The Radio Aurora Explorer (RAX) is a CubeSat that was developed to study space weather in Earth׳s ionosphere. The scientific payload is a bistatic radar system in which an onboard receiver works in cooperation with a ground-based transmitter. Accuracy of the onboard clock is critical for processing the radar measurements. The RAX timing system utilizes commercial off-the-shelf components integrated into custom subsystems. GPS is used to maintain absolute timing accuracy better than 1μs, but the subsystem is not always available due to power constraints, so a method has been developed to correct the onboard clock error without the use of GPS. The clock correction utilizes range measurements extracted from the pulses emitted by the transmitter, and resulting absolute clock accuracies of better than 0.20s with drift of less than 21ns/s have been demonstrated. The RAX timing system and the clock correction algorithm are presented as a reference for other spacecraft designers and are critical for those analyzing RAX data.

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.

A method is presented for the on-orbit calibration of photodiodes for sun sensing in an attitude determination system. The calibration estimates the scale factors and alignment angles of the photodiodes, resulting in a higher attitude determination accuracy than achieved with the preflight calibration parameters. The calibration is accomplished through the simultaneous estimation of the spacecraft attitude and calibration parameters. This approach, as opposed to an attitude-independent method, enables the calibration of an arbitrary number of photodiodes mounted in any orientation on the spacecraft and facilitates the use of an attitude-dependent Earth albedo model. The method is formulated within both an extended Kalman filter and an unscented filter. The filters are demonstrated by application to flight data from the Radio Aurora Explorer satellites and result in an average angular improvement of 10 deg in sun vector measurements with the photodiodes. Attitude determination accuracies of below 1 deg in ...

This paper presents flight results of the attitude determination system (ADS) flown on the Radio Aurora Explorer (RAX) satellites, RAX-1 and RAX-2, which are CubeSats developed to study space weather. The ADS sensors include commercial-off-the-shelf magnetometers, coarse sun sensors (photodiodes), and a MEMs rate gyroscope. A multiplicative extended Kalman filter is used for attitude estimation. On-orbit calibration was developed and applied to compensate for sensor and alignment errors, and attitude determination accuracies of 0.5° 1–σ have been demonstrated on-orbit. The approach of using low-cost sensors in conjunction with on-orbit calibration, which mitigates the need for pre-flight calibration and high-tolerance alignment during spacecraft assembly, reduces the time and cost associated with the subsystem development, and provides a low-cost solution for modest attitude determination requirements. Although the flight results presented in this paper are from a specific mission, the methods used and lessons learned can be used to maximize the performance of the ADS of any vehicle while minimizing the pre-flight calibration and alignment requirements.

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.

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.

An online attitude determination filter is developed for a nano satellite that has no onboard attitude sensors or gyros. Specifically, the attitude of NASA Ames Research Center's O/OREOS, a passively magnetically stabilized 3U CubeSat, is determined using only an estimate of the solar vector obtained from solar panel currents. The filter is based upon the existing multiplicative extended Kalman filter (MEKF) but instead of relying on gyros to drive the motion model, the filter instead incorporates a model of the spacecraft's attitude dynamics in the motion model. An attitude determination accuracy of five degrees is demonstrated, a performance verified using flight data from the University of Michigan's RAX-1. Although the filter was designed for the specific problem of a satellite without gyros or attitude determination it could also be used to provide smoothing of noisy gyro signals or to provide a backup in the event of gyro failures.

We present a method to optimize the orientation of directional sensors and instruments in a vehicle body-fixed frame. This technique can be used in spacecraft design to maximize the performance of directional sensors and instruments. The optimization formulation consists of using the attitude sphere to create directions over which to optimize and deriving an objective function that uses these directions along with their weights. The optimization method is presented and demonstrated by application to photodiodes for spacecraft attitude determination, in which the orientation of the photodiodes are optimized to provide the most accurate sun vector estimates with the given hardware. This technique maximizes subsystem performance and provides a design method to replace traditional, iterative design approaches to sensor placement.

The attitude determination capability of a nano satellite is limited by a lack of traditional high performance attitude sensors, a result of having small budgets for mass and power. Attitude determination can still be performed on a nano satellite with low fidelity sensors, but an accurate model of the spacecraft attitude dynamics is required. The passive magnetic stabilization systems commonly employed in nano satellites are known to introduce uncertainties in the parameters of the attitude dynamics model that cannot easily be resolved prior to launch. In this paper, a batch estimation problem is formulated that simultaneously solves for the attitude of the spacecraft and performs parameter estimation on the magnetic properties of the magnetic materials using only a measurement of the solar vector. The estimation technique is applied to data from NASA Ames Research Center's O/OREOS nano satellite and the University of Michigan's RAX-1 nano satellite, where clear differences are detected between the magnetic properties as measured before launch and those that fit the observed data. To date this is the first known on-orbit verification of the attitude dynamics model of a passively magnetically stabilized spacecraft.

The Radio Aurora Explorer (RAX) is a triple CubeSat that launched on November 19, 2010. RAX was designed to study plasma irregularities in the polar lower ionosphere (80–300km), and is the first CubeSat mission funded by the United States National Science Foundation. The scientific mission requires attitude knowledge within 5° (1−σ), and a custom attitude determination subsystem was developed for the mission. The subsystem utilizes rate gyros, magnetometers, coarse sun sensors, and an extended Kalman filter, and was designed to be a simple, low cost solution to meet the attitude determination requirements. In this paper, we describe the design, implementation, and testing of the RAX attitude determination subsystem, including derivation of the determination requirements, sensor selection, the integrated hardware design, pre-flight sensor calibration, and attitude estimation algorithms. The paper is meant to serve as a resource for others in the small satellite and nanosatellite communities, as well as a critical reference for those analyzing RAX data. Lessons learned from the design and performance of the RAX determination subsystem will be used in future designs of attitude determination systems for small satellites and similar platforms, such as high altitude balloons and autonomous aerial vehicles.

This paper discusses sun sensor calibration and initial results of on-orbit attitude estimation for the Radio Aurora Explorer (RAX) satellite. RAX is a triple Cube Sat that was launched November 19, 2010. RAX utilizes a passive magnetic attitude control system and magnetometers, coarse sun sensors, and a three-axis rate gyroscope for attitude determination. Sample data from the attitude sensors is shown to motivate on-orbit sensor calibration. A batch least-squares algorithm was developed to estimate the maximum current output of the sun sensors (photodiodes), which is a critical parameter for the measured sun vector. The calibration algorithm is one of two focuses of this paper. The second focus is the extended Kalman filter used for attitude estimation. The implementation, tuning, and results of filtering are presented. When PAX is in the sun, the 99% bound on total angular attitude accuracy varies between 3 degrees and 8 degrees; the 68% error bound is between 1.7 degrees and 4 degrees.

The Radio Aurora Explorer CubeSat detected the first radar echoes during the solar storm of March 8, 2012. The 300 s ground‐to‐space bi‐static radar experiment was conducted in conjunction with the Poker Flat Incoherent Scatter Radar in the local morning (∼8 am) over Poker Flat, Alaska. The geomagnetic conditions for theEregion field‐aligned irregularity generation were optimal due to strong (about 1500 m/s)F region ion drifts and sufficient E region ionization (electron densities were ∼2 × 1011 m−3). The corresponding Eregion electric field of ∼80 mV/m was larger than the excitation threshold for the Farley‐Buneman instability. An auto‐correlation analysis resolved, for the first time, the distribution of auroralEregion backscatter with 3 km resolution in altitude and sub‐degree resolution in aspect angle. Moreover, the measured Doppler velocities of the UHF scatter shows the phase speed saturation of the meter‐scale plasma waves. The measured Doppler velocity is in excellent agreement with theCs cos θ formula for auroral E region irregularities.

RAX-2 is a 3U CubeSat that is studying the formation of plasma irregularities in the ionosphere. The primary payload is a UHF radar receiver which is used in conjunction with ground-based incoherent scatter radar stations to characterize the irregularities. RAX is the first CubeSat funded by the United States National Science Foundation’s Small Satellite Program for Space Weather Research. The satellite, launched October 28, 2011, continues the scientific mission started by the RAX-1 CubeSat. This paper discusses the mission and the initial operations of the satellite. After successful checkout, RAX-2 began scientific operations on November 22, 2011. With the exception of an SD card anomaly, the spacecraft has performed well on orbit. 19 radar experiments have been performed, and RAX-2 measurements of radar scatter from the ionospheric irregularities have already provided unprecedented detail for characterization and improved understanding of the formation of the irregularities.

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.

The second Radio Aurora Explorer satellite, RAX-2, is a triple CubeSat studying the formation of plasma irregularities in Earth’s ionosphere. The spacecraft was developed jointly by SRI International and the University of Michigan, and it is the first satellite funded by the National Science Foundation. RAX-2 launched October 28, 2011 and is currently operating on orbit. RAX uses a bistatic radar configuration to study the ionospheric irregularities: a ground-based incoherent scatter radar station illuminates the irregularities, and the RAX-based radar receiver measures radar scatter from the irregularities. RAX has successfully measured radar scatter from the ionospheric irregularities, providing unprecedented auroral region measurements. In this paper, we review the mission goals and satellite development, and discuss initial flight results from the mission. This includes a summary of results from the first detection of radar scatter, power system performance, spacecraft attitude dynamics, global UHF noise measurements, and data download strategies and results of partnering with the amateur radio community.

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.

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.