A Comparative Analysis Between the ENVISAT and ICEYE SAR Systems for the Estimation of Sea Surface Current Velocity

Abstract

In this work, we present the results of a comparative analysis between the first-generation Advanced Synthetic Aperture Radar (ASAR) sensor mounted on board the ENVISAT platform and the novel ICEYE micro-satellite synthetic aperture radar (SAR) sensor in measuring the radial velocity of ocean currents through the Doppler Centroid Anomaly (DCA) technique. First, the basic principles of DCA and the theoretical precision of the Doppler Centroid (DC) estimates are introduced. Subsequently, the role of the DC measurements in retrieving the sea surface current velocity is addressed. To achieve this goal, two sets of SAR data gathered by ASAR (C-band) and from the X-band ICEYE instruments, respectively, are exploited. The standard deviation of DCA measurements is derived and tested against what is expected by theory. The presented analysis results are beneficial to evaluate the pros and cons of the new-generation X-band to the first-generation ASAR/ENVISAT system, which has been extensively exploited for ocean currents monitoring applications. As an outcome, we find that with inherently selected methods for DC estimates, the performance offered by ICEYE is comparable to, or even better than (with specific parameters selection), the consolidated approaches based on the ASAR sensor. Nonetheless, new SAR constellations offer an undoubted advantage regarding improved spatial resolution and time repeatability.

1. Introduction

The monitoring of the marine environment has conventionally been conducted through the utilization of in situ sensors, which offer a high degree of information content. However, these sensors are often costly and may not provide sufficient spatial and temporal coverage. In contrast, remote sensing techniques have the potential to offer cost-effective solutions and data for regions where information is limited or non-existent [1].

Microwave remote sensing methodologies, based on the use of Synthetic Aperture Radar (SAR) sensors, have been extensively developed for a variety of land surface monitoring applications [2]. In recent decades, the scientific community has shown a growing interest in the study of marine parameters through the use of SAR, which generally complements traditional remote sensing techniques based on optical or multispectral sensors. Among various remote sensing techniques employed to detect and monitor marine environments [1,3,4,5,6], Synthetic Aperture Radar (SAR) technology has progressively become a well-established practice. Differently from optical sensors, SAR allows obtaining all-weather and day–night imaging of wide areas of Earth’s surface [7]. SAR remote sensing for ocean, sea, and coastal applications mostly exploits the amplitude of the backscattered signal, for example, monitoring oil spills [8] and sea ice [9], ship detection [10], and high-resolution wind fields retrieval [11].

However SAR uses coherent radiation, and the complementary information carried in the phase of the received complex signal can be also exploited. By analyzing the complex backscattered (received) signal, it is possible to measure the Doppler properties of the scatterers. The latter are directly related to the motion of the scatterers along the radar line of sight (LOS) in both land and marine contexts. In ocean applications, these properties are currently used to retrieve near surface wind speed [12] and surface current [13].

The estimation of sea surface velocity [14,15] from SAR images represents today a “hot-point”. In this context, the process of hydrodynamic modulation of the sea surface roughness allows, for example, the estimation of the sea surface current signatures [14,15,16,17]. Extracting quantitative parameters of currents based exclusively on SAR images, however, is a rather complex matter. Indeed, numerous variables, including the wind vector and bathymetry [18], must be taken into account for comprehensive analysis.

In general, two SAR-based methods can be used to measure ocean surface current velocity: the along-track SAR interferometry (ATI) [19] and the Doppler Centroid Anomaly (DCA) [16] techniques. ATI, which was initially introduced in [19], needs the collection of data pairs from along-track displaced antennas. It measures the interferometric phase difference between the complex signals recovered from the two antennas, which is proportional to the Doppler shift of the backscattered radar echoes. ATI is particularly suited for fast-varying phenomena in marine observations, including sea current surface velocity and vehicle fluxes in aquatic environments [20,21,22,23,24,25,26]. This technique has undergone significant developments in recent years. However, ATI requires unique sensor characteristics, namely, the opportunity of having two antennas spaced along the azimuth direction, enabling the acquisition of images within a short time lag [16,20,21,27,28,29].

Conversely, the DCA technique [16] relies on the analysis of the Doppler Centroid Anomaly, i.e., the anomaly that accounts for the motion of surface roughness elements on the ocean surface corrected for the Earth’s rotation, allowing one to derive the estimates of the surface current velocity. Indeed, DCA computes the differences between the Doppler Centroid (DC) estimated from the SAR data and the frequencies predicted from the relative motion between the satellite and the Earth’s rotation, which reflect the geophysical information about the motion of the marine surface. Alternatively, the Doppler frequencies can be estimated using time- and frequency-domain algorithms.

Generally, the currently available SAR systems lack ATI mode; hence, DCA is preferred in practical cases since it exploits the direct measure of the surface velocity using single-look complex (SLC) images from one single SAR acquisition. Unlike ATI, DCA is, in principle, applicable to data acquired by any SAR mission. A quality comparison between the ATI and DCA techniques for retrieving surface current fields with TerraSAR-X and TanDEM-X SAR data was already presented in [21].

The pioneering work of Madsen [30] firstly addressed the problem of retrieving DC estimates from SAR images by referring to three distinctive algorithms. The former was based on calculating the azimuth Fourier spectrum and evaluating that frequency, i.e., the DC, to which the spectrum is symmetric. This operation was performed by splitting the azimuth spectrum into two non-overlapped slices and calculating their energy difference. DC is the frequency at which the energy is perfectly balanced. This frequency-based energy balance method was found to obtain DC estimates with a variance proportional to the scene contrast under the simplified assumption that the imaged scene is quasi-stationary. The second method proposed in [30] operated in the time domain and was based on calculating the complex correlation function between two SAR image samples displaced for a given number of pixels along the azimuth direction. It was proven that the phase of correlation estimate is dependent on the DC, estimated with a variance that, also in this case, is almost proportional to the scene contrast. This method works in the time domain, and it is preferable to the energy balance method, especially for real-time (or quasi-real-time) applications, when it can directly work on raw data without the need to preliminarily apply a focusing operation. A third method, also operating in the time domain, was also proposed in the same work [30], relying on the straightforward check of the Doppler sign alone to calculate the DC, speeding up the whole process.

Comprehensive calculations on the DC estimates precision were then presented by Bamler in [31], in which SAR signal statistical properties were exploited to derive a general formulation of the standard deviation of DC measurements. At the Cramér–Rao bound, it has been shown that DC standard deviation is proportional to the Pulse Repetition Frequency (PRF) and inversely proportional to the square root of the number of pixels in the box used to compute the correlation and/or the azimuth spectrum. These calculations were primarily carried out for stationary scenes with a uniform background. However, its primary outcomes can be extended to non-homogeneous targets by multiplying the box pixels by the scene contrast. Inaccurate estimates of the DC values arise in regions with low signal-to-noise ratio (SNR) and/or when the background is not uniform. These errors have been the subject of some investigations over the last decades [21,32,33].

In particular, the work of Cumming in 2004 [34] proposed two approaches to obtain reliable estimates of DC by adaptively selecting some spatially uniform boxes in the imaged scene to circumvent the problems arising in low SNR regions, partially.

Since 2005 [16,35,36,37,38], several works have analyzed the application of DCA to ASAR data, thus demonstrating its potential for successfully retrieving the radial components of the sea surface currents. The computed Doppler Centroid (DC) shift complements the Normalized Radar Cross-Section (NRCS) measurements. Many examples of the application of the DCA methodology on C-band SAR data are relevant, especially over regions where strong currents occur, like in the Gulf Stream [14,39] offshore of the USA coast, in the Agulhas Greater Current offshore of South Africa [36], and in the coastal area of the Normandy Gulf [16]. More recently, the DCA technique has been applied to areas with weaker currents than those mentioned above; in fact, some test sites in the Mediterranean Sea have been considered, e.g., the Gulf of Naples [15,17,40], the Northern Adriatic Sea [41] and the Black Sea [42]. Furthermore, the DCA technique has also been applied to inland waters, e.g., Lake Garda (the largest lake in Italy) [43].

Doppler and SAR backscatter information can also be complemented with wind information, for instance, provided by numerical models (e.g., ECMWF), to improve wind field estimation [13,41,42]. Concerning sea surface monitoring, the scientific literature provides a few examples of DCA applications to conventional spaceborne SAR data (large platform), mainly using C-band sensors [16,35,36,37,38]. However, DCA estimates are generally biased, leading to less accurate measurements (e.g., estimated in the order of 3–10 Hz for GAOFEN-3 SAR data) [33]. Consequently, the surface current velocity is also biased. To overcome this problem, some optimized filters have been designed to improve the precision of DC measurements at the Cramér–Rao bound, assuming the scene is quasi-stationary [33]. Newly updated equations for the calculation of the precision of DCA estimates have also recently been proposed in [44], which were verified with Monte Carlo simulations, providing a reference to develop future radar systems and identifying parameters design tailored to specific exigence of seawater and ocean currents monitoring.

Recently, a new family of SAR sensors has also been emerging. Among the others, in January 2018, ICEYE launched ICEYE-X1, Finland’s first commercial satellite and proof-of-concept micro-satellite mission [45]. This micro-satellite constellation is equipped with more than 30 X-band sensor satellites that operate with different acquisition modes, guaranteeing a spatial resolution of some meters and a daily/sub-daily revisit time.

In our work, we primarily focus on applying the DCA technique to ICEYE data and comparing its performance to previous generation C-band ASAR data, providing the readers with an assessment of the DC estimates precision, considering the operational parameters of the involved SAR systems. As said, the work of Bamler [31] derived some analytical expressions for the Doppler Centroid standard deviation (STD), considering different potential DC estimators. Since then, only a few other attempts have been made to characterize the precision of DCA estimates for stationary and non-stationary scenes. Considering the expected theoretical STD values of DCA for ENVISAT and ICEYE sensors, a cross-comparison analysis between the two SAR systems is provided here. The experimental results achieved by applying the DCA methodology to ASAR data are also presented. Since ASAR has broadly been used for surface current estimation, the relative results have been well assessed; indeed, it is used as a benchmark to provide valuable insights regarding DC estimation accuracy [32]. The remainder of the paper is organized as follows. Section 2 describes the set of SAR data used in our investigation. Section 3 briefly summarizes the theory behind the DCA technique for surface current velocity estimates. DCA is then applied to selected SAR scenes collected by ENVISAT and ICEYE, and the results of such a comparison analysis are presented in Section 4. Finally, the discussion and concluding remarks are reported in Section 5.

2. Materials

In this section, we summarize the main characteristics of SAR data used for our experiments and acquired by the ENVISAT ASAR sensor (which has been primarily exploited for marine applications), as well as by the newly launched ICEYE constellation. The interest in the proposed comparison analysis resides in the growing availability of a wide range of spaceborne-based SAR missions operating at different microwave frequencies [2]. Figure 1 shows a diagram that pictorially describes SAR systems’ development over time, grouped for operative bands (e.g., X-band, C-band, and L-band). The following subsections describe the main characteristics and the acquisition modes of the specific SAR data exploited for the experiments presented in Section 4.

2.1. ENVISAT Data

In March 2002, ESA launched the ENVISAT mission, a multi-sensor satellite equipped with the C-band ASAR sensor, thus ensuring the continuity of data acquisition with the previous ERS-2 mission (as also shown in Figure 1) [46,47]. This polar-orbiting satellite measured the atmosphere, ocean, land, and ice until April 2012.

ASAR was a key instrument, featuring a coherent SAR system with distributed transmitter and receiver elements. ASAR offers five polarization modes, VV, HH, VV/HH, HV/HH, and VH/VV, and the following mutually exclusive acquisition modes:

• Global Monitoring (GM): This mode uses ScanSAR to generate low-resolution images (1 km) over a 405 km swath in HH or VV polarization;
• Wave Mode (WM): This mode measures changes in sea surface backscatter due to ocean waves, generating vignettes of 5 km × 5 km size with 100 km along-track spacing in HH or VV polarization;
• Image Mode (IM): This mode produces high-resolution products (30 m) on one of seven swaths spanning incidence angles from 15 to 45 degrees in HH or VV polarization;
• Alternating Polarization (AP): This mode generates high-resolution products like in IM but with polarization changing between subapertures within the synthetic aperture. ScanSAR is used without varying the subswath, resulting in two images of the same scene in different polarization combinations (HH/VV or HH/HV or VV/VH) with approximately 30 m resolution;
• Wide Swath (WS): This mode uses ScanSAR to provide medium-resolution images (150 m) over a 405 km swath in HH or VV polarization, composed of five subswaths transmitted in turn to build up continuous along-track images for each subswath.

Finally, it should be noted that in Stripmap (IM) mode, ASAR covers up to 100 km with a single swath with a spatial resolution of about 5 m (azimuth) and 20 m (ground range).

The main operational parameters of the ASAR products, made accessible from ESA archives [48], are summarized in

Table 1. ENVISAT/ASAR parameters.

Parameter	Value	Unit
Wavelength (Center Frequency)	0.05624624	m
Band type	C
Instrument mass	832	kg
Platform velocity	7120	m/s
Pulse Repetition Frequency (PRF)	1650 to 2100	Hz
Chirp bandwidth	up to 16	MHz
Polarization modes	Single VV, HH, or Dual VV + HH, VV + VH, HH + HV
Antenna size	10 × 1.3	m
Incidence Angle range	15–${45}^{\circ }$	degree
Acquisition modes	GM, WM, IM, AP, WS

.

In our research, we profit from the main outcomes of a previous study [41,49], describing the most impressive results obtained by applying the DCA methodology to ASAR data related to the coastal area of the northern Adriatic Sea (Northeast Italy), collected on Ascending (track 358) and Descending (track 351) orbits. Unlike [41,49], in this work, we use one single ENVISAT ASAR data frame acquired on the Ascending orbit. Figure 2 shows the location of the test-site area. Specifically, the red rectangle highlights the swath of the ASAR frame used for the experiments shown in this study.

2.2. ICEYE Data

Unlike ENVISAT, the ICEYE mission is a constellation of micro-satellites currently consisting of more than 30 X-Band SAR satellites orbiting Earth, capable of operating through different acquisition modes [50].

The ICEYE satellites are in sun-synchronous orbit at an inclination of ${97.7}^{\circ }$ with an orbital frequency of about 96 min. The first satellite of the constellation, ICEYE-X1, was launched in January 2018 [45]. The satellites work at X-band at a frequency of $9.65$ GHz with left- and right-looking directions. Each satellite has a 17-day ground track repeat time, and as soon as all 48 satellites are in orbit, a twice-daily revisit time over the same locations on Earth is guaranteed.

The ICEYE sensors are imaging only in vertical polarization (VV), offering products acquired in the following [51]:

• Stripmap mode (STRIP): It enables imaging any area on Earth at incidence angles of 15–${30}^{\circ }$ with a ground spatial resolution of 3 m × 3 m (azimuth × range) and scene size of 50 km × 30 km (azimuth × range). The slant range resolution is $0.5$ m based on the range bandwidth of 300 MHz and $1.5$ m based on the range bandwidth of 100 MHz [45]. Although it is well known that the theoretical azimuth spatial resolution (in Stripmap mode) is given by half the antenna length (along the azimuth direction), the ICEYE azimuth pixel size of the SLC products is fixed to 3 m, whereas the azimuth antenna length is $3.2$ m. This results from a system design parameters optimization that is carried out to reduce the azimuth ambiguities caused by aliasing. Accordingly, during the SLC product formation, an azimuth bandwidth reduction is performed [45].
• Scan imagining mode (SCAN): It is a wide area imaging mode able to create a scene size of 100 km × 100 km, with a ground resolution of 15 m × 15 m at incidence angles of 21–${29}^{\circ }$.
• Spotlight mode (SPOT): It offers the finest resolution available with a ground resolution of $1.0$ m ×$1.0$ m, and it can image a scene of size 5 km × 5 km at incidence angles of 20–${35}^{\circ }$. The spot extended area (SLEA) mode provides the largest very-high resolution SAR imagery with ground resolution of $1.0$ m ×$1.0$ m and a scene size of 15 km × 15 km, or slant resolution of $1.0$ m ×$0.5$ m (azimuth × range) at incidence angles of 20–${35}^{\circ }$.
• Dwell mode (DWELL): It is characterized by a ground resolution from 50 cm and 1 m and a scene size of 5 km × 5 km. Specifically, with its DWELL mode, ICEYE allows creating videos based on a single-pass radar acquisition. This capability enables a new dimension for analyzing in-scene motion [52,53].

Table 2. ICEYE parameters.

Parameter	Value	Unit
Wavelength (Center Frequency)	0.03106658	m
Band type	X
Instrument mass (single sensor)	85	kg
Platform velocity (single sensor)	7377.33	m/s
Pulse Repetition Frequency (PRF)	2000 to 10,000	Hz
Chirp bandwidth	37.6 to 299	MHz
Polarization modes	VV
Antenna size	3.2 × 0.4	m
Incidence Angle range	15–35°	degree
Acquisition modes	STRIP, SPOT, SCAN, SLEA, DWELL

summarizes the main observational parameters of the ICEYE mission.

The experiments carried out in our research with ICEYE data refer to a region over the Perù coastal area (South America) north of Lima, which is shown in Figure 3. In particular, the used SAR image was collected in Stripmap mode on 26 January 2022 through an Ascending orbit. The SAR image covers a coastal area of about 50 km × 30 km (azimuth × range).

By inspecting the archive of the available ICEYE data on [54], we identify a SAR image, related to an area in the Pacific Ocean, showing an interesting pattern which can be possibly related to a surface marine current. The scientific literature shows the capabilities of SAR to map sea currents in ocean regions mainly characterized by large flows [16].

3. Rationale of the Doppler Centroid Anomaly (DCA) Method

Section 3.1 provides readers with a concise overview of the diverse techniques employed to estimate the Doppler Centroid, illustrating the different accuracies achieved through each method. Then, Section 3.2 presents the basic rationale of the DCA technique and its performances.

3.1. Doppler Centroid (DC) Estimation

The DC methodology is grounded in the principles of spectral estimation. Specifically, it hinges upon analyzing the variations in the image spectrum caused by the motion of the observed target, i.e., the sea surface. If the area under observation is stationary, the Doppler shift will be zero. For distributed targets, the azimuth signal is a superposition of many point-target responses. Therefore, one needs to find the central value of the spectrum, i.e., the Doppler Centroid.

DC is estimated using a sliding window throughout the entire focused SAR image. The dimensions of the estimation window are typically set in order to ensure a good balance between spectral and spatial resolution [40].

Many methods have been used for the DC estimation, such as the Energy Balancing (EB) method [55], the Matched-Correlation (MC) method [31] and the Correlation Doppler Centroid Estimator (CDCE) [30]. In particular, in this work, we exploit the CDCE method, which is based on a time-domain approach consisting on the calculation of the correlation function between two image patches separated by $M_{az}$ samples along the azimuth direction. Interested readers may directly refer to [30] to deepen the topic. In particular, Equations (16) and (18) in [30] make explicit the mathematical expression of the correlation function and the estimated DC frequency, respectively.

A Maximum-Likelihood (ML) estimator meeting the Cramér–Rao bound was also discussed in [31]. It is self-evident that an accurate DC estimation is required for more reliable DCA estimation.

Under the white Gaussian assumption for the signal and noise, assuming an area with homogeneous scattering, it was shown in [31] that the standard deviation (STD) of the DC estimate is given by

$${\sigma }_{DC}=a{\displaystyle \frac{PRF}{\sqrt{M}}}$$

(1)

where a is a constant that varies for each of the above-mentioned techniques, $PRF$ is the sensor Pulse Repetition Frequency, and $M=M_{az}\times M_{rg}$ is the number of independent samples in the box used for the estimation (az and rg stand for the azimuth and range coordinates).

Table 3. The a parameter for the different DC estimation approaches. [31].

	EB	MC	CDCE	ML
a	0.3985	0.3407	0.3407	0.2516

shows the values of a in Equation (1) for the different approaches presented in [31].

DC estimates may also be affected by inaccuracies caused by gradients in surface backscatter along the azimuth direction and antenna mis-pointing, which have only been briefly commented on in the literature [16,38]. A more detailed analysis of such phenomena was carried out in [32] referring to an ASAR dataset.

About the DC estimate perturbances due to NRCS azimuthal variations, it must be considered that overwater the local NRCS varies enormously in space and time due to effects such as the weighting of advancing and receding Bragg resonance waves, which depend strongly on the wind direction, specular reflection and wave breaking, as well as tilt and hydro- and aero-dynamic modulations of the scattering elements [38].

In addition, as reported in [55], the backscattering gradient along the azimuth direction within the DC estimation area may introduce a bias into the DC estimation.

Finally, in [17,40], an undesired DC azimuthal component for ENVISAT data was modeled as a sinusoidal contribution taking place at a constant frequency of $31.72$ Hz and subsequently compensated for by using notch filtering.

3.2. DCA Technique

DCA is performed by subtracting from the estimated DC the term corresponding to a “stationary” scene [40,56]. In a stationary scenario or when all targets in the scene are moving at the same speed as Earth’s rotation, the SAR sensor uses the phase shifts measured in the sequence of transmitted pulses while the target is within the real beam of the antenna [15,17]. The compensated DC of the stationary contribution due to Earth rotation is related to the radial component of the sea surface velocity. More specifically, given a target moving with a radial velocity $v_r$, the Doppler Centroid Anomaly $f_{DCA}$ is related to $v_r$ as follows:

$$f_{DCA}(x,r)=f_{DC}(x,r)-f_{DC0}(x,r)={\displaystyle \frac{2}{\lambda }}{v}_r(x,r)$$

(2)

where $f_{DC}$ is the DC measured from the data, $f_{DC0}$ is the DC corresponding to the stationary scene, i.e., the predicted Doppler shift arising from the relative velocity of the satellite and rotating Earth, $\lambda$ is the sensor wavelength, and x and r are the azimuth and range coordinates, respectively.

The radial velocity is the component of the (relative) velocity vector (achieved by subtracting the scene and sensor velocity vectors) along the radar-to-target line of sight (LOS) direction defined by the versor $\widehat{\mathbf{r}}$, i.e., $v_r(x,r)=v(x,r)·\widehat{\mathbf{r}}$. Finally, for each pixel of the SAR image, $v_r$ can be estimated as follows:

$$v_r(x,r)={\displaystyle \frac{\lambda }{2}}{f}_{DCA}(x,r)$$

(3)

Figure 4 shows the block diagram of the DCA methodology used to estimate the $v_r$ map [40,56]. It is worth noting that the use of azimuth spectrum reduction techniques (e.g., Hamming filters [57]) can have a negative impact on DCA estimation since Doppler bandwidth filtering can potentially lead to the removal of a useful part of the signal.

Considering Equation (3), it is straightforward to derive the precision of the radial sea surface velocity estimate as follows:

$${\sigma }_{\Delta v_r}={\displaystyle \frac{\lambda }{2}}{\sigma }_{{\Delta }_{f_D}}={\displaystyle \frac{\lambda }{2}}a{\displaystyle \frac{PRF}{\sqrt{M}}}$$

(4)

Of course, from Equation (4), it is evident that at the X-band, the standard deviation of the radial velocity is better than at the C-band.

However, as earlier outlined the DC estimate is biased [55], i.e.,

$$E\left[f_{DCA}\right]=f_{DCA,true}+f_{DCA,bias}$$

(5)

where $E\left[f_{DCA}\right]$ is the measured DCA value, $f_{DCA,true}$ represents the true (unknown) DCA value, and $f_{DCA,bias}$ is the bias term. Indeed, DC is estimated by searching for the maximum of the azimuth SAR power spectrum, which exhibits a pattern similar to the antenna power one. This circumstance leads to the presence of the biased term, diminishing the precision of the aforementioned methodology [55]. Accordingly, any region with relatively strong or weak intensity away from the center of the radar beam (e.g., at land–water boundaries) can bias the DC estimate. A novel technique based on the ML method was recently introduced in [33] to correct the DC biased estimates using simulated and Gaofen-3 SAR data.

4. Results

This section presents the experimental results achieved by using ENVISAT ASAR and ICEYE data. For our experiments, among the different DC estimators present in the literature and discussed in Section 3.1, DC estimation are carried out by using the method based on the calculation of the azimuth autocorrelation function proposed in [30]. DC estimates are determined over the entire scene using three different sliding windows, corresponding to a coverage on the ground of (about) 1 km × 1 km, 2 km × 2 km and 2.5 km × 2.5 km (see

Table 4. Expected and measured STD for ENVISAT and ICEYE data.

	Window Size (az × rg)	Ground Covered Area [km2]	Expected DC STD Value [Hz]	Measured DC STD Value [Hz]	Error (Exp.-Meas.) [Hz]
ENVISAT	256 × 64	1.3 × 1.3	4.48	5.15	0.67
ICEYE	400 × 400	1.2 × 1.2	4.43	4.62	0.19
ENVISAT	426 × 106	2.1 × 2.1	2.7	3.61	0.91
ICEYE	600 × 600	1.8 × 1.8	2.95	3.87	0.92
ENVISAT	512 × 128	2.5 × 2.5	2.24	3.34	1.1
ICEYE	800 × 800	2.4 × 2.4	2.22	3.56	1.34

).

Figure 5 shows the histograms of the estimated DC STD for ENVISAT ASAR (Figure 5A) and ICEYE (Figure 5B) data considering the three windows reported in Table 4. Of note, for each dataset, the theoretical STD (according to Equation (1)) decreases as the size of the aforementioned DC estimation windows increases. This is evidenced by the fact that the histogram peaks shift towards the left as the estimation window size increases.

Table 4 shows the expected (theoretical) values of the STD, as well as the corresponding measured ones according to the median value of the histograms. In addition, we also show the difference (error) between the expected/measured values of the STD. Table 4 demonstrates that utilizing the proposed sliding window on ICEYE data yields an overall DC behavior that is analogous to that observed in the ENVISAT results in terms of standard deviation. This provides a framework for selecting the pertinent parameters to be employed when applying DCA to ICEYE data.

Furthermore, for each DC estimation window, the spectral resolution (SR) and velocity resolution (VR) values are evaluated. As previously stated in Section 3.1, the DC estimation is conducted using sliding windows, which are selected to ensure an optimal balance between spatial resolution and spectral resolution (SR). The latter is given by the ratio between platform velocity $v_{sensor}$ and the extent of the area along the azimuth direction, corresponding to the selected sliding window [30], i.e.,

$${\delta }_{SR}={\displaystyle \frac{v_{sensor}}{M_{az}{d}_{az}}}$$

(6)

where $M_{az}$ and $d_{az}$ are the number of azimuth samples of the DC estimation window and the azimuth pixel spacing, respectively.

In order to obtain radial velocity resolution (VR), it is straightforward to convert ${\delta }_{SR}$ as follows:

$${\delta }_{VR}={\displaystyle \frac{\lambda }{2}}{\delta }_{SR}={\displaystyle \frac{\lambda }{2}}{\displaystyle \frac{v_{sensor}}{M_{az}{d}_{az}}}$$

(7)

Figure 6 shows the trend of the SR (Figure 6A) and VR (Figure 6B) with respect to the covered ground area along the azimuth direction of the DC estimation window.

It can be appreciated that the SR is inversely proportional with respect to the length of the estimation window along the azimuth direction as expected from the theory. Moreover, ENVISAT data provide always better SR values with respect to ICEYE data. Conversely, the VR values retrieved from ICEYE benefits from the smaller radar wavelength with respect to the C-band one. This evidence encourages the use of such data for DCA-based marine applications.

Finally, according to the DCA methodology in Section 3.2, we derive the radial surface velocity map for ENVISAT and ICEYE data.

Figure 7 shows the result obtained by applying DCA methodology to ENVISAT data presented in Section 3.2. Unlike [41], which adopted a preprocessing step to join up to five frames to obtain a long strip over the area of interest, this work involves a single ENVISAT ASAR data frame acquired over the Ascending orbit already presented in [41].

Figure 7 (on left) shows the SAR amplitude image relevant to the ASAR acquisition collected on 16 January 2009 over the Trieste gulf. This area has a distinctive and persistent wind, “named Bora”, which originates from the mountains on the eastern side of the Adriatic Sea [41]. This specific wind phenomenon can result in significant surface currents as evidenced by the amplitude of the focused SAR images on the left of Figure 7. On the right side of Figure 7, the estimated radial surface velocity ($v_r$) is shown. The DCA is estimated on the SAR image over a sliding tile of 512 (azimuth) by 128 (range) pixels. This corresponds to a square patch on the sea surface of edge $2.5$ km, a spectral resolution of $2.85$ Hz, and a velocity resolution of almost 8 cm/s. The front of the surface current generated by the Bora wind is recognizable. The estimated radial component of the sea surface velocity is within the range of $\pm 1$ m/s; the direction of the sea surface velocity is orthogonal to the flight direction. The red and blue colors (redshift and blueshift) of the estimated sea surface velocity component indicate a motion towards and away from the radar antenna, respectively [41,49].

Figure 8 shows the experimental results relevant to ICEYE data achieved by using sample data available on [54]. The DCA is estimated on the SAR image over a sliding tile of 400 (azimuth) by 400 (range) pixels. This corresponds to a square patch on the sea surface of edge $1.2$ km and a spectral resolution of $6.1$ Hz and a velocity resolution of almost $9.5$ cm/s. Among the available ICEYE data, we select the data described in Section 2.2 because from a visual inspection of the Quick Look image, the sea surface backscattering shows an interesting pattern, which can be possibly related to a surface marine current. Furthermore, being that the area of interest is located in the Pacific Ocean, the scientific literature shows the capabilities of SAR to map the sea currents in ocean regions mainly characterized by large flows [16]. Therefore, since this work is a first demonstration of the application of DCA on ICEYE data, we select a case study that may potentially offer a promising starting point of DCA analysis.

From a preliminary qualitative analysis of the amplitude SAR image, a variation of the backscattering in the marine surface region is well recognizable on the left of Figure 8.

Since, as already stated in Section 2.2, for ICEYE only, Level-1A and Level-1B products are available, the DCA analysis starts from focused SAR data. Following the steps outlined in the block diagram of Figure 4, a map of surface radial marine velocity is generated according to the DCA methodology. It is shown (see the right of Figure 8) that $v_r$ varies in the range of $\pm 1$ m/s.

As for ENVISAT case, red values represent a motion toward the sensor, and the blue ones, that away from the sensor. The blue pattern in Figure 8 near the coastline is due to the azimuthal variations in NRCS at the land–water boundary [32]. This is made more evident in the map shown in Figure 9 showing the NRCS of the ICEYE data: the backscattering gradient is strong due to the presence of an urbanized area near the coast [32]. This produces a bias in the DC estimates, which indeed affects the radial surface velocity measurement.

5. Discussion and Conclusions

In this work, we have shown the preliminary results achieved by analyzing a set of SAR data collected by recently launched ICEYE SAR micro-satellites for the estimation of marine current velocity, using the DCA methodology. In recent years, many private space companies have invested heavily in innovative and low-cost space radar platforms, which can be exploited for this kind of application. Specifically, micro-satellite constellations (100–500 kg [24]) for SAR missions, such as the Surrey Satellite Technology Limited’s (SSTL) NovaSAR [58], the ICEYE-X1, X2, and X3 [45], and the Capella Space’s Capella X-SAR [59] have the potential to provide improved monitoring capabilities to traditional SAR missions on larger platforms, in terms of shorter revisit times, innovative acquisition modes, flexibility and redundancy of the measurements, and lower costs. One of the main benefits of the micro-satellite approach is the ability to operate with many spacecraft at a reasonable cost [60]. In addition, future bistatic space-based SAR missions, such as the European Space Agency’s (ESA) C-band Harmony mission [61] and the Italian Space Agency’s (ASI) X-band PLATiNO-1 mission [62,63], will provide significant added value for Earth observation applications compared to more conventional monostatic SAR systems, particularly in the context of marine monitoring.

Historically, ENVISAT data have been widely used for marine environment monitoring [13,16]. Therefore, since to our knowledge the literature lacks surface marine velocity estimation by using micro-satellite SAR data and particularly ICEYE data, this work is aimed at providing operational indications for this aim when applying the DC estimation method in [30] on micro-satellite X-Band SAR data. Consequently, based on the experience gained with C-Band ENVISAT data, we compare the quality indicator related to theoretical STD [31] and the one estimated on real data in different operative conditions, i.e., different DC estimation windows. A further comparison between ENVISAT and ICEYE data is provided concerning the achievable spectral and velocity resolution with the above-said specific parameters selection. The general aim is to provide to the reader with straightforward parameter selections that allow to achieve comparable performance results to those of the well-evaluated ENVISAT data.

In order to achieve a superior DC estimation (the lowest standard deviation according to [31]), when considering ICEYE data, our experiments indicate that utilizing a DC estimation window size of $400\times 400$ (see Table 4) is optimal.

From the perspective of marine applications, the resolution of the surface radial velocity is a crucial parameter. Therefore, given that the wavelength of the X-Band radar is smaller than that of the C-Band (see Table 2), this results in superior radial VR (see Equation (7)) as evidenced by the results presented in Section 4. The discrepancy in radial velocity resolution between ENVISAT and ICEYE is amplified as the DC estimation window size diminishes. This is a noteworthy phenomenon from a marine perspective, as there is a potential benefit in achieving low radial velocity resolution to ensure compatibility with in situ measurement instruments.

In the event that a particular marine application necessitates an enhanced velocity resolution value, this study also demonstrates that it is feasible to achieve favorable outcomes by extending the DC estimation window while maintaining a reasonable degree in terms of STD.

A more detailed analysis including the application of ocean modeling techniques and/or real data acquired from in situ measurement instruments can provide a quantitative evaluation of the relation between the local ocean dynamic and the information derived from SAR. It is necessary to point out, however, that the radar Doppler frequency is the result of many factors, i.e., the sea current, the wind field, and the sea waves, besides the wave–current and the wave–wave interactions [16,38,64], which require future work in order to be able to separate the various mechanisms concurring to their determination. In conclusion, the experimental results obtained for the recent ICEYE micro-satellite constellation represent a preliminary and encouraging result for future applications.