Extension of the undifferenced and uncombined CDMA PPP-RTK for not-common-frequency GNSS observations

Integer ambiguity resolution enabled precise point positioning, PPP-RTK, which is becoming one of the most popular global navigation satellite system (GNSS) positioning modes. Owing to the presence of rank deficiencies in the system of GNSS observation equations, one needs to choose some of the GNSS parameters as S-basis and let the remaining parameters absorb them. Doing so forms a full-rank PPP-RTK model whose combined parameters are estimable. To simplify the model construction, previous contributions assume that observations are tracked on common-frequency (CF) bands for all the involved receiver-satellite pairs. Such a model is referred to as CF PPP-RTK. However, the coexistence of legacy and modernized GNSS signal systems, together with the presence of outdated and updated receiver firmware, leads to not-common-frequency (NCF) cases where some of the involved receivers fail to track observations on certain frequencies. For such cases, the CF PPP-RTK model discards part of the observations so as to maintain the CF assumption. In this contribution, we refrain from making the CF assumption and extend the GNSS undifferenced and uncombined formulation to NCF cases. Such a NCF PPP-RTK model ensures that all observations contribute to the parameter estimation process, avoiding losing any information content in the data. As a result, our proposed NCF PPP-RTK avoids any potential reduction in both the availability and the precision of the corrections. To evaluate the positioning performance of the proposed model, we conducted three experiments with continuously operating reference station data in Hong Kong, Australia, and Europe. The superiority of the NCF PPP-RTK model over its conventional CF PPP-RTK version is illustrated in terms of both the time-to-first-fix and root mean square positioning errors.