The navigation potential of signals of opportunity-based time difference of arrival measurements

This research introduces the concept of navigation potential, NP, to quantify the intrinsic ability to navigate using a given signal. In information theory, the Shannon Hartley capacity theorem provides the theoretical limit on the amount of information that may be recovered error-free over a bandlimited channel corrupted by Gaussian noise. As developed under this research, NP theory is a new, analogous concept that provides a theoretical performance limit on estimating navigation parameters from a received signal that is modelled through a stochastic mapping of the transmitted signal and measurement noise. Essentially, NP theory is an information theory-like concept applied to navigation systems and is particularly useful when using signals of opportunity (SOP) for navigation.; SOP-based time difference of arrival (TDOA) measurements are a promising positioning alternative when the Global Positioning System (GPS) is not available. SOP are signals that are transmitted for a purpose other than navigation; however, SOP may also be used for positioning if properly exploited. A SOP-based TDOA measurement navigation process, for which the navigation solution may be found using well known GPS techniques, is introduced.; NP theory is applied to SOP-based TDOA systems through the proper selection of a stochastic mapping. When the stochastic mapping assumes a rather simple model, e.g., the received signal is the transmitted signal in additive, Gaussian noise, NP results validate previously established performance metrics. In addition, by using a multipath mapping, the NP may be found for a received signal consisting of the transmitted signal; multiple delayed and attenuated replicas of the transmitted signal, and measurement noise. This innovative development captures the dominant error source foreseen in SOP-based navigation systems; consequently, multipath-based NP may be considered a better predictor of actual system performance than metrics based on the transmitted signal in measurement noise alone.; The general nature of NP theory accommodates its application to signals other than SOP. As an example, NP is used to predict GPS correlation error performance. NP provides novel theoretical performance bounds on GPS correlation error for the case in which the stochastic mapping is chosen to be a multipath mapping. Prior to this research, no theoretical performance bounds on GPS correlation error were available that address multipath. When the mapping is chosen to be the transmitted signal in measurement noise alone (i.e., no multipath), NP provides additional insight beyond, yet consistent with, previously developed GPS correlation error performance bounds.