Several strategies are presented for dealing with various situations where traditional estimation techniques may fail. These methods complement existing solutions by improving estimation robustness or by providing analysis of the estimator performance. Applications include spacecraft attitude and orbit determination problems. The first contribution determines attitude and angular velocity for a spinning spacecraft using only time-spaced unit vector measurements. Several algorithms are developed that are suitable for initialization of an extended Kalman filter so as to prevent filter divergence due to high nonlinearity. A second focus is on orbit determination for multiple satellites encountering highly uncertain environmental perturbations to their orbits and signals. A filter that incorporates estimation of upper atmospheric and ionospheric parameters along with the satellite orbits is shown to be observable. Consider covariance analysis demonstrates the improvement in the orbit solution that results from this additional state estimation. Lastly, the technique of Consider covariance analysis is extended to analyze square-root information filters and smoothers with a wide variety of modeling errors. The new analysis is the most general Consider analysis for square-root information filters, and the only generalized Consider analysis for Rauch-Tung-Striebel square-root information smoothers. It can study filters and smoothers with incorrect noise, incorrect initialization, unmodeled biases or dynamics, erroneous system matrices, and other error classes.