Observability Analysis of Opportunistic Navigation with Pseudorange Measurements

The observability analysis of an opportunistic navigation (OpNav) environment whose states may be partially known is considered. An OpNav environment can be thought of as a radio frequency signal landscape within which a receiver locates itself in space and time by extracting information from ambient signals of opportunity (SOPs). Available SOPs may have a fully-known, partially-known, or unknown characterization. In the present work, the receiver is assumed to draw only pseudorange-type measurements from the SOP signals. Separate observations are fused to produce an estimate of the receiver’s position, velocity, and time (PVT). Since not all SOP states in the OpNav environment may be known a priori, the receiver must estimate the unknown SOP states of interest simultaneously with its own PVT. The observability analysis presented here first evaluates various linear and nonlinear observability tools and identifies those that can be appropriately applied to OpNav observability. Subsequently, the appropriate tools are invoked to establish the minimal conditions under which the environment is observable. It is shown that a planar OpNav environment consisting of a receiver and n SOPs is observable if either the receiver’s initial state is known or the receiver’s initial position is known along with the initial state of one SOP. Simulation results are shown to agree with the theoretical observability conditions.