Abstract
Global Navigation Satellite System Radio Occultation (GNSS-RO) is a technique used to sound the atmosphere and derive vertical profiles of refractivity. Signals from GNSS satellites are received in a low-Earth orbit, and they are then processed to produce bending angle profiles, from which meteorological parameters can be retrieved. Generating two-dimensional images in the form of spectrograms from GNSS-RO signals is commonly done to, for instance, investigate reflections or estimate signal quality in the lower troposphere. This is typically implemented using, e.g., the Short-Time Fourier Transform (STFT) to produce a time-frequency representation that is subsequently transformed to bending angle (BA) and impact height (IH) coordinates by non-linear mapping. In this paper, we propose an alternative method based on a straightforward extension of the Phase Matching (PM) operator to produce two-dimensional spectral images in the BA-IH domain by applying a sliding window. This Sliding Window Phase Matching (SWPM) method generates the spectral amplitude on an arbitrary grid in BA and IH, e.g., along the coordinate axes. To illustrate, we show both SWPM and STFT methods applied to operational MetOp-A data. For SWPM we use a constant window in the BA-dimension, whereas for STFT we use a conventional constant time window. We show that the SWPM method produces the same result as STFT when the same window length is used for both methods. The sample points in impact parameter and bending angle are those generated by and the main advantage is that SWPM offers the user a convenient way to freely sample the BA-IH space. The cost for this is processing time that is somewhat longer than implementations based on the Fast Fourier Transform, such as the STFT method.
Highlights
Since their inception, Global Navigation Satellite System (GNSS) constellations have come to play an important part for geographic positioning, and for Earth observation purposes [1]
The extension involves applying a sliding window defined in terms of bending angle (BA), which is mapped to the time axis using the optical path length function for a ray
Phase Matching (SWPM) operator is equivalent to the Short-Time Fourier Transform (STFT), by using the kernel of PM as range model
Summary
Global Navigation Satellite System (GNSS) constellations have come to play an important part for geographic positioning, and for Earth observation purposes [1]. Time-frequency representations of GNSS-RO measurements have been widely used for a long time, as they visualize BA profiles as two-dimensional spectral images rather than one-dimensional profiles (see [4,5,6,7,8]) They have since found a wider use. 2021, 13, 970 in distinct deviations in Doppler frequency, visualized in spectrograms generated from RO signals This idea has been developed further, leading to automatic classification of reflections [11,12,13] using supervised machine learning techniques. It is very common to make time-frequency representations using the ShortTime Fourier Transform (STFT) or related methods, Gorbunov et al [20] instead applied the Wigner Distribution Function (WDF) [21].
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