Observability Analysis of Collaborative Opportunistic Navigation With Pseudorange Measurements

The observability analysis of a collaborative opportunistic navigation (COpNav) environment whose states may be partially known is considered. A COpNav environment can be thought of as a radio frequency (RF) signal landscape within which one or more RF receivers locate themselves in space and time by extracting and, possibly, sharing information from ambient signals of opportunity (SOPs). These receivers, whether vehicle mounted or integrated into handheld devices, exploit signal diversity to improve navigation and timing robustness compared with stand-alone Global Positioning System (GPS) receivers in deep urban, indoor, or, otherwise, GPS-hostile environments. Available SOPs may have a fully known, partially known, or unknown characterization. In this paper, the receivers are assumed to draw only pseudorange-type measurements from the SOPs. Separate observations are fused to produce an estimate of each receiver's position, velocity, and time (PVT). Since not all SOP states in the COpNav environment may be known a priori, the receivers must estimate the unknown SOP states of interest simultaneously with their own PVT. This paper establishes the minimal conditions under which a COpNav environment consisting of multiple receivers and multiple SOPs is completely observable. Moreover, in scenarios where the COpNav environment is unobservable, the unobservable directions in the state space are specified. Simulation and experimental results are presented to confirm the theoretical observability conditions.