Presented by, Mr. Sandip Aghav Department of Electronic Science, University of Pune, Pune

1. 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

2. Orbit Determination Techniques Ground Based Space borne Doppler Measurement Laser Ranging Sun sensor, star sensor GNSS Measurements Introduction • Classification of Orbit determination techniques

3. Problem Definition • A method is proposed to use onboard GPS Receiver stand-alone 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

4. Disadvantages of Ground Based Orbit Determination Techniques Common disadvantage: Data can be collected from satellite only when the satellite is in the line of sight of the controlling Ground Station.

5. 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

6. 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.

7. Concept of Autonomous Navigation System

8. 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.

9. Methodology Orbit Integration Orbit Estimation R-K method, Cowell’s Method Least Square, Kalman Filter

10. 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 LAST OBSERVATION ? N Y PROPAGATE Xk(tk) TO ANY TIME OF THE INTREST END

11. Kalman Filter and Orbit Estimation

12. 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

13. 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}

14. Kalman FilterMathematical Background H relates the state to the measurement z at step k. R is the measurement noise covariance.

15. Kalman Filter: Non Linear System

17. State Vector Propagation/Update: • 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.

18. 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

19. 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

20. 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.

21. Kalman filter: Initial Calculations Table 1: Initial State Vector Table 4:System Jacobian matrix Table 2:Initial Covariance matrix Table 3:Propagated error Covariance matrix

22. Fig:1: Orbital Elements with Pure Keplerian Equations Fig:2: Orbital Elements with J2 Effect

23. 4000 4000 2000 2000 0 0 -2000 -2000 -4000 1 -4000 0.5 1 1 0.5 0 4 0.5 1 x 10 0 4 -0.5 x 10 0.5 -0.5 0 4 x 10 -1 0 -1 4000 4 -0.5 x 10 -0.5 -1 -1 2000 0 z[km] -2000 -4000 1 0.5 1 0.5 0 4 x 10 0 4 -0.5 x 10 -0.5 -1 -1 y[Km] x[Km] Fig: Effect of Secular variation J2 ,J3, J4 on orbit geometry (a) Pure Keplerian (b) J2 (a) J2,J3,J4

24. 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

25. Thank You