Small satellites are becoming increasingly appealing as technology advances and shrinks in both size and cost. The development time for a small satellite is also much less compared to a large satellite. For small satellites to be successful, the navigation systems must be accurate and very often they must be autonomous. For lunar navigation, contact with a ground station is not always available and the system needs to be robust. The extended Kalman filter is a nonlinear estimator that has been used on-board spacecraft for decades. The filter requires linear approximations of the state and measurement models. In the past few years, the unscented Kalman filter has become popular and has been shown to reduce estimation errors. Additionally, the Jacobian matrices do not need to be derived in the unscented Kalman filter implementation. The intent of this research is to explore the capabilities of the extended Kalman filter and the unscented Kalman filter for use as a navigation algorithm on small satellites. The filters are applied to a satellite orbiting the Moon equipped with an inertial measurement unit, a sun sensor, a star camera, and a GPS-like sensor. The position, velocity, and attitude of the spacecraft are estimated along with sensor biases for the IMU accelerometer, IMU gyroscope, sun sensor and star camera. The estimation errors are compared for the extended Kalman filter and the unscented Kalman filter for the position, velocity and attitude. The analysis confirms that both navigation algorithms provided accurate position, velocity and attitude. The IMU gyroscope bias was observable for both filters while only the IMU accelerometer bias was observable with the extended Kalman filter. The sun sensor biases and the star camera biases were unobservable. In general, the unscented Kalman filter performed better than the extended Kalman filter in providing position, velocity, and attitude estimates but requires more computation time. / text

A perfect duality exists between the problem of space-based orbit determination from line-of-sight measurements and the problem of designing an interplanetary autonomous navigation system. Mathematically, these two problems are equivalent. Any method solving the first problem can be used to solve the second one and, vice versa. While the first problem estimates the observed unknown object orbit using the known observer orbit, the second problem does exactly the opposite (e.g. the spacecraft observes a known visible planet). However, in an interplanetary navigation problem, in addition to the measurement noise, the following "perturbations" must be considered: 1) light-time effect due to the finite speed of light and large distances between the observer and planets, and 2) light aberration including special relativistic effect. These two effects require corrections of the initial orbit estimation problems. Because of the duality problem of space-based orbit determination, several new techniques of angles-only Initial Orbit Determination (IOD) are here developed which are capable of using multiple observations and provide higher orbit estimation accuracy and also they are not suffering from some of the limitations associated with the classical and some newly developed methods of initial orbit determination. Using multiple observations make these techniques suitable for the coplanar orbit determination problems which are the case for the spacecraft navigation using visible planets as the solar system planets are all almost coplanar. Four new IOD techniques were developed and Laplace method was modified. For the autonomous navigation purpose, Extended Kalman Filter (EKF) is employed. The output of the IOD algorithm is then used as the initial condition to extended Kalman filter. The two "perturbations" caused by light-time effect and stellar aberration including special relativistic effect also need to be taken into consideration and corrections should be implemented into the extended Kalman filter scheme for the autonomous spacecraft navigation problem.

Solar radiation pressure (SRP) is one of the major non-gravitational forces acting on spacecraft. Acceleration by radiation pressure depends on the radiation flux; on spacecraft shape, attitude, and mass; and on the optical properties of the spacecraft surfaces. Precise modeling of SRP is needed for dynamic satellite orbit determination, space mission design and control, and processing of data from space-based science instruments. During Earth penumbra transitions, sunlight is passing through Earth's lower atmosphere and, in the process, its path, intensity, spectral composition, and shape are significantly affected. This dissertation presents a new method for highly physical SRP modeling in Earth's penumbra called Solar radiation pressure with Oblateness and Lower Atmospheric Absorption, Refraction, and Scattering (SOLAARS). The fundamental geometry and approach mirrors past work, where the solar radiation field is modeled using a number of light rays, rather than treating the Sun as a single point source. This dissertation aims to clarify this approach, simplify its implementation, and model previously overlooked factors. The complex geometries involved in modeling penumbra solar radiation fields are described in a more intuitive and complete way to simplify implementation. Atmospheric effects due to solar radiation passing through the troposphere and stratosphere are modeled, and the results are tabulated to significantly reduce computational cost. SOLAARS includes new, more efficient and accurate approaches to modeling atmospheric effects which allow us to consider the spatial and temporal variability in lower atmospheric conditions. A new approach to modeling the influence of Earth's polar flattening draws on past work to provide a relatively simple but accurate method for this important effect. Previous penumbra SRP models tend to lie at two extremes of complexity and computational cost, and so the significant improvement in accuracy provided by the complex models has often been lost in the interest of convenience and efficiency. This dissertation presents a simple model which provides an accurate alternative to the full, high precision SOLAARS model with reduced complexity and computational cost. This simpler method is based on curve fitting to results of the full SOLAARS model and is called SOLAARS Curve Fit (SOLAARS-CF). Both the high precision SOLAARS model and the simpler SOLAARS-CF model are applied to the Gravity Recovery and Climate Experiment (GRACE) satellites. Modeling results are compared to the sub-nm/s^2 precision GRACE accelerometer data and the results of a traditional penumbra SRP model. These comparisons illustrate the improved accuracy of the SOLAARS and SOLAARS-CF models. A sensitivity analyses for the GRACE orbit illustrates the significance of various input parameters and features of the SOLAARS model on results. The SOLAARS-CF model is applied to a study of penumbra SRP and the Earth flyby anomaly. Beyond the value of its results to the scientific community, this study provides an application example where the computational efficiency of the simplified SOLAARS-CF model is necessary. The Earth flyby anomaly is an open question in orbit determination which has gone unsolved for over 20 years. This study quantifies the influence of penumbra SRP modeling errors on the observed anomalies from the Galileo, Cassini, and Rosetta Earth flybys. The results of this study prove that penumbra SRP is not an explanation for or significant contributor to the Earth flyby anomaly. / Ph. D.

<div>In order to answer the most pressing scientific questions about the two Martian moons, Phobos and Deimos, new remote sensing observations are required. The best way to obtain global high resolution observations of Phobos and Deimos is through dedicated missions to each body that utilize close-proximity orbits, however much of the orbital tradespace is too unstable to realistically or safely operate a mission.</div><div><br></div><div>This thesis explores the dynamics and stability characteristics of trajectories near Deimos. The family of distant retrograde orbits that are inclined out of the Deimos equatorial plane, known as quasi-satellite orbits, are explored extensively. To inform future mission design and CONOPS, the sensitivities and stability of distant retrograde and quasi-satellite orbits are examined in the vicinity of Deimos, and strategies for transferring between DROs are demonstrated. Finally, a method for designing quasi-satellite science orbits is demonstrated for a set of notional instruments and science requirements for a Deimos remote sensing mission.<br></div>

<p dir="ltr">The future of the global economy lies in space. As the economic and scientific benefits from space become more accessible and apparent to the public, the demand for more spacecrafts will only increase. However, simply using the current space architecture to sustain any major activities past low Earth orbit is infeasible. The limiting factor of relying on ground operators via the Deep Space Network will blunt future growth in cislunar space traffic as the bandwidth is insufficient to satisfy the needs of every spacecraft in this domain. For this reason, spacecrafts must begin to operate autonomously or semi-autonomously for operators to be able to manage more missions at a given time. This thesis focuses on the guidance and navigation policies that could help vehicles such as logistical or resupply spacecrafts perform their rendezvous autonomously. It is found that using GNSS signals and Moon-based optical navigation has the potential to help spacecrafts perform autonomous orbit determination in near-Moon trajectories. The estimations are high enough quality such that a stochastic controller can use this navigation solution to confidently guide the spacecraft to a target within a tolerance before proximity operations commence. As the reliance on the ground is shifted away, spacecrafts would be able to operate in greater numbers outside of Earth's lower orbits, greatly assisting humanity's presence in space. </p>