Estimators are critical to modern society and are present everywhere from automobile cruise control systems to satellite attitude determination and control. Ensuring that estimators produce reliable, trustworthy estimates is key to keeping users safe and systems functioning correctly. While many systems and metrics have been proposed to ensure estimator reliability, these come with disadvantages such as requiring time-consuming Monte Carlo simulations or encapsulating poorly performing estimators rather than addressing core issues. This dissertation examines the various factors that affect estimator reliability, specifically for Kalman Filter variants, and presents a new trustworthiness metric that quantifies a filter’s reliability without requiring Monte Carlo simulations: the covariance trust ratio (CTR).

The reliability factors examined here include the type of Kalman filter used, whether a filter incorporates elements of the measurement source’s state, the type of process noise covariance model used, and the type of measurement sources used. To examine how these factors affect a Kalman filter’s reliability, this dissertation uses two existing methods from the literature, Normalized Estimate Error Squared (NEES) and Normalized Innovation Squared (NIS), in addition to the CTR.

The impact of these reliability factors on a Kalman filter’s trustworthiness are demonstrated using a case study which explores how a spacecraft’s orbital state can be estimated using relative angle and range measurements of Resident Space Objects (RSOs). This case study shows that the CTR is an effective method for quantifying an estimator’s trustworthiness, highlights the effects of the various reliability factors studied here, and demonstrates that these factors can be quantitatively assessed to provide confidence in a filter’s trustworthiness. In order for new estimation methods to become commercially viable, they must demonstrate their reliability and trustworthiness to potential users. The estimator reliability analysis and estimator trust quantification work presented in this dissertation form an enabling technology that may aid in the more rapid adoption of state estimation techniques.