How GNSS SNR Values Are Connected to Antenna Heights; the Geometry of SNR-Based GNSS Interferometric Reflectometry

You may know what formula I am talking about; one of the most famous formulas in GNSS reflectometry that magically links the reflected SNR values, satellite elevation angle, and the signal wavelength to the antenna height. I have created a short animated video to explain where this formula comes from.

In October 19, 2020, at 11:00 a.m., when I was defending my master’s thesis, which was on the applications of GNSS interferometric reflectometry, both my committee members asked questions about the origin of this formula. First, Dr. Richard Kelly, asked me how we can geometrically connect the SNR to the antenna height, and I referred to some basic trigonometric equations to clarify the geometry of SNR-based GNSS-Reflectometry. Afterwards, Dr. Grant Gunn, asked how bending effect and penetration delay can be ignored in this technique; so, I refered to its geometry and mentioned that this technique is classified as a “phase altimetry” method, in which the delay and bending effects are significantly reduced compared to those method categorized as “range altimetry”.

Although I successfully passed my defense, I felt that the origin of this formula might be unclear for researchers whose main fields of interest are not GNSS reflectometry. Therefore, I decided to create this short video to simply explain how the antenna height can be retrieved from SNR values. This video is a part of my i-poster submitted to the Global Water Future 4th Annual Open Science Meeting (GWF2021) in where a large number of researchers and scientists present their recent findings on Canada’s water future. As I guess that many of them are not super expert in GNSS reflectometry, I decided to create this short video and put it in my poster. The link to my poster will be shared when it becomes available.

CYGNSS and Spatial Interpolation; a Review

“Why talk to others when you can talk to yourself?” This is how Clara Chew captioned her fantastic YouTube video in LinkedIn to start suggesting a spatial interpolation method for CYGNSS data.

First of all, I should say what a great idea form one of my most inspiring and favorite researchers. Establishing a YouTube channel to talk to ourselves about GNSS reflectometry is what we’d need, and to be honest, that’s the main encouragement for myself to kick off this website. Although I am currently the only writer here, but this platform is going to become an online magazine for GNSS-R researchers to freely read and write others’ opinions. It’s yet to be widely advertised, but the core idea is the same: let’s just talk to ourselves : )

About the video, let’s start from the end; this method is not going to be used for every application. “If you are trying to do some sort of analysis where you need exact knowledge of reflectivity at a certain point,” Clara clarifies “you might not want to use this method”. It sounds very true for my current research focusing on Qinghai Lake, Tibet Plateau, where I restricted Fresnel Zones to only the central region of the lake to make sure that I am not receiving reflections from the surrounding lands or even the shore lines. So, no interpolation is required at any level. But aside from the Qinghai’s research, it’s been a few months that I’ve been thinking about expanding my CYGNSS explorations to a wider region, say central desert of Iran, and meanwhile, one of my greatest concerns has been how to do data interpolation over a large area. Clara has also mentioned it somewhere in her video that “trust me, it won’t be too frustrating”, but it is for me :)) because I haven’t started yet.

But when I’m saying my concern is on how to do it, I wouldn’t say that choosing the interpolation method is not a big concern, as it really is, but it is not the biggest issue for me, because I had practiced a method years ago. The story took place in 2013-2015, when I was working on geodynamics of the Earth, and my specific research at that time was calculating strain tensors. I found out that routine methods for interpolating crustal movement values, e.g. IDW and Spline, are way off the road. I spent couple of months on that, and realized that “deterministic interpolation methods” do not perfectly work for those problems which require “geo-statistical interpolation methods”, such as Kriging. That was the point.

In short, despite deterministic methods which only consider distance as the effective parameter in weighting procedure, geo-statistical interpolation methods also take the correlation into account as a weighting function. This is exactly what Clara suggested: “correlation coefficients“. In Kriging, for example, a covariance matrix is created among node points based on statistical constraints, and then, that matrix plays a key role in establishing the weighting function. The same idea can be seen in another powerful interpolation method called Least-Square Collocation, which is widely used in geoid problems and potential field anomaly interpolations.

I employed Ordinary and Universal Kriging interpolation techniques for estimating strain matrix components, and improved the accuracy up to 70%. As Clara has remained the discussion open at the end of her video, I would invite her to a collaboration in order to explore the ability of geo-statistical methods of interpolation in CYGNSS cases.

Animated Video: GPS-Reflectometry for Soil Moisture Monitoring

To clarify a subject to non-specialists, creating a video is a much more efficient way compared to giving lectures, preparing graphs, and even writing plain language articles.

Gradflix is a competition held each year at the University of Waterloo encouraging grad students to create 1-minute videos to explain their research topics. Then, based on a set of predefined criteria, three videos are chosen as the winners.

I participated last year (2020) and made a very simple video to explain the very basic idea of GPS-Reflectometry. Surprisingly, I was chosen as a finalist. Although I did not place among the first three winners, it was a great inspiration for me to walk on the red carpet as a finalist.

This year (2021), I spent more time and created a more professional video to explain our research on the GNSS-Reflectometry capability of soil water content monitoring. After a month, I was waiting for another confirmation email, like the one that I received last year, saying that I have been chosen again as a finalist for this year, but I received a rejection email saying “although your video is an excellent number one fantastic phenomenon piece of art work, BUT your video was not qualified to be chosen among finalists.” Such a retrogression :)) I can’t deny that I got disappointed when I received that rejection email, but when I got back to my video and showed it to a couple of animation specialists, they confirmed that it was just a bit better than awful =))

By the way, I would say that this video could still be beneficial for those who want to get more familiar with daily applications of GNSS-Reflectometry.