John C. Springmann

Attitude-Independent Magnetometer Calibration with Time-Varying Bias

We present a method for on-orbit, attitude-independent magnetometer calibration that includes the effect of time-varying bias due to electronics on-board a spacecraft. The calibration estimates magnetometer scale factors, mis-alignments, and constant as well as time-varying bias. Time-varying effects are mitigated by including spacecraft telemetry in the measurement model and estimating constant parameters that map the telemetry data to magnetometer bias. The calibration is demonstrated by application to flight data from the Radio Aurora Explorer satellite and significantly reduces the uncertainty of off-the-shelf magnetometers embedded within the satellite and subject to spacecraftgenerated fields. This method simplifies the satellite design process by reducing the need for booms and strict magnetic cleanliness requirements.

Magnetic aspect sensitivity of high‐latitude E region irregularities measured by the RAX‐2 CubeSat

The second Radio Aurora Explorer (RAX-2) satellite has completed more than 30 conjunction experiments with the Advanced Modular Incoherent Scatter Radar chain of incoherent scatter radars in Alaska and Resolute Bay, Canada. Coherent radar echoing occurred during four of the passes: three when E region electron drifts exceeded the ion acoustic speed threshold and one during HF heating of the ionosphere by the High Frequency Active Auroral Research Program heater. In this paper, we present the results for the first three passes associated with backscatter from natural irregularities. We analyze, in detail, the largest drift case because the plasma turbulence was the most intense and because the corresponding ground-to-space bistatic scattering geometry was the most favorable for magnetic aspect sensitivity analysis. A set of data analysis procedures including interference removal, autocorrelation analysis, and the application of a radar beam deconvolution algorithm mapped the distribution of E region backscatter with 3 km resolution in altitude and ∼0.1° in magnetic aspect angle. To our knowledge, these are the highest resolution altitude-resolved magnetic aspect sensitivity measurements made at UHF frequencies in the auroral region. In this paper, we show that despite the large electron drift speed of ∼1500 m/s, the magnetic aspect sensitivity of submeter scale irregularities is much higher than previously reported. The root-mean-square of the aspect angle distribution varied monotonically between 0.5° and 0.1° for the altitude range 100–110 km. Findings from this single but compelling event suggest that submeter scale waves propagating at larger angles from the main E×B flow direction (secondary waves) have parallel electric fields that are too small to contribute to E region electron heating. It is possible that anomalous electron heating in the auroral electrojet can be explained by (a) the dynamics of those submeter scale waves propagating in the E×B direction (primary waves) or (b) the dynamics of longer wavelengths.

Magnetic Sensor Calibration and Residual Dipole Characterization for Application to Nanosatellites

In this paper, we describe the techniques used to calibrate the individual (non-integrated) magnetometers onboard the Radio Aurora Explorer (RAX) satellite and describe a technique to characterize the residual dipole of small satellites. Magnetometer calibration is a critical part of RAX’s magnetic-based attitude determination system. Our technique uses vector knowledge of the local magnetic field, a three-axis Helmholtz cage, and a leastsquares regression. Using this calibration, we can also quantify magnetometer uncertainty. The satellite residual dipole, in addition to affecting the onboard magnetic measurements, can be a dominant disturbance torque for nanosatellites. We present a method to characterize the residual dipole of nanosatellites that uses redundant external magnetic measurements, a least-squares minimization, and does not require large magnetically clean facilities. These techniques are used on RAX but can be extended to other fields of study involving magnetic measurements.

Optimization of Directional Sensor Orientation with Application to Sun Sensing

A method is presented to optimize the orientation of directional sensors and instruments in a vehicle body-fixed frame. Directional dependence is included by creating a uniformly distributed set of directions in the body-fixed frame and formulating the objective as a function of these directions. The method is demonstrated by application to photodiodes for sun sensing, for which the covariance of the sun vector estimate is derived as a function of the photodiode configuration. The measured sun vector angular accuracy is then minimized as a function of the configuration, which enables the most accurate sun sensing with the given hardware. This technique maximizes subsystem performance and provides a design method to replace traditional, iterative design approaches to sensor placement.

Satellite Dynamics Simulator Development Using Lie Group Variational Integrator

Simulation technology is becoming increasingly crucial in the design and optimization of satellites due to the difficulties in testing and verifying system parameters on the ground. Computationally tractable and accurate methods are required in order to test satellite parameters in the complex and dynamic space environment. Although various satellite teams have developed simulation tools, many suffer from inaccurate numerical integrators, resulting in their simulations being of low fidelity for long duration simulations. This paper presents a MATLAB/Simulink-based simulator which includes high fidelity integration and modeling for accurate and relatively quick results. The simulator includes an energy-preserving variational integrator for both translational and rotational dynamics. A Lie Group Variational Integrator is used for the rotational dynamics, which enforces an orthogonality constraint for improved accuracy. This approach requires less computational time relative to other integration methods such as Runge-Kutta method for the same level of integration accuracy. The simulator includes perturbations to the orbital motion and attitude, including Earth oblateness, aerodynamic drag, solar pressure, gravity gradient, and residual dipole. The simulator also includes an advanced hysteresis model for improved modeling of magnetic attitude control systems. Simulation results are provided for a representative small satellite mission in low earth orbit with a passive magnetic stabilization control system. We compare the novel integration and hysteresis techniques to conventional simulators for long duration simulations for a realistic mission scenario.

Adaptive State Estimation for Nonminimum-Phase Systems with Uncertain Harmonic Inputs

We develop a method for obtaining state estimates for a possibly nonminimum-phase system in the presence of an unknown harmonic input. We construct a state estimator based on the system model, and then introduce an estimator input provided by an adaptive feedback model whose goal is to drive the estimated output to the measured output despite the presence of the unknown harmonic input. Using input reconstruction based on a retrospective surrogate cost, we reconstruct the unknown harmonic input. Using the reconstructed input we update the parameters of the adaptive model using recursive least squares identification. We then extend the method to nonlinear systems. The performance of this method is compared with the Kalman filter for linear examples, as well as with the extended and unscented Kalman filters for nonlinear examples.

Investigation of the on-orbit conjunction between the MCubed and HRBE CubeSats

On October 28, 2011 six CubeSats were launched as secondary payloads with the NASA NPP satellite aboard a Delta II rocket. Two of the 1U CubeSats, MCubed and HRBE, became unintentionally stuck together on orbit. The conjunction has been verified through the Doppler characteristics of the periodic telemetry transmissions of both satellites and by the fact that the U.S. Joint Space Operations Center is providing a single two line element set for both objects. The exact cause of the conjunction is unknown, and it is hypothesized that it was caused by the magnets in both satellites. Both CubeSats include a permanent magnet for passive attitude control. We have developed a simulation to determine if magnetic conjunction is possible, and if so, under what range of initial conditions. Using the actual mass and magnetic properties of both satellites, we have shown that magnetic conjunction is possible if the initial translational separation velocity between the CubeSats is sufficiently slow. This study provides useful lessons learned for CubeSat developers as well as a method for further investigation into CubeSat deployment dynamics.