# Improving Consistency of GNSS-IR Reflector Height Estimates between Different Frequencies Using Multichannel Singular Spectrum Analysis

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## Abstract

**:**

## 1. Introduction

^{2}around a 2-m-high antenna, is higher than that of classical satellites or aircrafts with a resolution of several square kilometers. GNSS-IR’s validity is not impacted by weather conditions, such as rain or fog, or by changes in illumination between day and night, making it an ideal choice for continuous monitoring. GNSS-IR is an intriguing and complementary remote sensing technique, and has been validated for measuring surface soil moisture [4], snow depth [5,6], permafrost melt [7], and ocean tides [8].

## 2. Methods and Data

#### 2.1. Basic Principle of GNSS-IR Inversion Model

#### 2.2. Mathematical Framework of M-SSA

#### 2.3. SNR Measurements

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Photograph of P351 GNSS site. The antenna is attached to a ~2-m-height monument. The surrounding environment is open, with a topography gently inclined and undulating. Photo courtesy of UNAVCO. (

**b**) Typical SNR measurements (one rising arc at day 274) as a function of elevation $e$. All three time-series show interference patterns with low-frequency trends (black curves). Arbitrary constants are added for clarity to the S2C and S5Q signals. (

**c**) The detrended and uniformly interpolated version of (

**b**). A quadratic polynomial is used to remove the direct signal, and a linear interpolation is used to transform the SNR measurements into equally spaced intervals. Note that the x-axis has changed from elevation $e$ to $2\mathrm{s}\mathrm{i}\mathrm{n}(e)/\lambda $. The SNR measurements within the red box are used to form the input dataset for M-SSA. The black curves are the reconstructed time series, by adding the first two reconstructed components, after M-SSA preprocessing. The reconstructed time series effectively recovers the interference patterns in the original time series.

**Figure 3.**The first 8 reconstructed components (RCs) of the dSNR time series of different frequency using M-SSA.

**Figure 5.**Scatters of estimated reflector heights between S1C, S2C, and S5Q frequencies. (

**a**–

**c**) show scatter plots obtained using the original dSNR time series, and (

**d**–

**f**) show scatter plots obtained using the reconstructed dSNR time series.

**Figure 6.**The average reflector height in an increasing order and its corresponding standard deviation.

**Figure 7.**Scatters of estimated reflector heights between S1C, S2C, and S5Q frequencies using 2-channel M-SSA and univariate SSA. (

**a**–

**c**) are scatter plots of the inverted ${H}_{R}$ from the reconstructed dSNR time series using 2-channel M-SSA, which is composed of S1C–S2C, S1C–S5Q, and S2C–S5Q, respectively. (

**d**–

**f**) are scatter plots between the inverted ${H}_{R}$ obtained using the univariate SSA individually on S1C, S2C, and S5Q, respectively.

**Table 1.**Linear fitting statistics between estimated reflector heights from different frequencies using LSP, 3-channel M-SSA + LSP, 2-channel M-SSA + LSP, and SSA + LSP.

Original | 3-Channel M-SSA | 2-Channel M-SSA | SSA | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

S1–S2 | S1–S5 | S2–S5 | S1–S2 | S1–S5 | S2–S5 | S1–S2 | S1–S5 | S2–S5 | S1–S2 | S1–S5 | S2–S5 | |

a | 0.77 | 0.76 | 0.94 | 0.97 | 0.99 | 1.01 | 1.00 | 1.00 | 0.99 | 0.82 | 0.86 | 0.96 |

b | 0.49 | 0.51 | 0.13 | 0.07 | 0.03 | −0.01 | 0.01 | 0.01 | 0.01 | 0.40 | 0.32 | 0.08 |

${R}^{2}$ | 0.69 | 0.67 | 0.89 | 0.95 | 0.96 | 0.98 | 0.88 | 0.94 | 0.98 | 0.67 | 0.73 | 0.88 |

RMSE (m) | 0.10 | 0.10 | 0.06 | 0.04 | 0.04 | 0.02 | 0.06 | 0.04 | 0.02 | 0.09 | 0.09 | 0.06 |

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**MDPI and ACS Style**

Lei, J.; Li, W.; Zhang, S. Improving Consistency of GNSS-IR Reflector Height Estimates between Different Frequencies Using Multichannel Singular Spectrum Analysis. *Remote Sens.* **2023**, *15*, 1779.
https://doi.org/10.3390/rs15071779

**AMA Style**

Lei J, Li W, Zhang S. Improving Consistency of GNSS-IR Reflector Height Estimates between Different Frequencies Using Multichannel Singular Spectrum Analysis. *Remote Sensing*. 2023; 15(7):1779.
https://doi.org/10.3390/rs15071779

**Chicago/Turabian Style**

Lei, Jintao, Wenhao Li, and Shengkai Zhang. 2023. "Improving Consistency of GNSS-IR Reflector Height Estimates between Different Frequencies Using Multichannel Singular Spectrum Analysis" *Remote Sensing* 15, no. 7: 1779.
https://doi.org/10.3390/rs15071779