Satellite Trajectory and Animal Movement

Our satellite of interest is SARAL, and it can be described by its six orbital parameters, which are the six Keplerian elements: eccentricity, the semimajor axis, inclination, longitude of the ascending node, argument of periapsis, and true anomaly (the definitions of each of these elements are provided in the subsection to the right).  Figure 1 below presents data obtained from  The first column is the line number, which indicates that there are two different ways to present data on SARAL.  In line 1, the values are respectively the satellite number with classification, international designator, epoch, first time derivative of the mean motion divided by two, second time derivative of the mean motion divided by six, BSTAR drag term, the number 0, and element set number with checksum.  Line 2 contains respectively the satellite number, inclination, right ascension of the ascending node, eccentricity, argument of perigee, mean anomaly, and mean motion with revolution number of epoch and checksum.

Fig. 1. Obtained from Contains data on SARAL Parameters in TLE format, which describes the satellite’s orbit.

To create the forward model, it was necessary to collect data on the trajectory of SARAL for one rotation around the Earth, also known as the satellite’s period (which takes about 100.6 minutes), as well as the movement of a false killer whale.  Data on SARAL’s trajectory for one period was manually taken from Live Real Time Satellite Tracking and Predictions at, and a false killer whale’s movement was taken from Movebank, a free online database of animal tracking data hosted by the Max Planck Institute for Orinthology.

A portion of the table generated from is shown in Table 1.  This same data was used when conducting simulations to test the Least Squares and Extended Kalman Filter.  To confirm the values obtained, we collected data from multiple times, and found that our values are reasonable.  The table also includes in its first row the variables we used in association with values of interest, such as λ for latitude.

Table 1. Data obtained from Contains data on SARAL’s latitude, longitude, altitude, and speed for one period.