^{1}

^{1}

^{1}

^{*}

^{2}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Some outcomes of a feasibility analysis of a spaceborne bistatic radar mission for soil moisture retrieval are presented in this paper. The study starts from the orbital design of the configuration suitable for soil moisture estimation identified in a previous study. This configuration is refined according to the results of an analysis of the spatial resolution. The paper focuses on the assessment of the spatial coverage

A spaceborne bistatic radar system is defined when antennas for reception and transmission are physically separated and located aboard two spacecraft. The system could be either cooperating (transmitter and receiver designed for the specific bistatic application), or non-cooperating (receiver designed independently of the transmitter) [

As for land applications, Ceraldi

In a previous work [

We point out that investigations on the design of a spaceborne mission implementing a configuration of bistatic radars devoted to specific environmental applications are generally lacking in the literature. Moreover, the literature generally deals with fixed bistatic configurations (

In the present study, the nominal bistatic mission is considered, so that problems such as the orbit and attitude controls are not tackled, thus implicitly assuming that the passive system is periodically controlled in order to maintain the designed bistatic formation.

In Section 2, the findings regarding the bistatic configurations most suitable for SMC retrieval are summarized and the selection of one configuration, based on the evaluation of the spatial resolution, is described. In Section 3, the orbit design approach is depicted, while, in Section 4, the results of the analysis of the spatial coverage are presented and discussed. Section 5 draws the main conclusions.

Bistatic configurations are defined in terms of frequency, polarization, and transmitter-target-receiver relative geometry. This geometry is shown in the left panel of _{i}_{s}_{s}

In [

The findings in [

The range of valuable scattering directions, for a C-band radar, singled out in [_{s}_{s}_{s}

The ground range and azimuth resolutions could be very poor in some bistatic configurations, thus implying a bad radar image quality. For instance, the ground range resolution is critical in specular configuration [

Starting from the relationships found in [_{gr}_{a}

In _{T}_{R}

Starting from the above formulas, and supposing that the satellites’ velocity vectors are directed normally to the incidence plane (_{T}_{R}_{gr}_{gr}^{back}_{a}_{a}^{back}_{s}_{s}_{i}_{i}

By observing _{a}^{back}_{gr}_{gr}^{back}_{gr}_{gr}^{back}_{s}_{s}_{s}

According to the chosen frequency (

We have firstly designed the orbit of the receiver by choosing its observation geometry at the equator based on the requirements for SMC estimation (

We have made a number of assumptions. Firstly, that the bistatic system is non-cooperative, so that orbit, attitude (including yaw-steering) and antenna pointing of the active system are not subordinated to the bistatic acquisition requirements. This is of course a worst case assumption, which aims to use existing radar as source of opportunity. Secondly, the transmitting antenna is right-looking. Moreover, the satellite carrying the receiver (hereafter denoted also as the passive satellite) flies in formation with that carrying the illuminator (the active one), on a parallel orbit, thus establishing a “parallel orbit pendulum” configuration, in which the platforms move along orbits with the same inclination, but different ascending nodes. In principle, also the “leader-follower” configuration, in which the spacecraft fly on the same orbit, but with different crossing times of ascending node, would be possible. However, it does not allow any of the bistatic observation geometries previously selected if a non-cooperative bistatic system and a side-looking illuminator are assumed.

Another hypothesis we have made for the static design of the orbits is that the receiver performs bistatic acquisitions only along the ascending pass, since the crossing of the orbits near the poles makes the transmitter to illuminate out of the footprint of the receiver. Note that an eventual left/right looking capability of the receiver would dramatically change the bistatic angles with respect to the required ones, whereas only a cooperative transmitter with left/right looking capability would enable valuable data acquisition in the descending pass.

The orbit of a spacecraft is described by means of the well-known six Keplerian parameters: semi-major-axis, eccentricity, inclination, right ascension of the ascending node (Ω), perigee argument, and mean anomaly (

The remaining design parameters (Ω and _{s}

_{i}_{s}

By choosing _{s}_{s}_{s}_{RX}) has to be located within the area illuminated by the transmitting antenna (see _{TX}) cannot be less than 10 km. Hence, the best choice for the initial _{s}

The Satellite Tool Kit (available at: _{2} geo-potential harmonic, to maintain a heliosynchronous orbit and assuming negligible the orbital decay (

To produce coverage data, an appropriate software tool, which accounts for spacecraft propagated orbits, yaw-steering maneuvers of both spacecraft, sensors pointing geometry, Earth rotation and estimates the targeted area, has been developed. At each time point of the simulation, whose overall period is 35 days, _{I}_{s}_{s}

ISM1 and WSM reach the highest latitudes (almost 72° in both the geographic hemispheres). In addition, the far range capability of the considered transmitter operating mode limits the latitude range of bistatic acquisitions. As stated when discussing

To quantify the spatial coverage of the bistatic measurements, we have evaluated the ratio between the sum of the areas of bistatic targets and the area of the Earth surface within the covered latitude range. Such a computation sums up all the areas imaged during a complete Envisat cycle of 35 days, including also zones already observed in previous orbits. This result is therefore an estimate of the fractional coverage that does not ensure that every point within a specific latitude range is actually covered by a bistatic acquisition, but that can indicate whether full coverage could be potentially obtained in such a range. The ratio is minimum for ISM4 and is in the order of 65% for WSM, while for ISM1 and ISM2 our evaluation indicates that full coverage might be achieved within 35 days.

Finally, _{x}_{y}_{z}_{y}_{z}

Some outcomes of a coverage analysis of a spaceborne bistatic mission for SMC estimation have been presented. The study has started from the identification of the bistatic configurations suitable for SMC retrieval, in terms of frequency and ideal transmitter-target-receiver relative geometry accomplished in a previous study. An evaluation of the spatial resolution of the bistatic system has been firstly carried out. It has led us to restrict our analysis to observations around nadir and in the backward quadrant. Then, the study has assessed the feasibility of the nominal mission in terms of spatial coverage and duty cycle, assuming a non-cooperative system, with Envisat/ASAR as illuminator.

We have shown that the Wide Swath Mode has the best duty cycle (∼40%). Higher resolution image modes yield acceptable results in terms of this parameter (never less than 12%), considering that, in our hypothesis of fully non-cooperative system, the maximum achievable value is 50%. It has been found, that, for high resolution modes, the minimum and maximum latitudes do not necessarily identify one latitude belt, so that their setting may allow focusing on a particular geographic region, such as mid-latitude areas. In a selected latitude band, it might be possible to achieve full coverage within the Envisat orbit repeat cycle (35 days), while for a larger latitude range, almost covering the entire planet, it is unfeasible.

The improvement of soil moisture retrieval that we have demonstrated, in a previous work, to be achievable through a bistatic mission, may be actually obtained by designing a simple and cheap (even in terms of power requirements) receiver that flies in formation with a standard C-band SAR. Combining the active monostatic with the bistatic measurements can strengthen the contribution of single frequency radar observations in many disciplines needing an evaluation of soil moisture, such as hydrology, agriculture and climate change monitoring.

The methodology based on a study of the sensitivity to a geophysical target parameter of bistatic radars, followed by a system performance analysis can be useful for other applications (e.g., vegetation biomass retrieval) and for future missions. For instance, this approach can provide support to a possible employment of a passive receiver flying in formation with the forthcomong European Space Agency (ESA) Sentinel satellites. In particular, the wide swath capability of the Sentinel-1 C-band SAR is expected to improve the coverage performances of the bistatic mission with respect to that computed for Envisat.

In this section,

Geometry for evaluating the bistatic spatial resolution. T, R and P represent the positions of transmitter, receiver and target, respectively.

By assuming the incidence plane as a reference, let us consider a three-dimensional Cartesian coordinates system in which the (_{T}_{T}_{i}_{s}_{s} scattering angles. Then, we can determine, as function of these parameters, the following ones: _{T}_{i}_{T}_{i}_{s}_{s}_{T}_{s}_{s}

Denoting by _{0}, _{0} and _{0} the versors of the considered Cartesian system, the vectors directed from the transmitting (_{T}_{R}

The transmitter-to-target and receiver-to-target ranges are the modules of _{T}_{R}

Now we can consider the relationship for the ground range resolution proposed in [_{w}_{xy}_{eff}

Accounting for

The application of the Γ_{xy}

By substituting the norm of 2Γ_{xy}_{eff}_{gr}

Considering that the ground range resolution of a conventional monostatic radar is _{w}_{i}_{gr}_{gr}^{back}

It is worth noting that, if _{s}_{gr}_{gr}^{back}_{s}_{i}_{s}_{s}_{gr}_{gr}^{back}_{s}_{s}_{gr}_{gr}^{back}

To derive the azimuth resolution, we have to consider the transmitting (_{T}_{R}_{T}_{R}_{T}_{R}_{T}_{R}

The expression for the azimuth resolution proposed in [_{int} is the time interval during which the target is observed, _{eff}

In (15), _{Tn}_{T}_{T}_{Rn}_{R}_{R}_{Tn}

By replacing (12) in (16) it turns out:

The projection of _{Tn}

The calculation of _{Rn}_{Tn}

By replacing (13) in (19) and by applying the operator that project onto the horizontal plane, it turns out:

By taking into account the relationships (5), (6), (15), (18) and (20), we can determine the projection of the vector 2ω_{eff}

Having assumed that the two spacecraft fly at the same height, we can make the simplifying hypothesis that the velocity vectors have the same amplitude (_{T}_{R}

The final expression for the azimuth resolution of a bistatic system is derived by replacing (22) in (14):

The azimuth resolution of a conventional monostatic SAR is given by:
_{a}_{a}^{back}

This work was realized under ESA/ESTEC contract 19173/05/NL/GLC, “Use of Bistatic Microwave Measurements for Earth Observation”. We thank Dr. N. Floury from ESA for his useful advice.

Left panel: geometric elements that identify the transmitter-target-receiver (Tx-TG-Rx) bistatic configuration. Right panel: sketch of observing configurations suitable for SMC retrieval.

Maps of _{gr}_{gr}^{back}_{a}_{a}^{back}_{i}_{i}_{s}_{s}

Relative position of the satellites at the initial epoch (γ is the yaw-steering angle of the active satellite).

Bistatic observation geometry at the initial time in terms of zenith incidence (_{i}_{s}

Data acquisition (red dots) for a one week scenario considering a passive system acquiring ASAR signal in WSM (upper panel), ISM4 (central panel) and ISM2 (lower panel). Green/blue lines are the Envisat/passive satellite ground tracks.

Baseline length (absolute value) and components in the active satellite orbital reference frame versus the orbital period percentage. One orbit is considered for the sake of figure clarity.

Some parameters of the ASAR illuminator in Image Swath and Wide Swath Modes. Note that both the swath and the ground range resolution refer to the backscattering acquisition; regarding the latter, its value is related to a nominal incidence angle (e.g., 23° for ISM2).

| ||||
---|---|---|---|---|

ISM1 | 105 | 15.0 | 22.9 | 30 |

ISM2 | 105 | 19.2 | 26.7 | 30 |

ISM3 | 82 | 26.0 | 31.4 | 30 |

ISM4 | 88 | 31.0 | 36.3 | 30 |

WSM | 405 | 15 | 37 | 100 |

Selected bistatic configuration (in terms of zenith incidence angle, and zenith and azimuth scattering angles), and orbital parameters at the initial epoch (static design).

zenith incidence angle _{i} |
35 |

zenith scattering angle _{s} |
1 |

azimuth scattering angle _{s} |
180 |

Semi-major-axis [km] | 7,159.48 |

Eccentricity | 0.00115 |

Inclination [deg] | 98.5 |

Perigee argument [deg] | 90 |

Ascending nodes difference (ΔΩ) [deg] | 4.20 |

Mean anomaly difference (Δ |
0.91 |

Coverage statistics and duty cycle, assuming Envisat in different Swath Modes as illuminator. Minimum and maximum acquisition latitudes, and mean width of the bistatic swath (minimum is 10 km) are reported. Note that for ISM1, ISM2 and ISM3, two latitude belts are identified.

| |||||
---|---|---|---|---|---|

13.0 | 12.9 | 11.9 | 21.5 | 40.1 | |

−71.7 | −66.2 | −53.2 | −43.5 | −71.7 | |

−48.5 | −39.6 | −24.2 | 42.9 | 71.6 | |

48.9 | 40.5 | 25.6 | |||

71.7 | 66.2 | 51.3 | |||

39.9 | 37.2 | 29.2 | 24.1 | 39.1 |