Abstract
In this paper we propose an outlier detection approach for GNSS vector networks based on the specific direction (i.e., SD approach), along which the test statistic constructed reaches the maximum. We derive the unit vector of this specific direction in detail, and prove that the unit vector is the same as that determined by the outlier estimates in three-dimensional (3D) approach, while the distribution of the maximum test statistic in this direction is the square root of Chi-squared distribution. Therefore, eliminating an outlier along this specific direction can get the same result as that of eliminating all three components of outlier vector in 3D approach. The mathematical equivalence of SD approach and 3D approach is further demonstrated by a real GNSS network. Moreover, preliminary application of the SD approach to detect the abnormal antenna height measurement is carried out in terms of numerical simulations of multiple baseline solutions, and it shows that the SD approach can effectively detect baselines that are directly infected by corresponding receiver antenna height errors.
Highlights
When a weight matrix is chosen as the inverse of observables’ covariance matrix, the weighted least-squares (WLS) estimation is the best linear unbiased estimator (BLUE), assuming that no outlier exists
The test statistic can be constructed according to various statistical distributions, e.g., standard normal distribution, τ-distribution, and F-distribution [4,5,6,7], and one can determine the existence of outliers by a comparison with correspondent critical value at a given significance level [8,9]
We proposed the specific direction-based outlier detection approach (SD approach), for 3D Global Navigation Satellite System (GNSS) networks
Summary
When a weight matrix is chosen as the inverse of observables’ covariance matrix, the weighted least-squares (WLS) estimation is the best linear unbiased estimator (BLUE), assuming that no outlier exists. There can be various outliers’ sources in GNSS networks such as satellite orbit error, impractical tropospheric model, wrong measurement of GNSS antenna height, antenna centering and positioning, etc. These factors usually come from a specific direction in the space, and have varying effects on all coordinate components of baseline vectors [39].
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