Observability and Estimability of Collaborative Opportunistic Navigation with Pseudorange Measurements

The observability and estimability of collaborative opportunistic navigation (COpNav) environments are studied. A COpNav environment can be thought of as a radio frequency signal landscape within which one or more radio frequency receiver locate themselves in space and time by extracting and possibly sharing information from ambient signals of opportunity (SOPs). Available SOPs may have a fully-known, partially-known, or unknown characterization. In the present work, 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. In scenarios where the COpNav environment is not completely observable, the observable states, if any, are specified. Moreover, for the completely observable scenarios, the degree of observability, commonly referred to as estimability, of the various states is studied, with particular attention paid to the states with exceptionally good and poor observability.