Precise point positioning (PPP) and real-time kinematic (RTK) stand for two representative techniques employed by global navigation satellite systems (GNSS) to provide positioning, navigation, and timing services. In formulating the PPP functional model, a common assumption is that the receiver code biases (RCBs) remain time-constant, whereas the classical double-differenced RTK model considers these biases unlinked in time. This contradictory assumption underlying PPP and RTK implies potential inconsistencies in a broad spectrum of GNSS applications. In this chapter, we formulate a modified multi-frequency PPP model and a between-receiver single-differenced RTK model. Both models treat the RCBs as time-varying parameters, allowing for the incorporation of a realistic dynamic model of RCBs. Through the proposed PPP and RTK models, we analyze the impact of different RCB dynamic models on positioning and timing performance. The results demonstrate that the formal precision of position estimates remains consistent regardless of whether RCBs are modeled as time-constant or time-varying parameters. However, an inappropriate RCB modeling strategy increases the Allan deviation of the receiver clock, adversely affecting timing performance. These findings underscore the significance of establishing a realistic dynamic model for RCB, a task facilitated by utilizing the formulated modified PPP and RTK model to extract epoch-by-epoch RCB estimates.

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Temporal Modelling of GNSS Receiver Code Biases in High-Precision Positioning and Timing

  • Pengyu Hou,
  • Jintao Jiang,
  • Baocheng Zhang

摘要

Precise point positioning (PPP) and real-time kinematic (RTK) stand for two representative techniques employed by global navigation satellite systems (GNSS) to provide positioning, navigation, and timing services. In formulating the PPP functional model, a common assumption is that the receiver code biases (RCBs) remain time-constant, whereas the classical double-differenced RTK model considers these biases unlinked in time. This contradictory assumption underlying PPP and RTK implies potential inconsistencies in a broad spectrum of GNSS applications. In this chapter, we formulate a modified multi-frequency PPP model and a between-receiver single-differenced RTK model. Both models treat the RCBs as time-varying parameters, allowing for the incorporation of a realistic dynamic model of RCBs. Through the proposed PPP and RTK models, we analyze the impact of different RCB dynamic models on positioning and timing performance. The results demonstrate that the formal precision of position estimates remains consistent regardless of whether RCBs are modeled as time-constant or time-varying parameters. However, an inappropriate RCB modeling strategy increases the Allan deviation of the receiver clock, adversely affecting timing performance. These findings underscore the significance of establishing a realistic dynamic model for RCB, a task facilitated by utilizing the formulated modified PPP and RTK model to extract epoch-by-epoch RCB estimates.