Poltronieri, Sara (2008) *Determination of the orbit of Titan from Cassini. Altimeter data.* [Tesi di dottorato]

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## Abstract (inglese)

The research presented in this thesis concerns the improvement of Titan’s orbit determination by the

means of the altimetric data captured by the Cassini’s RADAR instrument. The work carries out the

development and implementation in the SOSYA (SOlar SYstem Astrometry) software tool, of a module,

called SOSYA?ART (SOlar SYstem Astrometry?Altimetric Run Tool), that computes bodies’Orbit Determination

by an altimetric type process. Moreover, the Measurements Simulation part of SOSYA has

been enriched the introduction of the module that creates synthetic altimetric measurements at given

observation times set. This research can be divided in four parts.

The first part gives a brief introduction of the Cassini mission and a detailed description of the

RADAR instrument on board the satellite with its features and scientific purposes. RADAR is a multimode

instrument that uses the five beam antenna feed assembly associated with the spacecraft high

gain antenna to transmit and receive electromagnetic radiation according to different operative modes:

imaging mode, altimeter mode, radiometer and scatterometer mode. A precise observation sequence of

observations is performed during each Titan’s encounter: within 25,000 km range active scatterometer

measurements start, then the low resolution altimeter mode is planned between 9000 and 22.500 while the

high resolution altimeter mode is performed between 4000 and 9000 km. The imaging mode is selected

while the spacecraft altitude passes from 4000 km to its minimum value, then outbound observations are

repeated in reverse order.

Basic concepts of the radar theory and signal modulation are presented. Radar data acquisition is a

type of remote sensing technique. These techniques acquire information detecting and measuring changes

that the object causes on the surrounding field (potential, electromagnetic or acoustic field). In fact, radar

altimetry involves bouncing microwave pulses off the surface of the target body and measuring the time

it takes the echo to return to the spacecraft.

The second part is concerned with the fundamentals of orbit determination. Statistical orbit determination

is the set of techniques that allows the estimation of the orbital parameters of a spacecraft

or a celestial body during its motion in the Solar System. It is the problem of determining the best

estimate of the orbital parameters of a spacecraft or a celestial body, whose initial state is unknown,

from observations influenced by random and systematic errors, using a mathematical model that is not

exact. Then we give the detailed development of the geometrical observation model used to determine

the altimetric measurement for the residuals computation at each observation time.

The problem of orbit determination is solved by SOSYA?ART for Titan’s state at epoch, t0, keeping

fixed the trajectory of Cassini spacecraft. Titan’s surface is considered as a sphere of 2575 km radius and

the problem is solved in the reference frame centered on the barycenter of the Saturnian system. At each

observation time, Cassini’s ephemeris and attitude values are read from SPICE’s SPK and CK kernels

files and corrected for light time, while Titan’s states are integrated and interpolated by the means of

SOSYA’s Orbit Simulation capability [2]. Then, as the field of view direction of RADAR beam is strictly

connected to the spacecraft’s attitude, the intersection point with the surface is computed and residual

value is found. The weighted least squares method is applied to fit to the observational data and the set

of adjustable parameters are Titan’s position and velocity.

The third part is dedicated to the altimetric data used and to the flybys during which they were

collected by the Cassini RADAR. The altimetric observation processed in the software tool is the distance,

or rather the range-to-target (RTT), measured from the antenna’s center of phase to the surface of the

target body. The altimetric data have been received from CO.RI.S.T.A. (Consortium for Research on

Advanced Remote Sensing Systems) and they have been collected in 12 of 44 Titan’s flybys, beginning

from the flyby completed on 26th October 2004 (Ta) and up to the one completed on 20th December

2007 (T39). The total number of altimetric measurements processed is 13080 and they are not uniformly

distributed in the 14 flybys: T13 and T25 have the lowest numbers of observations so they are precessed

but not included in results discussion. For each of these encounters we searched for the SPK kernels,

containing Cassini’s ephemerides, and the relative CK kernels, containing the spacecraft attitude matrices.

In order to give a description of the flybys used in the Orbit Determination process, we implemented

a simple SPICE-based routine that reads the ephemeris files and gives three output files containing

respectively: 1) Cassini barycentric states, 2) Titan barycentric states and 3) Cassini states in Titancentered

reference frame. Then by the use of Matlab, the states have been plotted in order to visualize

the entire encounters in two different ways: the first one is the Titan-centric representation of the flyby

while the second one is the orthogonal projection on the xy plane of the Saturn-barycentric passage. For

each available flyby, we give its general description, as duration and the closest approach distance and

time. Moreover we give tables that summarize the distribution over time of the altimetric observation

sequence.

The last part of the work is entirely dedicated to the Orbit Determination process and to the discussion

about the solutions obtained for Titan’s states computed at the batch epochs by SOSYA?ART. Since

the altimetric observation errors were not available, we have used a constant value for the weight of 80

m for all the observations corresponding to the maximum resolution value that the instrument achieves

approximatively. Titan’s flybys T13 and T25 are have been processed but they are not discussed with the

others results obtained because they have very few observations. The mean of all the rms values at first

iteration is 4.703 km and it decreases to the value of 81.67 m at last iteration underlining the goodness

of the solutions for Titan’s states obtained with respect the initial ones. The global mean of residuals

at the first iteration is -340 m and it decreases to the global mean at the last iteration of ?4.296 · 10?4

km, giving the possibility of neglecting the bias estimation. The minimum value of standard deviation

of the estimated position is 294 m, while the maximum value is 5.233 km. The standard deviation of

the velocity ranges from a minimum of 6.322 · 10?2 m/s to a maximum value of 7.2 m/s. Although our

estimation has been made only for Titan and yields particular and local solutions, the results are fully

satisfying. Jacobson [8] obtained 1- uncertainties for Titan of 40 km along R, 150 km along T and 50

km along N. These results come from astrometry, radiometric tracking and spacecraft imaging data and

estimating all the major Saturnian satellites. The accuracy of our solution is limited by the altimetric

measurement errors and by the a priori covariance matrix values applied to the initial conditions of the

natural bodies integrated. In fact we proved that the standard deviation errors effectively decrease by

the use of different a priori variance matrices. In addition, the resulting accuracy of the estimation is due

to the short orbital arcs considered in the orbit determination process over which the measurements are

taken.

Our research can be further extended to other mission scenarios in order to reach a better accuracy in

the orbit determination of natural satellites by the means of altimetric data collected on board spacecrafts

by radar or laser instruments.

New data sets coming from the last part of the nominal mission and from its extended part will

be included in the research and processed by SOSYA?ART. In this way we have a sufficient numbers

of points at which Titan’s state has been computed and this becomes the basis on which starting the

reconstruction of the improved moon’s orbit together with the other types of observation. In order to

compute a global solution all over the entire tour with more accurate estimation of Titan’state, a multi-arc approach would be probably indicated.

SOSYA?ART will be enriched by the consider covariance analysis module testing the impact of the

introduction of the altimetric observations on the state estimation process without having the real data.

The altimetric measurements simulation module will be improved by the introduction of the possibility

of adding noise to the signal.

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