Trajectory estimation studies for long coasting phase of mars mission

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 03 Issue: 11 | Nov-2014, Available @ http://www.ijret.org 557
TRAJECTORY ESTIMATION STUDIES FOR LONG COASTING
PHASE OF MARS MISSION
V. Seshagiri Rao1
, D. Narayana Rao2
1
Satish Dhawan Space Centre SHAR, Sriharikota, India
2
SRM University, Chennai, India
Abstract
At Sriharikota range, configuration of down range tracking network, Real-time tracking and trajectory estimation play a
critical role during a satellite launch for flight safety as well as mission monitoring. Criticality is more when the mission
parameters vary during the launch window to meet the mission requirements. PSLV-C25, the 320 T XL version is intended to
inject the 1337.24 Kg MARS Orbiter into 250 Km * 23500 Km * 19.2 deg Sub-GTO orbit. MARS Orbiter Mission [MOM] is the
first Indian interplanetary mission to orbit a spacecraft around MARS in an elliptical orbit of 360km * 80000 km. This paper
deals with the trajectory estimation and prediction methodologies studied and established at Sriharikota Range for this launch.
The major challenge in the Mars orbiter mission is to configure the Down range network of Telemetry stations in view of large
variation in the Argument of Perigee (AOP) requirement ranging from 2760
to 2890
during injection over the period of launch
window. Requisite AOP facilitates transit of the Spacecraft from Earth to Mars using minimum energy Hohmann transfer. The
change in the requirement of AOP each day in turn demanded a new trajectory with its characteristic changes in long coasting
duration, fourth stage ignition time and subsequent MARS Orbiter injection time into sub-GTO. It is mandatory to capture the
Telemetry data during those critical events to assess the success of the mission. The flight duration was around 3000s and the
coasting duration was 1600s before the ignition of the PS4 stage. Study of configuration of mobile Telemetry stations on Ship-
borne terminals is carried out to cater to visibility requirements of critical events such as fourth stage ignition time and
subsequent MARS Orbiter injection. State vector accuracy studies are carried out for the Ship-borne radar data of the vehicle
during long coasting using Linear Kalman filter. Also a trajectory extrapolation algorithm is designed and studied to provide
extrapolated trajectory during the long coasting period after 3rd
stage burn out which in turn is used to compute and display
trajectory parameters to mission executives and provide antenna-pointing information to the ship-borne terminals. This paper
presents the trajectory estimation methodology proposed, extrapolation techniques adopted and accuracies achieved for the
long coast duration.
Keywords: Mars Orbiter Mission (MOM), Flight Safety, Trajectory estimation, Network simulations, Argument of
Perigee (AOP).
-------------------------------------------------------------------***-------------------------------------------------------------------
1. INTRODUCTION
Configuration of down range tracking network, Real-time
tracking and trajectory estimation play a critical role
during a satellite launch catering to flight safety as well as
mission monitoring[1]. This demands design and
development of a robust Real time system [RTS] consisting
of down range tracking and telemetry network to meet the
functional and performance requirements for launch
operations. To meet the mission requirements at Sriharikota,
the space port of India, there is established a long range
tracking network consisting of 4 C-Band radars and two S-
Band radars. For the MARS orbiter mission, the challenge
was to design a real time system which can provide
continuous data flow during the long coast duration due to
the requirement of higher value of Argument of Perigee
(AOP) and Right Ascension of Ascending Node (RAAN).
The existing network of telemetry stations caters to 1600 sec
of trajectory visibility. To meet the additional real time
requirement of long coasting, two ship-borne terminals were
located at a pre-designated locations in the Pacific Ocean to
capture the fourth stage ignition and spacecraft separation
events. The Day to day variation in the AOP requirement
demanded varying ship positions such that the PS4
ignition and spacecraft separation events are captured. As
standby arrangement, two Brazilian ground stations at
Cuiaba and Alcantara were also hired to acquire these events
in the post-injection period through onboard stored data.
To have continuous real time display during the non
visibility period, a trajectory extrapolation module
[TRAJEX] was designed and developed to compute the
extrapolated trajectory for display to the mission
executives in the Mission Control Centre [MCC]. Accuracy
of the extrapolated trajectory was assessed by comparing it
with filtered state vector of the vehicle tracked by a
precision radar onboard the ship terminal. A C-band radar is
proposed to track the vehicle in coasting phase as well as in
thrusting phase. Trajectory estimation by a Linear Kalman
filter is studied and the filtered state vector is compared
against its theoretical trajectory as well as extrapolated
trajectory to assess its accuracy.

_______________________________________________________________________________________
2. REAL TIME SYSTEM FOR MARS ORBITER
MISSION
Mars Orbiter Mission is ISRO’s first interplanetary mission
with a spacecraft designed to orbit Mars. The launch
vehicle is monitored in real time by the mission executives
to evaluate its performance. Tracking systems and telemetry
systems at the range as well as down the range provide the
trajectory information and vehicle sub-systems’ health for
performance evaluation.
The Real Time system for Mars Orbiter Mission consists of
dual processing chains. Each chain is configured with a
server, which receives data from all the tracking and
telemetry sources, processes and transmits onto the
network[2]. The tracking data and the telemetry data are
acquired at 10 Hz and 2 Hz respectively, processed and
logged. Figure.1 depicts the configuration of range safety
Real time system.
The processing software edits and filters the tracked data.
The telemetry data is converted into engineering units as per
data formats and is scaled . Kalman filter is used to
estimate the state vector from each tracking source.
Trajectory display parameters like Position, velocity and
on-board systems’ performance data are computed. Each
graphic station displays processed data from all tracking
and telemetry sources at each instant. The antenna pointing
information for various tracking and telemetry stations
including Port Blair, Brunei, Biak, Ship-borne terminals
OP1 and OP2 is derived from a single selected source based
on priority logic. The telemetry parameters to be displayed
on flight parameter display are taken from the valid sources.
Fig.1 Block Diagram of Real time system
After an exhaustive study and analysis, extrapolated state
vector from f and g series is used for generating trajectory
and antenna pointing information during the long visibility
gap. On chain–1 INS-based extrapolated state vector is used
and on chain – 2 GAINS-based extrapolated state vector is
used. For Mission Control Centre displays INS-based
extrapolated state vector is used.
3. REAL TIME MISSION REQUIREMENTS
The major challenge encountered in the PSLV C-25 mission
is to provide continuous flow of data to the mission
executives for the long coast duration of 1600s which was
never encountered before. This was mainly due to the
Optimal departure of satellite from EPO [Earth parking
orbit] to TMO [Trans MARS Orbit] requiring large

_______________________________________________________________________________________
Argument of Perigee (AOP) value. PSLV trajectory design
demands long coast duration of the order of 1600s between
third stage burnout to Fourth stage ignition to meet the AOP
constraints.
Due to long coast duration, additional ship-borne terminals
are required for vehicle telemetry. All these constraints
posed a major challenge for the designers to design a robust
real time system which can provide for real time
monitoring. To accomplish the above challenging tasks in
real time and near real time, the following strategies and
services were evolved.
 a). Study of Linear Kalman filter for processing the
ship-borne radar data during coasting phase and
PS4 thrusting phase. Process noise for this period is
computed using the technique of model
compensation using Ideal state estimation.
 b).Development of trajectory extrapolation module
using f and g series. This extrapolated state vector is
used for trajectory computation and antenna pointing
information to tracking stations.
 c). Locating the Ship borne Terminal OP1 and OP2.
4. LINEAR KALMAN FILTER
The well known and widely used Kalman filter is 40 years
young and it has been exploited for many applications
ranging from putting man on the moon to monitoring fuel
efficiency of a car to alert mechanical degradation using a
personal computer. In this chapter the basic equations of
Kalman filter are given with the assumptions used to obtain
them. Given the dynamics, the measurement equations and
other related parameters and measurements up to time TK
the filtering problem is to find the best optimal estimate in
the sense linear, unbiased and minimum variance. A
minimum variance unbiased estimate has the property that
its error variance is less than or equal to that of any other
estimate.
Kalman Filter structure
The predicted state using the State Transition matrix and
previously estimated state
XK = Φ K/K-1 XK/K-1 (1)
Predicted measurement using predicted state and
Observation matrix is
ZK/K-1 = H K XK/K-1 (2)
Covariance of the predicted state is
PK/K-1 = Φk PK-1/K-1 ΦK/K-1
T
+ QK-1 (3)
Kalman gain is computed using predicted state covariance,
measurement noise matrix and Observation matrix
KK = PK/K-1 HK
T
[ HK PK/K-1 HT
+ RK ] – 1
(4)
State estimate from actual measurement is
XK/K = XK/K-1 + KK (ZK - ZK/K-1 ) (5)
Covariance of the estimated state is
PK/K = [ I – KK HK] PK/K-1 (6)
By knowing the initial state X0 and its covariance P0, state
process noise Q, measurement noise R the first four steps
can be executed using the equations 1-4. As soon as
measurements are available last two equations 5 and 6 can
be used to estimate the state and its covariance. The cycle is
repeated for the next measurements.
4.1 Trajectory Extrapolation during Coasting
Phase using f and g Series
Precise determination of the launch vehicle performance in
realtime is through the telemetry data acquired from various
telemetry stations located on the launch site and down the
range. It is useful for monitoring the performance of the
launch vehicle, health of the satellite and also useful in
determining the preliminary orbit of the spacecraft. But for
certain missions there exists certain constraints which result
from imposing physical limitations on trajectory or earth
orbit, where the telemetry ground stations cannot provide
the launch vehicle performance for the entire mission till
injection of the satellite. In order to determine the trajectory
of such missions, f and g series predictor algorithm can be
used to provide the rapid trajectory computation of the
vehicle. Launch vehicle trajectory can be determined based
the expansion of the solution of the Newton’s laws into
Taylor series, known in celestial mechanics as the f and g
power series. These power series can be used to integrate the
equations of the motion of bodies and obtain trajectory from
the initial position and velocity when the body is purely
under the influence of acceleration due to gravity and
atmospheric drag[3].
The particle in the 3D is considered. The equation of the
motion for a particle in 3D is given by the following
expression
R=
𝑥
𝑦
𝑧
(7)
where r is given by the expression R= (𝑥2 + 𝑦2 + 𝑧2)
So, the 3D position of the particle at each time instant can be
written as
𝑟𝑡=
𝑥𝑡
𝑦𝑡
𝑍𝑡
(8)

_______________________________________________________________________________________
The 3D velocity of the particle is given by
V =
𝑑𝑟
𝑑𝑡
= 𝑟 =
𝑥
𝑦
𝑧
=
𝑉𝑋
𝑉𝑌
𝑉𝑍
The acceleration of the particle is given by
a =
𝑑𝑣
𝑑𝑡
= 𝑟 =
𝑥
𝑦
𝑧
=
𝑎 𝑥
𝑎 𝑦
𝑎 𝑧
(9)
The generalized equation of the f and g series is given below
𝒓 𝟏 =f 𝑻 𝒓 𝒐 + + 𝒈 𝑻
𝒅𝒓
𝒅𝒕
(10)
Where r is the position, T = (t1 – t0), f and g are the power
series. If the position and the velocity (1st
derivatives of the
position) components at t0 are known then the 2nd
, 3rd
and 4th
derivatives of the position components at t0 are computed.
Substituting the 2nd
, 3rd
and 4th
derivatives of position
components at t0 the position and velocity components at
time t1 is obtained. This computation is continued till the
end of coasting phase. For the Mars Orbiter Mission, the
coasting period starts at third stage burn out and continues
up to fourth stage ignition. The fourth stage ignition was
around 2005s on the launch day of 05th
November 2013.
State Vector is extrapolated at 10 Hz up to 2005s using f
and g series. Figure.2 gives the real time and extrapolated
trajectory for MARS mission
4.2 Ship – Borne Terminals for Telemetry
Acquisition
Two ship – borne terminals were used in real time to meet
the long coast duration constraint imposed by large AOP
requirement. It was a challenging exercise for the range
team in finalizing the suitable designated locations for the
ships so as to acquire real time information on Fourth stage
ignition and spacecraft separation. Every day the trajectory
was changing to meet the required AOP. Range team
carried out extensive trajectory simulations to determine the
visibility of these ships at various locations, such that ship-
borne radars can acquire and track the vehicle and ship-
borne telemetry can provide the tracking telemetry data of
fourth stage ignition and MOM separation to mission
executives. “All begins well will end well”, this exercise by
range team was fruitful in arriving at vantage locations for
ships based on sea roughness.
Fig 2 Real time and extrapolated trajectory for MARS mission

_______________________________________________________________________________________
5. RESULTS AND DISCUSSION
For study the tracking accuracies of ship-borne radar are
considered as 10 m in Slant range , and 1 milli rad in angles.
Process noise is generated by the authors using the
established technique of model compensation by ideal state
estimation. Tracking data is generated at 10 Hz w.r.t the
ship-borne radar and is processed using Linear Kalman
filter. The errors in the tracking parameters are plotted
against their theoretical bounds are plotted in Figure.3 to
Figure.5. The position error and velocity error are plotted in
Figure.6. The errors in the tracking parameters are within
their theoretical bounds. This deduction amply establishes
the fact that Linear Kalman filter with process noise as
model compensation by ideal state estimation provides
optimal state estimate of the vehicle during long coasting
also. The state vector accuracy in terms of position error
and velocity error are within 10 m and 10 m/sec except at
time of the time of closet approach. This fact proves the
suitability of Linear kalman filter for coast phase
deployment. Also f and g algorithm could provide
extrapolated trajectory for display as well as antenna
pointing information to the ship-borne terminals. This aided
the ship-borne terminals to acquire the critical events such
as PS4 ignition and MOM separation.
Fig 3 Error in Slant range against its 3σ limits
Fig 4 Error in Azimuth against its 3σ limits

_______________________________________________________________________________________
Fig 5 Error in elevation against its 3σ limits
Fig 6 Position and velocity errors for LKF with easurements 1σ noise
6. CONCLUSION
Various mission constraints imposed by the MARS orbiter
mission on the Real time systems were met by incorporating
validated trajectory estimation and extrapolation algorithms.
The Range team also came out with a definitive solution to
locate the ships in pre designated locations. The modules
developed by the range safety team provided vital inputs in
configuring the real time systems for the mission. All the
mission-critical requirements of PSLV-C25/MARS Orbiter
mission were met by Range real time systems[4].
ACKNOWLEDGEMENTS
The authors wish to thank Dr. MYS Prasad, Director SDSC
SHAR for granting permission to publish this paper.
Success in this critical area would not have been possible
but for the dedicated support and unstinted cooperation of
colleagues in Range Operations at SDSC SHAR.

_______________________________________________________________________________________
REFERENCES
[1] Flight Safety Plan for PSLV–C25/Mars Orbiter
Mission by Flight safety team, ISRO-SHAR-04-C-
TR-11-2013
[2] PJC Reddy, P Sunil, R Varaprasad and V Seshagiri
Rao “Reliability Practices for Real Time Systems at
SDSC SHAR”, Presented at ICPAP 2011,
Bangalore, 2011
[3] KM Dinesh babu et al, “Trajectory Extrapolation
using f and g series for MARS orbiter mission”.
ISRO-SHAR-04-C-TR-10-2013
[4] R.Gnanasambanthan et al, “PSLV-C25/MARS
orbiter Mission: Post flight data analysis of tracking
and telemetry data” ISRO-SHAR-03-R-TR-10-2014

Trajectory estimation studies for long coasting phase of mars mission

More Related Content

What's hot (20)

Viewers also liked (10)

Similar to Trajectory estimation studies for long coasting phase of mars mission (20)

More from eSAT Journals (20)

Recently uploaded (20)

Trajectory estimation studies for long coasting phase of mars mission