Accurate Estimation Of Vehicle Attitude For Satellite Tracking

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2014 UKSim-AMSS 8th European Modelling Symposium Accurate Estimation of Vehicle Attitude for Satellite Tracking in Ka Band SOTM Salvatore Coco, Gianluca Chisari, Patrizia Di Falco, Enza Iraci and Simona Militello Antonino Laudani Department of Engineering, Roma Tre University Roma, Italy [email protected] DIEEI, University of Catania Catania, Italy [email protected] size and satellite steering are more constraining [5-6]. In this contest, phased array antenna and digital beam-forming based systems are convenient in term of size and performances, but they required the study and the implementation of specific tracking algorithm (acquisition, stabilization and tracking of the satellite) [7]. The satellite tracking/pointing in SOTM land applications is a very critical aspect: differently from aeronautic SOTM systems, the terrestrial ones are influenced by the transmission channel conditions (Line-Of-Sight/LOS or Not-Line-OfSight/NLOS) and by the environmental interferences. Generally, most of tracking methods (step tracking, CONSCAN, etc)[8] are based on the measures of signal power connected to small angular movements (both in azimuth and in elevation) of the receiver antenna; in other words, they use small de-pointings, which allow to find the higher power direction. All these approaches are for this reason known as closed loop tracking methods. Unfortunately, NLOS conditions occur during the usual operation (due to the presence of hindrance as buildings, trees, bridges, tunnels, etc,) this causes the immediate failure of tracking system based only on the power measures of the received signal. This drawback is usual overcome by adding to the closed loop tracking system a pointing system realized with an open loop tracking block (the so called blind pointing) that gives information (sometimes not very accurate) about satellite positions based on the vehicle attitude gathered from gyroscopes, accelerometers, magnetometers and spatial location systems. The closed loop block and the open loop one often interact in order to improve the performance of the overall tracking system. In Ka band, the maximum pointing error admitted is one tenth of degree: this foist on the use of very accurate open loop systems to reduce the application of closed loop approaches [6]. The algorithms presented in this paper are developed ad hoc to improve the performances of open loop block: in these algorithms the information derived from Inertial Measurement System (IMS) and from gyroscopes are connected together by means of tailored filter to obtain a better estimation of the vehicle attitude in order to be used in open loop tracking block. Abstract— The development of Satcom on-the-Move (SOTM) systems for land applications has led to the use higher frequency, with new problems that SOTM aeronautic systems do not own. Above all, the satellite tracking/pointing is a very critical issue in Ka band. For this reason, accurate open loop systems making use of inertial measurement system are fundamental. In order to improve the performance of these open loop systems and making them accurate for Ka band, novel solution in the prediction of the vehicle attitude are studied. In this paper a simple solution is proposed for the enhancement of the performance of inertial measurement system without changing architecture or adding new sensors, by using a tailored filtering and extended Kalman filters. Keywords: SOTM; vehicle attitude modeling; satellite tracking; Inertial Measurement Unit; Kalman Filter I. INTRODUCTION SOTM (Satcom on-the-Move) is an acronym used for satellite mobile communication: SOTM consists of antennas mounted on land platforms, aircraft or ships; these antennas are able to connect and communicate with satellite while the vehicle is on the move [1]. SOTM is a traditional approach in military applications [2]; it is widely used for maritime communication on warship, both for narrow band (Inmarsat and UHF) and broadband (X, Ku and Ka bands) transmissions. Recently, SOTM systems are applied on aircrafts for widespread implementation of broadband and high connectivity communication systems, both for commercial users and governmental authority. The development in antennas for satellite communications leads to use this technology also on land applications, such as military and broadband communications implementations for commercial users (for example internet or TV on the move) [3]. On the other hand, governmental authority for civil protection is most interested on SOTM systems for field control, risk management and emergency intervention for the possibility to establish a connection and to manage communications using land platform on territory destroyed by a natural disaster [4]. The development of SOTM systems for land applications increased the demand for communication band and, consequently, the need of use higher frequency; it also introduced new problems related to land SOTM systems that do not exist in aeronautics applications; indeed, in Ka band the negative effects of the move of the vehicle/platform is increased and, at the same time in this band, the regulatory requirements about beam 978-1-4799-7412-2/14 $31.00 © 2014 IEEE DOI 10.1109/EMS.2014.57 II. BRIEF DESCRIPTION OF SOTM AND VEHICLE ATTITUDE A schematic representation of a SOTM land system is shown in fig. 1. In this picture, the antenna is placed on 409 vehicle top and tracking/pointing sensors are located close to it. If the antenna were placed on the land on a fixed platform, it is possible to steer it to the satellite target settling azimuth (A) and elevation (E) angles and using polarization (V) [9]. In SOTM systems, since geostationary satellites are used, these angles depend only on the platform position on the land after the choice of satellite target. Since antenna is installed on a vehicle, we must settle these angles in the coordinate system of the vehicle itself. In order to do this, it is required to introduce three reference systems to relate the attitude of the vehicle with that of the antenna. The first coordinate system is the local geodesic, named n–frame, that is the Est–Nord–Up frame; its origin is chosen as the platform coordinate system origin projection on the terrestrial geoid. A n–frame vector is expressed with the superscript n, Pn. Platform coordinate system (vehiclefixed), also indicated as body coordinate system (b-frame), is connected with the vehicle and aligned with its longitudinal (forward), lateral (right) and vertical (upward) axis. As described in fig. 1, for sake of simplicity, it begins in the gravity center of the antenna. The third reference system is the beam coordinate system (s–frame); since in SOTM system antenna could be mounted with arbitrary position and direction, only z axis is steering toward satellite target. A vector in s–frame is indicated with Ps [10-13]. Figure 1. Schematic representation of a land SOTM system As stated before, balance matrix charts from n–frame to b–frame, is produced by the three Euler angles, that is by the yaw angle (), the pitch angle (), and the roll angle (); it is represented by the orthogonal matrix shown below: Cnb = ªcψ cϕ + sψ sθ sϕ « sψ cθ =« « cψ sϕ − sψ sθ cϕ ¬ A. Vehicole Attitude The vehicle attitude can be described by the followed equation: C ns ( A, E ,V ) P n = = C (α , β , γ ) ⋅ C (ψ ,θ , ϕ ) P s b where b n n C nb (ψ ,θ , ϕ ) , which − sψ cϕ + cψ sθ sϕ cψ cθ − sψ sϕ − cψ sθ cϕ − cθ sϕ º » (2) sθ » cθ cϕ »¼ where c=cos() and s=sin(), with = ,  or . The kinematic of a solid unit returns (1) ªϕ º ª sin ϕ tan θ «θ » = « cos ϕ « » « «¬ψ »¼ «¬ − sin ϕ sec θ C ns ( A, E ,V ) is the transformation matrix of coordinates or attitude matrix, generated from the three angles (A, E and V), and that represents s–frame orientation compared to n–frame. Similarly, , , and  are the antenna angles stated in the n–frame. When the vehicle is on the move, the three attitude angles of the vehicle change continuously. The tracking system on the SOTM must check constantly the angles , ,  to correct the effects on the antenna pointing produced by the vehicle attitude variations: for this reason, it is possible to steer the antenna toward satellite target with precision only if the vehicle attitude can be accurately estimated. In this way, the problem of antenna attitude estimation is converted in that of the vehicle attitude valuation. 1 − cos ϕ tan θ º ªω x º » «ω » (3) 0 sin ϕ »« y» 0 cos ϕ sec θ »¼ «¬ω z »¼ where x, y, and z are the angular speed of roll, pitch and yaw expressed in the b–frame [9-10]. III. ATTITUDE ESTIMATION BY SENSORS The continuous changes in attitude of a moving vehicle strongly influence the pointing and tracking of the satellite. The estimation of the vehicle attitude could be done by using gyroscopes, accelerometers, magnetometers, and the global positioning system (GPS) [14-16]. A survey of the different possible approaches can be found in [9, 16]. The gyroscopes could be integrated to give angles, but they introduce errors due to gyroscopic bias [17-18]. The accelerometer could aid pitch and roll angles measuring gravity vector if the vehicle is fixed or on the move at constant speed [16, 19]. The attitude based on accelerometer is without deviation, but it is affected by platform accelerations and vibrations. The magnetometers are widely used, but they suffer of large disturbances due to ferromagnetic materials [19-22]. Also the multi-baseline GPS technology is able to set the balance, but it suffers from signals blocks and from low upgrade frequency [18, 20]. In the following a brief recall about these approaches is proposed with advantages and drawbacks. B. Attitude Representation Different representations of the vehicle attitude can be used to describe its kinematic, such as Euler angles, quaternions and Rodrigues’ formula [9-10]. The fundamental problem is that each representation is singular or redundant in a specific application. Euler angles are the basic representation without redundancies, even if they present singularity when inclination angle is about ± 90°. However, this singularity does not appear in the case of land SOTM application. Therefore, Euler angles are the usual choice to define the vehicle attitude. 410 A. Gyroscopes based estimation Gyroscopes are used for the measurement of the angular speed. It is possible to obtain attitude angles by integrating the gyroscopes measurements according to the (3). Unlucky, the error in the measured data can determine high mistakes in the long term attitude estimation. The most common used gyroscope model is [9-10]: ωm = ωt + b + ηω (4) single-baseline GPS is subject to be affected by obstacles such as trees, buildings, overpasses and light poles; in these cases although the satellites are in LOS condition, the two GPS antennas cannot provide the correct yaw angle and speed. For this reason, it is necessary to take care of GPS system work status when using it. The GPS system can also provide two other important variables: the vehicle speed and the drift angle. The drift angle is the difference between the speed and the vehicle directions; then it can be easily obtained when the yaw angle is available. However, during the GPS interruptions, the vehicle yaw and drift will not be available, and the speed of the vehicle will be noisy [9, 23]. b = ηb (5) where m stands for angular speed measured value, t is the actual angular speed, influenced by a slow time-variant bias b and by a measurement noise ; b is the white noise that makes the bias slowly variable.  and b are independent null-mean Gaussian white noise processes, with standard deviation  and b. If one directly integrates the data measurements by gyroscopes, errors in the angles come out and accumulate in time. Consequently, it is not possible to adopt this estimation as it is. D. Estimation by using Magnetometer The magnetometer is a typical example of reference sensor for the measurements of the motion direction. A three axis magnetometer measure directly the direction and intensity of the local magnetic field on the sensor frame; this is performed by the combination of three sensor elements mounted on an orthogonal base. Usually the magnetometer is mounted on the vehicle in proximity of the antenna, then the sensor frame coincides with vehicle frame (b–frame) and consequently a transformation is required to chart to n– frame. The attitude is determined from magnetometer by comparing the measured geomagnetic field with a reference field determined by a suitable model. Unfortunately, the use of magnetometers for attitude determination is limited to regions with a strong and well known field, and must be coupled with other sensors, usually accelerometers to provide sufficiently accurate estimation [19-22]. B. Accelerometers based estimation The accelerometer can provide vehicle attitude if accelerations are considered as disturb and the gravity vector is assumed to be the desired variable to be measured. Taking into account the system transformation (from n– to b–frame), the output of the accelerometer can be modeled as n amb = Cnb ( abody + g ) + ηa where g=[0, 0, -g]t is the gravity vector (g=9.81m/s2), (6) n abody is the vehicle acceleration expressed on the n–frame, and a is a zero-mean Gaussian white noise process with co2 variance matrix Ra = σ a I 3×3 . If we substitute (2) into (6) we achieve: E. Fusion of data from different sensors for accurate attitude estimation In order to fix the above mistakes when using singularly the mentioned sensors, and in order to accurately estimate the vehicle attitude, the best solution is to connect together the elements of these sensors using a suitable algorithm to verify and correct all the attitude data. For this reason, usually the most SOTM employ a reference system (AHRS Attitude and Heading Reference System) [9, 18-20, 22, 23], which usually employs specific algorithms (usually based on Kalman filter [24]) in order to fuse the data from different sensors and to improve the estimation accuracy. On the other hand, the high cost of these devices limits the diffusion of the systems SOTM, and in the case of Ka band the resulting accuracy is often insufficient. For this reason in literature different solution are proposed to develop low cost systems for attitude estimation by using low cost sensors with a limited accuracy, or to improve accuracy by adding multiple sensors with a not negligible hurdle of the architecture [9]. On the contrary, we propose a solution for the enhancement of the accuracy without modify architecture or adding new sensors. b ª amx º ª cos θ sin ϕ º « « » b » b n amb = « amy » = « − sin θ » g + Cn abody + ηa (7) b » « amz ¬ ¼ «¬ − cos θ cos ϕ »¼ If the vehicle is fixed or if it is moving at a constant speed, n abody = 0 and the gravity is the only acceleration source: thus the pitch () and roll () angles can be determined by measuring the gravitational acceleration. This approach has a long-term precision since the attitude errors do not increase with the time. However, the acceleration of the vehicle n abody cannot always be 0. The accelerometer based attitude estimate is inevitably corrupted by accelerations disturbs caused by the vehicle movement [9]. C. GPS based estimation A couple of GPS antennas (also called single-baseline GPS) can be used to estimate with accuracy yaw angle, by using carrier-phase differential technology, in which both GPS antennas capture the same five or more satellites simultaneously. In spite of a common GPS antenna, the IV. ENHANCEMENT OF THE ACCURACY OF ATTITUDE ESTIMATION BY USING KALMAN FILTER The solution proposed uses of the data coming from gyroscopes and AHRS and improves the precision by means 411 V. of extended Kalman filter for non linear dynamic systems and a suitable treatment of the measured signals. The extended Kalman filters, also in adaptive configuration or the so-called unscented Kalman filter, are widely used for this kind of problems and we refer to the wide literature for further discussions on this topic [24-28]. The main novelty herein proposed is instead the adoption of an estimator/filter, which provides the observable data to the Kalman filter block. A block diagram is represented in fig. 2. The IMS senses accelerations (angular and linear) and other quantities and elaborates these (usually by means of In order to verify the proposed approach a campaign of measurements were setup at SELEX-ES laboratory in Catania. In particular, we have used a motion platform (Sarnicola Simulation Systems HEXAD-1000E)[29] to simulate picht/roll/yaw variations and an inertial measurements device (LandMark 30 GPS/AHRS “LN Series)[30], containing gyroscopes, accelerometers, GPS system and magnetic sensors, to perform the measurements, as in the following indicated. A. Description of the Platform The HEXAD-1000E is an electrically actuated sixdegree-of-freedom motion platform capable of carrying a 1000 pound load. It is suitable for a wide variety of equipment test and simulation applications. The platform itself uses the classic "hexapod" or "Stewart" configuration of six electric legs to provide controlled motion in six degrees of freedom. The platform is controlled by a standard PC-type computer running Microsoft Windows XP equipped with custom control software and an Ethernet enabled outboard controller in a separate cabinet. The software provides a means of manual control of the platform and basic performance measurement tools. A variety of separate custom programs are available to produce a variety of motion profiles. For example: the ability to store and replay customer-producer motion profiles; programs to interface to a host computer for real-time motion control; a Fourier Analysis program; Wave Form Generator program and others. By separately controlling the six leg extensions, the platform can produce motion in any combination of the six spatial axes: surge, sway, heave, yaw, pitch and roll. suitable filter) to return attitude estimate (ϕ , θ ,ψ ) . It also is able to provide the raw sensed data and, among these, the gyroscopes measurements ( x, y, z). These latter data are directly used as input of the extended Kalman filter for the dynamic system (2), whereas the attitude estimate (ϕ , θ,ψ ) is given as input at the estimator block of fig. 2. This block uses a temporal series of these data to evaluate a corrected measurement of attitude (ϕ ′, θ ′,ψ ′) to be used as observable data of Kalman filter. B. Description of the Inertial Measurement System The LandMark 30 GPS/AHRS "LN Series" is a digital 6 Degree of Freedom MEMS (Micro-Electro-Mechanical System) GPS-Aided AHRS that provides velocity and attitude information: in addition it also provides GPS heading as well as roll and pitch (degrees) and GPS altitude (meters) outputs enabling position determination from a known starting point. The AHRS 100Hz output is combined with 50 channel C/A code GPS receiver with 4 Hz data update rate. This unit is fully temperature compensated for bias and scale factor and corrections for misalignment and gsensitivity. The available output are gyroscopes’ measurements ( x, y, and z), accelerometers’ Figure 2. Block diagram describing the proposed solution. The output of Kalman is then used as corrected and real estimation of the attitude. The actually implemented formula of the estimator block is measurements N α ′ = ¦ λiα N −i N ¦λ i b b b (amx , amy , amz ) , pitch, roll and yaw angles (8) (estimated by fusion of sensors output by means of suitable algorithms which compensate temperature drift and bias). = 1 . This is C. Tests performed Before executing the tests, a phase of calibration of the platform was necessary in order to exactly individuate the correspondence between the assigned motion profiles and the real movements performed by the platform. In order to do this, several profiles consisting of pure sinusoidal pitch, roll, and yaw separately, and the combinations of roll/pitch, roll/yaw and pitch/yaw were used. These signals were i =1 where  stands for ,  or , and VALIDATION OF THE PROPOSED APPROACH i =1 done in order to filter (it corresponds to a FIR filter) the frequency noise due to the sampling frequency (100 Hz). Usually just N = 2 with = (0.25, 0.75) are good for such purpose. In the test proposed in the validation section these values for have been used. 412 acquired by the inertial measurements device and were then analyzed in frequency and in time domain in order to establish bias of the platform. In addition an accurate procedure based on the efficient CFSO3 optimization algorithm [31] was used to synchronize the assigned signal (pitch, roll and yaw) with the correspondent measured one, returned in output by AHRS. In this way, it was possible to individuate that a ratio of 1.00147 was between measured frequency and the platform assigned one. After this phase two long tests were performed by acquiring the two different pitch/roll/yaw combinations (as indicated in tables I and II) for respectively 10 and 5 minutes. Also these data have been analyzed and synchronized in order to filter noise and to extract the reference waveforms of pitch, roll and yaw correspondent to those established by the platform. The roll/pitch/yaw angles predicted by using these measurements with our approach are compared with those coming from inertial measurement system (IMS). The results of this comparison are summarized in table III and IV and in the fig. 3 and 4. In particular table III and IV report, respectively, the mean square error (MSE) computed with the formula MSE = 1 N ¦ (x estimated i −x real 2 i ) roll error [°] 0.2 0 -0.2 error [°] -0.5 Pitch 0.5 2 0 Roll 1 3 20 Yaw 0.5 4 45 500 600 0 100 200 300 400 500 600 400 500 600 error [°] 0.5 0 -0.5 0 100 200 300 seconds Figure 3. Error in roll, pitch and yaw of the proposed approach (blu) and of IMS (red) for test #1. TABLE III. MEAN SQUARE ERROR ON TEST #1. Proposed approach IMS MSE Pitch 0.001 0.001 MSE Roll 0.009 0.016 MSE Yaw 0.005 0.008 pitch error [°] 0.2 0 -0.2 0 50 100 150 roll 200 250 300 0 50 100 150 yaw 200 250 300 0 50 100 150 seconds 200 250 300 error [°] 0.5 0 -0.5 error [°] 2 0 -2 Initial phase (°) 400 yaw DATA OF TEST #1. Amplitude (°) 300 0 (9) Frequency [Hz] 200 0.5 for estimates achieved with our approach and with IMS. In almost all the examined case the results are better than those coming from IMS. Only in the case of roll for the test #2 there is a small deterioration of the performance. This is, on the other hand, compensated by the improvements in the estimation of the yaw in the same case. It is worth noticing that in all the other case the MSE achieved is lower than 0.1%. In addition it is important to consider that being the measurements performed in laboratory (that is inside a building) the GPS system was deactivated and this influences a lot the performance of the system in the estimation of yaw. The fig. 3 and 4 show the plot of the absolute error in pitch, roll and yaw estimation of our approach (blue) compared with the one obtained by IMS (red). In almost all the case (excluding the estimation of yaw), the error is about 0.1/0.15°, that is in the limit of admissible de-pointing for Ka band, and which can be considered a satisfactory results. TABLE II. 100 pitch N TABLE I. 0 Figure 4. Error in roll, pitch and yaw of the proposed approach (blu) and of IMS (red) for test #2. DATA OF TEST #2. TABLE IV. MEAN SQUARE ERROR ON TEST #2. Frequency [Hz] Amplitude (°) Initial phase (°) Pitch 0.3 5 0 MSE Roll 0.001 0.001 Roll 0.4 4 20 MSE Pitch 0.008 0.002 Yaw 0.5 3 45 MSE Yaw 0.491 0.614 Proposed approach 413 IMS VI. [11] D. Gebre-Egziabher, R. C. Hayward, and J. D. Powell, “Design of multisensor attitude determination systems,” IEEE Trans. Aerosp. Electron. Syst., vol. 40, no. 2, pp. 627–649, Apr. 2004. [12] A. L. Lee and J. H. Kim, “3-dimensional pose sensor algorithm for humanoid robot,” Control Eng. Pract., vol. 18, no. 10, pp. 1173–1182, Oct. 2010. [13] H. Rehbinder and X. Hu, “Drift-free attitude estimation for accelerated rigid bodies,” Automatica, vol. 40, no. 4, pp. 653–659, Apr. 2004. [14] U. Maeder and M. Morari, “Attitude estimation for vehicles with partial inertial measurement,” IEEE Trans. Veh. Technol., vol. 60, no. 4, pp. 1496–1504, May 2011. [15] D. Titterton and J. Weston, Strapdown Inertial Navigation Technology., 2rd ed. London, U.K.: IEE, 2004. [16] J. L. Crassidis, F. L. Markley, and Y. Cheng, “Survey of nonlinear attitude estimation methods,” J. Guid. Control Dyn., vol. 30, no. 1, pp. 12–28, Jan./Feb. 2007. [17] Kang, Chul Woo, and Chan Gook Park. "Euler Angle Based Attitude Estimation Avoiding the Singularity Problem." World Congress. Vol. 18. No. 1. 2011. [18] Y. C. Lai and S. S. Jan, “Attitude estimation based on fusion of gyroscopes and single antenna GPS for small UAVs under the influence of vibration,” GPS Solut., vol. 15, pp. 67–77, Jan. 2011. [19] Kuga, Helio Koiti, and Valdemir Carrara. "Attitude determination with magnetometers and accelerometers to use in satellite simulator." Mathematical Problems in Engineering 2013 . [20] Crassidis, John L., and E. Glenn Lightsey. "Attitude determination using combined gps and three-axis magnetometer data." SPACE TECHNOLOGY-OXFORD- 20.4 (2001): 147-156. [21] Crassidis, John L., Kok-Lam Lai, and Richard R. Harman. "Real-time attitude-independent three-axis magnetometer calibration." Journal of Guidance, Control, and Dynamics 28.1 (2005): 115-120. [22] Han, Songlai, and Jinling Wang. "A novel method to integrate IMU and magnetometers in attitude and heading reference systems." Journal of Navigation 64.04 (2011): 727-738. [23] Rios, Jose A., and Elecia White. "Fusion filter algorithm enhancements for a MEMS GPS/IMU." Crossbow Technology, Inc (2002): 1-12. [24] Lefferts, Ern J., F. Landis Markley, and Malcolm D. Shuster. "Kalman filtering for spacecraft attitude estimation." Journal of Guidance, Control, and Dynamics 5.5 (1982): 417-429. [25] Markley, F. Landis. "Attitude error representations for Kalman filtering." Journal of guidance, control, and dynamics 26.2 (2003): 311-317. [26] Li, Wei, and Jinling Wang. "Effective adaptive Kalman filter for MEMS-IMU/magnetometers integrated attitude and heading reference systems." Journal of Navigation 66.01 (2013): 99-113. [27] J. L. Crassidis and F. L. Markley, “Unscented filtering for spacecraft attitude estimation,” J. Guid. Control Dyn., vol. 26, no. 4, pp. 536– 542, Jul./Aug. 2003. [28] Garcia, R. V., H. K. Kuga, and M. C. Zanardi. "Unscented Kalman filter for spacecraft attitude estimation using quaternions and Euler angles." Journal of Aerospace Engineering 3.3 (2011): 51. [29] Sarnicola HEXAD-100E http://www.sarnicola.com/ [30] Gladiator Technologies http://www.gladiatortechnologies.com/ [31] Antonino Laudani et al., “CFSO3: A New Supervised Swarm-Based Optimization Algorithm,” Mathematical Problems in Engineering, vol. 2013, Article ID 560614, 2013. CONCLUSIONS In this paper a simple solution has been proposed for the enhancement of the accuracy of attitude estimation of terrestrial SOTM system in Ka band. This solution does not modify the architecture of the system and makes use of data from IMS, of an extended Kalman filter and of a block called estimator which operates a sort of filtering of data coming from IMS. The proposed approach has been validated by using laboratory measurements performed by means of a motion platform simulating real conditions and an IMS. Further development will regards the optimization of the filtering of the estimator, the hardware/firmware implementation of the proposed approach and the testing on a real land SOTM system. ACKNOWLEDGEMENTS This work has been partly funded by the “Programma Operativo Nazionale “Ricerca & Competitività” 2007–2013” within the project “PON01_00683 –SIGMA”. The authors would like to thank Barbara Maifreni and Sergio Ronchi for the collaboration during the measurement campaign performed at Selex ES laboratory. REFERENCES [1] Gonzalez, Lino, et al. "How to evaluate SOTM antennas, modems, and architectures." MILCOM 2012. IEEE, 2012. [2] C. Ozbay, W. Teter, D. He, M. J. Sherman, G. L. Schneider, andJ. A. Benjamin, “Design and implementation challenges in Ka/Ku dualband Satcom-on-the-move terminals for military applications,” in Proc. IEEE Mil. Commun. Conf., 2006, pp. 1–7. [3] Sewell, T.F.; Gopal, R., "Implementing SATCOM-on-the-move in the land environment - Relating technical solutions to operational reality," Communications and Information Systems Conference (MilCIS), 2011 Military, vol., no., pp.1,6, 8-10 Nov. 2011 [4] SIGMA Project, “Sistema Integrato di sensori in ambiente cloud per la Gestione Multirischio Avanzata”. http://sigma.cdc.unict.it (retrieved sept. 2014) [5] Weerackody, Vijitha, and Enrique Cuevas. "Current standards and Regulations for Vehicle-Mounted Earth Stations and their impact on performance." MILCOM 2011. IEEE, 2011. [6] Gonzalez, Lino, and R. E. Greel. "A regulatory study and recommendation for EIRP Spectral Density requirement/allowance for SOTM terminals at Ka-Band on WGS system." -MILCOM 2010. IEEE, 2010 [7] Alazab, Mostafa, et al. "Pointing accuracy evaluation of sotm terminals under realistic conditions." 34rd ESA Antenna Workshop on Challenges for Space Antenna Systems. ESTEC, Noordwijk, The Netherlands: ESA. 2012. [8] Weimin Jia; Luyao Hao; Kai Du, "Step tracking algorithm based on finite difference stochastic approximation for SATCOM on-themove," ICEICE 2011, pp.2632,2635, 15-17 April 2011 [9] Zongwei Wu; Minli Yao; Hongguang Ma; Weimin Jia; Fanghao Tian, "Low-Cost Antenna Attitude Estimation by Fusing Inertial Sensing and Two-Antenna GPS for Vehicle-Mounted Satcom-on-the-Move," Vehicular Technology, IEEE Transactions on , vol.62, no.3, pp.1084,1096, March 2013. [10] Jazar, Reza N. Theory of applied robotics. Springer Science+ Business Media, LLC, 2010. 414