Quality control procedures for GNSS precise point positioning in the presence of time correlated residuals

Abstract

Precise point positioning (PPP) is a technique for processing Global Navi- gation Satellite Systems (GNSS) data, often using recursive estimation methods e.g. a Kalman Filter, that can achieve centimetric accuracies using a single receiver. PPP is now the dominant real-time application in o shore marine positioning industry. For high precision real-time applications it is necessary to use high rate orbit and clock corrections in addition to high rate observations. As Kalman filters require input of process and measurement noise statistics, not precisely known in practice, the filter is non-optimal. Geodetic quality control procedures as developed by Baarda in the 1960s are well established and their extension to GNSS is mature. This methodology, largely unchanged since the 1990s, is now being applied to processing techniques that estimate more parameters and utilise many more observations at higher rates. \Detection, Identification and Adaption" (DIA), developed from an optimal filter perspective and utilising Baarda's methodology, is a widely adopted GNSS quality control procedure. DIA utilises various test statistics, which require observation residuals and their variances. Correct derivation of the local test statistic requires residuals at a given epoch to be uncorrelated with those from previous epochs. It is shown that for a non-optimal filter the autocorrelations between observations at successive epochs are non-zero which has implications for proper application of DIA. Whilst less problematic for longer data sampling periods, high rate data using real-time PPP results in significant time correlations between residuals over short periods. It is possible to model time correlations in the residuals as an autoregressive process. Using the autoregressive parameters, the effect of time correlation in the residuals can be removed, creating so-called whitened residuals and their variances. Thus a whitened test statistic can be formed, that satisfies the preferred assumption of uncorrelated residuals over time. The effectiveness of this whitened test statistic and its impact on quality control is evaluated.