PPP) observation for accurate ionosphere error modeling, by estimating Ionosphere delay using carrier phase observations from dual frequency GPS receiver. The proposed algorithm was written using MATLAB and was named VIDE program. The proposed Algorithm depends on the geometry-free carrier-phase observations after detecting cycle slip to estimates the ionospheric delay using a spherical ionospheric shell model, in which the vertical delays are described by means of a zenith delay at the station position and latitudinal and longitudinal gradients. Geometry-free carrier-phase observations were applied to avoid unwanted effects of pseudorange measurements, such as code multipath. The ionospheric estimation in this algorithm is performed by means of sequential least-squares adjustment. Finally, an adaptable user interface MATLAB software are capable of estimating ionosphere delay, ambiguity term and ionosphere gradient accurately.

Effects of Hard and Soft Equality Constraints on Reliability Analysis

“…A of Equation (8). In that case, the false decisions are restricted to Type I error and Type II error.…”

“…where |∇ i | is the Minimal Detectable Bias (MDB 0 (i) ) for the case in which there is only one single alternative hypothesis, which can be computed for each individual alternative hypothesis according to Equation (8). For a single outlier, the variance of an estimated outlier, denoted by…”

Which Are the Effects of Hard and Soft Equality Constraints on the Iterative Outlier Elimination Procedure?

“…Such constraints are a prior knowledge embedded into a model to avoid a trivial solution; to guarantee the stability of estimates; to improve the precision and accuracy of the results by reducing the number of unknown parameters or accordingly by increasing the redundancy of the system; and to mitigate (or even estimate) a possible systematic effect [1][2][3]. For example, [4] adopted constraints to determine the transponder coordinates in a problem of combining satellite positioning (GNSS) of a surface platform with acoustic ranging to seafloor transponders; [5][6][7][8][9][10] have used constraints to model the atmospheric effects on GNSS signals; and [11] have imposed the constraints of predicted satellite clocks to improve the precise orbit determination (POD) processing during maneuvers.…”