# Analysis of Wide-Lane Ambiguities Derived from Geometry-Free and Geometry-Based Precise Point Positioning Models and Their Implication for Orbit and Clock Quality

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## Abstract

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## 1. Introduction

## 2. WL Ambiguities Derived from the GF Model

**H**is the coefficient matrix derived from Equation (5) only for ambiguity parameters as follows:

^{s}is the elevation of the satellite. According to the error propagation law, the variance-covariance of ambiguity terms can be derived as:

## 3. WL Ambiguities Derived from the GB Model

## 4. Impact of Orbit and Clock Residual Errors on Ambiguity Estimation

#### 4.1. Orbit and Clock Residual Error Being Time-Constant Bias

#### 4.2. Orbit and Clock Residual Error Being Time-Variant Error

## 5. Experiment and Results Analysis

#### 5.1. Analysis of GB and GF Ambiguities

#### 5.2. Orbit and Clock Residual Error Effects

## 6. Simulation Study of Orbit/Clock Error Effects

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**GF (blue) and GB (red) L1, L2 and WL ambiguities (

**left**) and their corresponding formal errors (

**right**) of PRN 09 computed from a single receiver (CEBR) observations and ESA final orbit and clock products.

**Figure 3.**GF (blue) and GB (red) L1, L2 and WL ambiguities (

**left**) and their corresponding formal errors (

**right**) of PRN 09 computed using a single receiver (REDU) observations and ESA final orbit clock products.

**Figure 4.**Differences of GB and GF WL ambiguities (red) and their formal errors (blue) of PRN 09 from the receivers CEBR (

**top**) and REDU (

**bottom**).

**Figure 5.**Differences of GB and GF WL ambiguities computed with ESA final orbit and clock products at site KOKV.

**Figure 6.**Various differences of PRN 09 WL ambiguities and orbit clock products computed at the receiver CEBR (

**left**) and REDU (

**right**): (1) differences of GB ambiguities computed with final and real-time orbit clock products are indicated in red in top panels; (2) differences of GF ambiguities computed with final and real-time orbit clock products are indicated in blue in top panels; (3) differences of GB and GF ambiguities computed with final orbit clock products (OC1) are indicated in blue in bottom panels; (4) differences of GB and GF ambiguities computed with real-time orbit clock products (OC2) are indicated in red in bottom panels; (5) differences of orbit clock impacts in LOS directions between final and real-time orbit clock products in green.

**Figure 7.**Differences of GB-GF WL ambiguities computed with real-time orbit and clock products at Site KOKV.

**Figure 8.**Variations of final orbit/clock and real-time orbit/clock differences projected into the LOS at Site KOKV for all visible GPS satellites.

**Figure 9.**GB-GF WL ambiguities computed with real-time orbit clock products for GPS PRN 09 at all selected sites.

**Figure 10.**Recomputed GB-GF WL ambiguities minus the previous ones in Figure 5 with the simulated constant bias (

**top**) and the time-variant errors (

**bottom**) added into orbit clock of PRN 30 at Site KOKV.

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**MDPI and ACS Style**

Chen, G.; Liu, S.; Zhao, Q.
Analysis of Wide-Lane Ambiguities Derived from Geometry-Free and Geometry-Based Precise Point Positioning Models and Their Implication for Orbit and Clock Quality. *Sensors* **2018**, *18*, 1760.
https://doi.org/10.3390/s18061760

**AMA Style**

Chen G, Liu S, Zhao Q.
Analysis of Wide-Lane Ambiguities Derived from Geometry-Free and Geometry-Based Precise Point Positioning Models and Their Implication for Orbit and Clock Quality. *Sensors*. 2018; 18(6):1760.
https://doi.org/10.3390/s18061760

**Chicago/Turabian Style**

Chen, Gang, Sijing Liu, and Qile Zhao.
2018. "Analysis of Wide-Lane Ambiguities Derived from Geometry-Free and Geometry-Based Precise Point Positioning Models and Their Implication for Orbit and Clock Quality" *Sensors* 18, no. 6: 1760.
https://doi.org/10.3390/s18061760