Babu R, Prasanta Mula and S. C. Ratnakara, A S Ganeshan ISRO Satellite Centre (ISAC) , Bangalore, India Abstract- Indian region...

#### Babu R, Prasanta Mula and S. C. Ratnakara, A S Ganeshan ISRO Satellite Centre (ISAC) , Bangalore, India

Abstract-Indian regional Navigation Satellite system (IRNSS) is
going to be an independent, indigenous navigation satellite
system fully controlled by India, planned by ISRO. A system was
designed of regional navigation satellite constellation, as an
alternate to GPS constellation, for providing space based
navigation support to various land, sea and air navigation users
over the Indian region. The proposed IRNSS constellation
consists of 7 satellites (3 in GEO and 4 in inclined GSO with 29
deg inclination). The continuous visibility of GEO and GSO
satellites for near-equator regions provides a promising
alternative for regional navigation. The Signal In Space (SIS)
broadcasts satellite ephemeris in quasi keplarian elements and
satellite clock coefficients which forms the primary navigation
parameters generated from navigation software located at INC
(ISRO Navigation Centre), bylalu, India. The determination of
these parameters is performed by two types of technique, batch
least square (BLS) and Extended Kalman Filter (EKF). A
combination of these strategies is being adopted in IRNSS to
broadcast the primary navigation parameters. The BLS based
navigation parameters are generated with longer validity period
whereas the EKF based outputs are generated with short period
validity. The main reason for this combination strategy is to limit
the outage duration of satellite as minimal as possible under all
circumstances. The events are triggered depending upon the
anomalies that occur in SIS, mainly due to onboard frequency
jumps and station keeping operations. The most facilitated
important fact is that the IRNSS satellite are continuously visible
to monitoring and control centre and thus able to uplink the
updated navigation parameters as and when required based on
the deviation from User Equivalent Range Error (UERE) as
monitored through SIS from IRNSS Reference station’s Line of
sight ( LOS).
In this paper we have discussed the combination strategy and
how user equivalent range error is mitigated during anomalous
events and results.

Keywords: Batch Least Square (BLS), Extended Kalman Filter (EKF), Signal in Space (SIS), Line of Sight (LOS),User Equivalent Range Error ( UERE)

Keywords: Batch Least Square (BLS), Extended Kalman Filter (EKF), Signal in Space (SIS), Line of Sight (LOS),User Equivalent Range Error ( UERE)

**GJSFR: Global Journals Blog**## I. INTRODUCTION

The IRNSS (Indian Regional Navigation Satellite
System) is an initiative to build an independent Regional
Navigation Satellite System based on a constellation of 3 Geo-
stationary (GEO) and 4 Geo-synchronous (GSO) satellites.
The first satellite (IRNSS-1A) was launched in July 2013 and
the second (IRNSS-1B) on April 4, 2014, the third satellite
IRNSS-1C on 16 October 2014. Currently three satellites are
in space, IRNSS-1A (longitude crossing 55degree, inclination
29degree, Right Ascending Node (RAAN) 130degree),
IRNSS-1B (longitude crossing 55degree, inclination 29degree and RAAN 310 degree) and IRNSS-1C (longitude crossing 83
degree with inclination 5degree). The 8 (IRIMS (IRNSS
Range and Integrity Monitoring Station) are currently
operational. The below plot shows the orbit determination
IRIMS stations and IRNSS satellites location.

The IRNSS Network Timing Facility (IRNWT) maintains the precise and stable IRNSS time using an ensemble of atomic clocks that includes Hydrogen Master and Caesium clocks. It will be aiding the user position through 7 IRNSS satellites. The IRIMS (IRNSS Range and Monitoring Stations) continuously provides the one-way ranging of the IRNSS satellites to estimate and monitor the satellite position and satellite clock offset with respect to IRNSS system time. Precise Orbit determination for Geostationary and synchronous satellites from observations remains a key operation for the emerging regional navigation satellite system due to its minimal relative motion of the satellite with ground reference stations. The challenge is the ability to accurately determine the current position and velocity of the satellite along with onboard clock offset. These estimated state parameters (Ephemeris, clock bias and drift) needs to be predicted for the future which is then broadcast to the users to provide independent navigation solution in the service area of IRNSS, primarily within Indian Land mass. The following figure shows IRNSS satellites location and all the satellite beam points at 85degree longitude with 5 degree latitude.

The IRNSS Network Timing Facility (IRNWT) maintains the precise and stable IRNSS time using an ensemble of atomic clocks that includes Hydrogen Master and Caesium clocks. It will be aiding the user position through 7 IRNSS satellites. The IRIMS (IRNSS Range and Monitoring Stations) continuously provides the one-way ranging of the IRNSS satellites to estimate and monitor the satellite position and satellite clock offset with respect to IRNSS system time. Precise Orbit determination for Geostationary and synchronous satellites from observations remains a key operation for the emerging regional navigation satellite system due to its minimal relative motion of the satellite with ground reference stations. The challenge is the ability to accurately determine the current position and velocity of the satellite along with onboard clock offset. These estimated state parameters (Ephemeris, clock bias and drift) needs to be predicted for the future which is then broadcast to the users to provide independent navigation solution in the service area of IRNSS, primarily within Indian Land mass. The following figure shows IRNSS satellites location and all the satellite beam points at 85degree longitude with 5 degree latitude.

All useful orbit determination methods produce orbit
estimates, and all orbit estimates have estimation error
because of input variation. Hence what methods can obtain
best solution? There are several choices to make from
available orbit determination methods. Should we prefer
sequential methods to batch methods? One way to improve
Orbit Determination (OD) of IRNSS satellites is to make use
of a hybrid estimation techniques, this has been accomplished
by applying the both estimation. This strategy provided
substantial improvements in accuracy and convergence over
the traditional techniques used in the existing orbit
determination techniques. This technique is validated with real
measurements and operational at INC.

## II. ORBIT DETERMINATION METHOD

Two types of technique are used in IRNSS
Navigation software for generation of primary parameter
estimation. Though both these methods BLS and EKF are
commonly used estimation process, here based on the
occurrence of events a combination strategy is used were one
compliments the other with inputs. In this section we discuss
about both the estimation technique employed in IRNSS.

In BLS, we use multi days of data to estimate the
parameter. The estimation parameters includes receiver clock
coefficients of all reference stations, satellite state vectors,
solar radiation pressure coefficients and satellite clock
coefficients with respect to IRNSS system time. During the
signal travel from transmitter to receiver, the measurement
undergoes different error sources. After modeling and removal
of medium errors, the main error contribution remains in each
LOS is the error due to onboard and receiver clock. The
separation of these errors from each LOS, mainly clock and
orbit separation becomes cumbersome in simultaneous
estimation. Thus differencing techniques were adopted to
overcome.

The differencing techniques used to estimate
receiver clock, satellite clock and satellite state vectors along
with SRP coefficients, by holding and estimating the other in
each of the process. By this method simultaneous estimation is
avoided and hence estimation of all parameters is accurate in
separation of errors.

But the limitation of the BLS comes in the event of
clock jump, since the measurement data used for estimation
contains the onboard clock frequency variation as shown in
Figure[8-10]. Then the resultant satellite clock coefficients if
obtained in this method will be inaccurate, also if parameters
uplinked the user solution will also be erroneous.

In such events the new set of uplink parameters is
estimated using EKF, since the sequential process depends
only on the current measurements. Thus the clock coefficients
obtained from this estimation process is more realistic than the
other method. In order to compute the updated clock biases
state vector is held fixed and used from previous estimate of
BLS. Under nominal conditions both these methods yields
results, and at every instant EKF results were compared with
BLS estimates and if found to be exceeding certain threshold
EKF is reinitialized. Thus EKF is controlled and aligned with
BLS, also the uplink parameters are generated and
broadcasted with frequent update intervals and validity. The
process noise and measurement noises [10] were obtained
from adaption process. The limitations of the EKF based
estimated solution is assumed to be poorer for long duration
propagation because of the slow varying relative motion
between the satellite and receiver geometry. Thus the
broadcast parameter from EKF solutions is valid for shorter
duration of about 900seconds and thus gets updated frequently
during such onboard satellite clock anomaly event occurrence.

## III. PROPAGATION MODEL

The two estimation techniques uses two types of
numerical integration techniques namely Runge Kutta 4th
order (RK4) and Adams-Bashforth-Moulton Method 12th
order (ABM) method. In EKF for satellite state vector
prediction RK4 is employed for simplicity and complexity
reduction for real time usage. Whereas BLS uses ABM
technique for long duration propagation under normal
behaviour of range measurements.

The satellite is usually assumed to be influenced by a
variety of external forces, including gravity, solar radiation
pressure, third-body perturbations, Earth tidal effects, and
general relativity in addition to satellite propulsive
manoeuvres. The complex description of these forces results
in a highly nonlinear set of dynamical equations of motion.
The IRNSS orbits are propagated by numerically integrating,
gravitational accelerations due to the Earth, Moon, Sun and
other solar planets, together with the accelerations due to solar
pressure. The gravity model used is of the order of 20x20
EGM-2008 model. The predicted positions of the Earth,
Moon, Sun and other planets such as Venus and Jupiter are
from JPL DE405 ephemeris. The solar pressure model used is
(SPIRS) Solar pressure model for Indian regional satellite.
The figure [3] shows the typical acceleration acting on the
IRNSS satellites. The IRNSS satellites orientation is
maintained in such a way that the sun is always contained in
positive yaw and negative roll plane. The other important
mission aspect is that the satellite under goes flipping twice a
day and positive roll direction of the satellite never allowed to
facing the sun as atomic clocks are mounted in the positive roll panel. The following figure [4] represents the IRNSS
spacecraft body axis definition.

## IV. RESIDUE COMPUTATION

Estimation technique is based on minimization of
residue by iterative update of state parameters. In orbit
determination method the residue is difference between
observed range measurement and computed range
measurements. To compute range residue to the computed
range sum of all measurement error models are added. The
error includes station displacement, sagnac effect, relativity
effect, Ionospheric delay, troposphere delay, receiver and
satellite clock error, satellite and receiver hardware delay,
phase centre offsets. Firstly the smoothened ionospheric free
measurements are obtained from observed range using code
carrier smoothening technique with dual frequency (L5 and S)
measurement combination and ambiguity resolution. The
accuracy of the estimation technique depends upon the
accuracy of measurement error model and quality of the
measurements. Typical range residues from all IRNSS
reference stations are shown in figure [5-7].

## V. STATION KEEPING OPERATION AND ONBOARD ANOMALIES

The broadcast navigation parameters becomes
obsolete during sudden variation in the measurements occurs.
In the event of pre-defined station keeping operations and
when sudden anomalous behaviour of the clock jumps occurs
such as phase or frequency jump happens, the user gets
affected due to large measurement variations. On such
occasions the user has to receive updated navigation
parameters. Like all other satellites, the IRNSS satellite has to
be maintained in the window of 0.1 deg Equatorial from its
desired longitude location. Since IRNSS works on minimum
satellite constellation design (7satellites), outage of single
satellite will increase the desired Dilution of Precision (DOP).
These make the ground operations challenging in
minimisation of the outage duration. In the first part of the
section describes the station keeping (SK) operations and
estimation strategy. For IRNSS satellites the station keeping
operations were carried out regularly within 30-45 days
interval. These are East west station keeping (EWSK)
operations with very small delta-V corrections. Thus during
EWSK the user may experience loss of SIS due to attitude
reorientations for SK operations.

In the event of SK operation as soon as the satellite
reoriented towards the earth view, in order to limit outage
duration as minimal as possible, new set of uplink parameters
are uploaded just before the SK operations with appropriate
delta-v corrections applied on earlier BLS estimates and on
the propagated state vectors. And when the signal emerges
back after re-orientation, the EKF estimates the satellite state
vectors holding clock parameters using the received
measurements from all reference receivers. Thus the outage is
minimised and frequent uplink of navigation parameters are
being done with short validity period of about ~900seconds,
with Issue of data (IODE) varying between 160 and 255. The
uplink process continues in this mode until BLS accumulates
sufficient hours of data post SK operations. Then after
reception and accumulation of sufficient data BLS estimates
updated satellite state vectors holding clock parameters. From
there onwards the uplink of navigation parameters will be
based on BLS with two hours validity and the process
continues and becomes normal until multi days data available
for all parameter estimation. The following graphs show the
normal user equivalent range error during normal and post SK
operations for IRNSS satellites.

The second part of the section deals with anomalous
behaviour of onboard clock. The SIS encounters sudden
change in range measurement variation in all LOS that
emerges from a satellite, called satellite clock jump (in
frequency or phase). In the event of this scenario the user
using the predicted broadcast clock coefficients may not be
valid yielding error in user solution and increased user
equivalent range error [11]. Several such phenomenons had
occurred in operational IRNSS satellites. In IRNSS through
telemetry, the relative performance of the onboard clock
(primary and secondary) is monitored through phase meter
data. The following figures [8-10] shows such frequency
variations from relative phase meter data of onboard atomic
clock. Through Ground reference receiver measurements the
jumps of the onboard were identified whether the jump is on
primary or secondary. The figure [8-10] shows occurrence of
jump on primary clock and its effect on UERE from one of the
IRNSS reference station (IRIMS at Bangalore 13deg N 77deg
E location)

In the below figure [8] shown the relative clock jump
variation between onboard RAFS for IRNSS-1C (SAT 03)

The below figure [9] shown the relative clock jump
variation between onboard RAFS for IRNSS-1B (SAT 02), In
this satellite we can observe a phenomenon such as the drift
variation in the clock was increasing with time.

In the below figure [10] shown the relative clock
jump variation between onboard RAFS for IRNSS-1A (SAT 01)

## VI. IRIMS BANGALORE UERE

This section deals with accuracy of the IRNSS SIS.
To access the accuracy of the IRNSS broadcast parameters
measurements from one of the reference receivers (IRIMS
Bangalore) were used for demonstration. These are dual
frequency receivers at precise surveyed locations. The LOS
measurement was treated for various measurement errors as
discussed earlier. The residual error due to broadcast signals is
plotted in figures [11-13] over a typical day in nominal
conditions and when there is no occurrence of any events. The
estimated solution (satellite state vectors and onboard clock
coefficients) is based on BLS with previous multi day’s data.

Currently, three satellites (IRNSS-1A, IRNSS-1B and IRNSS-1C)

The below figure shows the UERE variation along IRIMS
Bangalore before and after EWSK operations on IRNSS-1A
satellite. The satellite undergone SK operations after 11 Hrs.
The uplink parameters were EKF based estimates with short
period validity.

The below plots shows typical onboard primary clock jump
occurrence on IRNSS-1A . The Jump was occurred at about
3.6 Hrs. The UERE of IRIMS Bangalore shows the effect
of frequency jump , resulting in deviation and sharp increase
in UERE. The detection and uplink of new parameters were
done from 6Hrs onwards. The updated clock coefficients were
based on EKF estimates with short period validity

## VII. SUMMARY

In the present paper two different Orbit
determination methods were employed in determining the
state parameters such as satellite state vectors and onboard
clock parameters for IRNSS satellites. The Batch least square
techniques is unfavourable during the occurrence and sudden
inclusion of clock jump events. On the other hand EKF
techniques under considered circumstances yields good
solution but cannot be used for longer duration as the
propagation error increases. Thus combinations of both the
estimation strategies is employed in IRNSS navigation
software, thus overcomes and mitigates the anomalous event
limiting the user equivalent range error within certain
acceptable limit. We have discussed both the technique and its
utilization with the results from operational satellites.
Continuous efforts were being made to reduce the SIS error
both in modelling, measurement handling and in improved
strategy adaptation.

**ACKNOWLEDGMENT**This work was supported by IRNSS projects at SNG lab. Wish to acknowledge all the Space Navigation Group members.

## REFERENCES RÈFÈRENCES REFERENCIAS

1. [1] IRNSS Comprehensive Review Document , ISRO-ISAC-IRNSS-RR-
0992.

2.Athans M. and Falb P. L, Optimal Contro, Mcraw-Hill Book Co., Inc.,
New York, 1966.

3. Gelb A., 1966. Applied Optimal Estimation, Mcraw-Hill Book Co.,
Inc., New York.

4. Jerome R. Vetter, “Fifty Years of Orbit Determination: Development
of Modern Astrodynamics Method”, Johns Hopkins APL Technical
Digest ,2007, Vol 27, No. 3.

5. James R Wright, Optimal Orbit Determination, 2002, Analytical
Graphics, Inc. Printed by the American Astronautical Society.

6. Kalman, R. E., A New Approach to Linear Filtering and Prediction
Problems, Journal of Basic Engineering, 1960, Vol 82, pp-35-45.

7. Price C. F., An Analysis of the Divergence Problem in the Kalman
Filter, IEEE Trans on Automatic Control, 1968, Vol. AC -13, No. 6,
pp. 699-702.

8. Psiaki, M., Backward smoothing Extended Kalman Filter,Journal of
Guidance control and Dynamics, sept-Oct 2005, Vol. 28.

9. Sherma S, Non-Mean-Square Error Criteria, Trans. IRE Prof. Group
on Information Theory, IT-4,1958, pp-585-589.

10. A. H. Mohamed, K. P. Schwarz, Adaptive Kalman Filtering for
INS/GPS, Journal of Geodesy (1999) 73: 193-203.

11. Kavitha S Prasanta Mula Babu R Ratnakara S C Ganeshan A S,
“Adaptive Extended Kalman Filter for Orbit Estimation of GEO
Satellites” Journal of Environment and Earth Science, Vol.5, No.3,
2015.

**Published by Global Journals****© Global Journals Official Blog 2016**