Transcript Autonomous Navigation system for Low Earth Orbit (LEO

Development of On-board orbit
determination system for Low Earth Orbit
(LEO) satellite Using Global Navigation
Satellite System (GNSS) Receiver
Presented by,
Mr. Sandip Aghav
Department of Electronic Science,
University of Pune,
Pune
Introduction
 Classification of Orbit determination techniques
Orbit Determination Techniques
Ground Based
Doppler
Measurement
Space borne
Laser
Ranging
Sun sensor,
star sensor
GNSS
Measurements
Problem Definition

A method is proposed to use onboard GPS Receiver standalone with a direct measurement of position, velocity and
acceleration data for orbit determination instead of using
differential technique and combined observational technique.

Use of Simplified force models for orbit determination and reduce
the extra Burdon from hardware.

Application Target Area: Remote Sensing Satellites

Range: 500 Km to 1200 Km

Positional Accuracy: <50m and Velocity: 1m/sec
Disadvantages of Ground Based Orbit Determination
Techniques
Methods
Disadvantages
Doppler Shift Measurements
•Tropospheric,
ionospheric and
multipath errors
•Accuracy frequency dependent.
Triangulation Method
•Large
Laser Ranging Technique
•weather
number of Ground stations
and their maintenance
conditions,
•troposphere errors,
•laser system drift,
•station position errors, etc
Common disadvantage:
Data can be collected from satellite only when the satellite is in the
line of sight of the controlling Ground Station.
Why GPS based position determination

Ground station is reduced of several operational
burdens.

All time data collection is possible

The cost of planning experimental observations
is substantially reduced.

Scheduling the ground station operations and
data collection is easier and can be done in
advance as needed.

Autonomous orbit determination possible
Need of Autonomous On-board satellite Navigation
system

On-board collection of data reduces many errors in
the orbit determination.

On Board real time orbit determination is possible.

Data processing can be done on-board.

On-board orbit correction is possible.
Concept of Autonomous Navigation System
Objectives of the proposed work

To design/simulate orbit determination algorithm to be
used on-board for satellite navigation.

To design/simulate GPS data filtering technique to be
placed on-board satellite.

To select a simplified satellite orbit models for on-board
processing.

feasibility of Use of above mentioned software on-board
a satellite to make the navigation autonomous.
Methodology
Orbit Integration
R-K method,
Cowell’s Method
Orbit Estimation
Least Square,
Kalman Filter
Flow chart
START
ACQUIRE A PRIORI STATE AND COVARIANCE ESTIMATES AT t0
SET k=0, i.e Initialization
k=k+1
ACQUIRE A MEMBER OF OBSERVATION VECTOR Yk
PROPAGATE STATE VECTOR TO tk, CALCULATE STATE
TRANSITION MATRIX Φ (tk, tk+1)
CALCULATE EXPEXTED MEASUREMENT Xk AND PARTIAL
DERIVATIVES OF Xk WITH RESPECT TO Xk-1(tk)
PROPAGATE STATE NOISE COVARIANCE MATRIX Q(tk, tk-1)
PROPAGATE ERROR COVARIANCE MATRIX Pk-1(tk)
CALCULATE GAIN MATRIX K
UPDATE X*k-1 TO BECOME kth STATE ESTIMATE
UPDATE ERROR COVARIANCE MATRIX Pk
N
LAST OBSERVATION
?
Y
PROPAGATE Xk(tk) TO ANY TIME OF
THE INTREST
END
Kalman Filter
and
Orbit Estimation
Orbit Estimation Method

Estimation is the calculated approximation of
a result which is usable even if input data
may be incomplete or uncertain.

Uncertain: Model, Measurement,
Perturbations, etc.

Kalman Filter: Orbit Determination
Kalman Filter Basics:

“An optimal recursive data processing algorithm”

An efficient recursive filter that estimates the state
of a linear dynamic system from a series of noisy
measurements.

Very well suited for Real Time Data Filtering.

Estimate the state and the covariance of the state at
any time T, given observations, xT = {x1, …, xT}
Kalman Filter
Mathematical Background
H relates the state to the measurement
z at step k.
R is the measurement noise
covariance.
Kalman Filter: Non Linear System
State Vector Propagation/Update:
 x
x 
r3
y 
2


3  Re   z 2


1

J
5

1

 

2
2

2
r
r







y
x
x
2
 z 
3  Re  
z2
z 

 
1  J 2
3
3  5 r 2
2
r
r











Abovementioned equation of motion is numerically integrated
using Runge-Kutta 4th order method.

Integration is taken over initial to final time.

Results were tested for various time step.
Seed Orbital Elements
Six orbital elements
 semi major axis (a)
 eccentricity (e)
 inclination angle (i)
 longitude of ascending node (Ω)

argument of perigee ()

time of perigee passage ()
As a function of time ‘t’ from standard ground station.

From six orbital elements, ECEF coordinates of the satellites
are calculated.

Position vector r(t) = x(t)i + y(t)j + z(t)k
Position measurements using on-board GPS receiver


Collects data from GPS receiver (RINEX format) as a function of time ‘tc’
Conversion of RINEX format data into position and velocity (ECEF
coordinates).

GPS receiver measurements are in Geodetic co-ordinate system. It needs to
be converted in to geocentric coordinate system.

Again calculate of position, acceleration and velocity vectors by same
method which is used for reference orbit calculation.

Use Extended Kalman filer algorithm to estimate the optimal state vector.

Error calculation and error minimization

Generate new corrected orbit
Simplified force model:

Pure Keplerian and Newtonian model of
Satellite orbit is selected.

Gaussian nature with zero mean nose model
is selected.

J2, J3, J4 Earth Gravity model is selected.

4th Order Runge-Kutta method is selected
with fixed step size.
Kalman filter: Initial Calculations
Table 1: Initial State Vector
1823.2
470.7
7066.7
-6.6
2.9
Table 2: Initial Covariance matrix
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0.01
0
0
0
0
0
0
0.01
0
0
0
0
0
0
0.01
Table 4: System Jacobian matrix
1.5
Table 3: Propagated error Covariance matrix
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
1.027118
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
-8.29E-07
4.91E-08
7.36E-07
0
0
0
4.91E-08
-1.01E-06
1.90E-07
0
0
0
7.36E-07
1.90E-07
1.84E-06
0
0
0
-3
Time Vs Semi-major axis
9.0162
6829.04
Time Vs eccentricity
x 10
Time Vs Inclination Angle
28.474
9.016
9.0159
eccentricity(e)
Semi-major axis(a) in Km
28.474
Inclination Angle(i) in degrees
9.0161
6829.02
6829
6828.98
9.0158
9.0157
9.0156
9.0155
6828.96
9.0154
6828.94
0
2
4
6
8
10
28.474
28.474
28.474
28.474
28.474
28.474
0
2
4
6
8
Time Vs Right Assention of Ascending Node
28.474
10
t sec
4
x 10
35.9118
35.9118
35.9118
35.9118
35.9118
35.9118
35.9118
35.9118
4
6
8
t sec
6
8
10
4
x 10
Time Vs True Anomoly
160
-44.566
-44.567
-44.568
-44.569
-44.57
140
120
100
80
60
40
-44.571
-44.572
10
4
180
True Anomoly(v) in degrees
35.9118
2
2
t sec
-44.565
0
0
4
x 10
Time Vs Argument of perigee
35.9118
Argument of perigee(omg) in degrees
Right Assention of Ascending Node(OMG) in degrees
t sec
28.474
20
0
2
4
6
8
t sec
4
x 10
0
10
0
2
4
6
8
t sec
4
x 10
10
4
x 10
Fig:1: Orbital Elements with Pure Keplerian Equations
-3
Time Vs Semi-major axis
6830
9.5
Time Vs eccentricity
x 10
Time Vs Inclination Angle
28.475
28.47
eccentricity(e)
6827
6826
Inclination Angle(i) in degrees
9
6828
8.5
8
7.5
6825
28.465
28.46
28.455
28.45
28.445
28.44
6824
0
2
4
6
8
t sec
7
10
0
2
6
8
t sec
Time Vs Right Assention of Ascending Node
10
28.435
34
33
32
31
30
29
4
6
t sec
8
10
6
8
10
4
x 10
Time Vs True Anomoly
160
-35
-40
-45
-50
140
120
100
80
60
40
-55
20
-60
0
2
4
x 10
4
180
True Anomoly(v) in degrees
35
2
2
t sec
-30
0
0
4
x 10
Time Vs Argument of perigee
36
28
4
4
x 10
Argument of perigee(omg) in degrees
Right Assention of Ascending Node(OMG) in degrees
Semi-major axis(a) in Km
6829
Fig:2: Orbital Elements with J2 Effect
4
6
t sec
8
10
4
x 10
0
0
2
4
6
t sec
8
10
4
x 10
Fig: Effect of Secular variation J2 ,J3, J4
on orbit geometry
4000
4000
2000
2000
0
0
-2000
-2000
-4000
1
0.5
x 10
4
1
-4000
1
0.5
0
0.5
0
-0.5
(a) Pure Keplerian
x 10
-0.5
-1
4
1
0.5
0
4
x 10
0
-0.5
-1
-0.5
4000
-1
z[km]
2000
0
-2000
-4000
1
0.5
x 10
-1
(b) J2
4
1
0.5
0
0
-0.5
y[Km]
x 10
-0.5
-1
-1
(a) J2,J3,J4
x[Km]
4
4
x 10
Conclusion

Orbit Integration using Kepler’s and Newton’s Laws of
motion.

GPS RINEX data file decoding.

Extended Kalman Filter Representation

Calculation of Jacobian Matrix for system equation.

Calculation of Jacobian Matrix for system equation from
actual measurement (RINEX data file).

Calculation of System Matrix.

Calculation of initial Noise matrix and error covariance
matrix.
Continue
Thank You