Investigating suitable orbits for the Swarm constellation mission – The frozen orbit

This paper proposes a suitable orbit design for the lower pair of ESA's Swarm constellation mission, flying side-by-side in near-polar and circular orbits with a separation of only 1.4° at ascending node. Both orbits are suggested to be frozen orbits to minimize the evolution, and an along-track separation strategy is applied to avoid collision risk. The characteristics of the proposed orbit type are examined through numerical techniques including high-fidelity perturbation models. The prime change from the initial configuration is an along-track separation. The perturbations causing the along-track drift are analyzed by switching on/off certain perturbations. The results indicate that the tesseral harmonics and the atmospheric drag yield dominant effects. The atmospheric drag effect shows a dependence on the local time of the ascending node. From two months of orbit propagation for the altitude 300 km the maximum along-track drift we obtain is about 80 km, which is still within the measurement requirement range. Several maneuver strategies for maintaining the proposed orbit design are suggested. The results analyzed for the proposed orbit design show that collision risk can be avoided by along-track separation within the frozen orbit design. Consequently, this combination is considered as a suitable approach for Swarm's lower pair.     

Effect of Fading on FM Reception with Cochannel Interference

The combined effect of cochannel interference and nonselective Rayleigh fading on the reception of analog FM signals in additive Gaussian noise is analyzed. Rice's click model for the breaking region is used. Analysis in the absence of interference is performed first and the effect of modulation on the click rate is found to be nearly negligible. For the case with cochannel interference the click rate is computed in the absence of modulation. Curves are given for detected signal-to-noise ratio (SNR) versus carrier-to-noise ratio (CNR) with signal-to-interference ratio (SIR) as a parameter and SNR versus SIR with CNR as a parameter. The results agree well with recently published results of a simulation study.     

Suboptimal filter design with pseudomeasurements for targettracking

A suboptimal Kalman filter design method is presented for the problem of tracking a maneuvering target. The design method is essentially based on linear target dynamics and linear-like structured measurements called pseudomeasurements. The pseudomeasurements are obtained by manipulating the original nonlinear measurements algebraically. The resulting filter has computational advantages over other filters with similar performance. Also, a variant of the Berg model is proposed as a target acceleration model under the assumption of a coordinated turn maneuver. The proposed model is consistent with the underlying assumption. Monte Carlo computer simulation results are included to demonstrate the effectiveness of the proposed suboptimal filter associated with the target acceleration model     

Hardware-in-the-loop simulations of GPS-based navigation and control for satellite formation flying

A relative navigation and formation control algorithm for satellite formation flying was developed, and a hardware-in-the-loop (HIL) simulation testbed was established and configured to evaluate this algorithm. The algorithm presented is a relative navigation estimation algorithm using double-difference carrier-phase and single-difference code measurements based on the extended Kalman filter (EKF). In addition, a state-dependent Riccati equation (SDRE) technique is utilized as a nonlinear controller for the formation control problem. The state-dependent coefficient (SDC) form is formulated to include nonlinearities in the relative dynamics. To evaluate the relative navigation and control algorithms developed, a closed-loop HIL testbed is configured. To demonstrate the performance of the testbed, a test formation flying scenario comprising formation acquisition and keeping in a low earth orbit (LEO) has been established. The relative navigation results from the closed-loop simulations show that a 3D RMS of 0.07 m can be achieved for position accuracy. The targeted leader–follower formation flying in the along-track separation of 100 m was maintained with a mean position error of approximately 0.2 m and a standard deviation of 0.9 m. The simulation results show that the HIL testbed is capable of successful demonstration of the GPS-based satellite autonomous formation flying mission.     

Integrated orbit and attitude hardware-in-the-loop simulations for autonomous satellite formation flying

Development and experiment of an integrated orbit and attitude hardware-in-the-loop (HIL) simulator for autonomous satellite formation flying are presented. The integrated simulator system consists of an orbit HIL simulator for orbit determination and control, and an attitude HIL simulator for attitude determination and control. The integrated simulator involves four processes (orbit determination, orbit control, attitude determination, and attitude control), which interact with each other in the same way as actual flight processes do. Orbit determination is conducted by a relative navigation algorithm using double-difference GPS measurements based on the extended Kalman filter (EKF). Orbit control is performed by a state-dependent Riccati equation (SDRE) technique that is utilized as a nonlinear controller for the formation control problem. Attitude is determined from an attitude heading reference system (AHRS) sensor, and a proportional-derivative (PD) feedback controller is used to control the attitude HIL simulator using three momentum wheel assemblies. Integrated orbit and attitude simulations are performed for a formation reconfiguration scenario. By performing the four processes adequately, the desired formation reconfiguration from a baseline of 500–1000 m was achieved with meter-level position error and millimeter-level relative position navigation. This HIL simulation demonstrates the performance of the integrated HIL simulator and the feasibility of the applied algorithms in a real-time environment. Furthermore, the integrated HIL simulator system developed in the current study can be used as a ground-based testing environment to reproduce possible actual satellite formation operations.