Fundamental limits in signal Time-Of-Arrival estimation with application to next-generation satellite positioning

It is known that positioning accuracy of Global Navigation Satellite Systems (GNSSs) is related to the accuracy of signal Time-Of-Arrival (TOA) estimation performed by the receiver. This work investigates the Ziv-Zakai bound (ZZB) as a theoretical performance limit in signal time delay estimation (TDE). This bound has not any constraint on applicability, but reveals (very) cumbersome to compute in the presence of nuisance parameters (carrier amplitude/phase, channel coefficients) and therefore not attractive nor useful in the practice. This contribution shows how to overcome this problem, introducing a variant of the ZZB dubbed here modified ZZB (MZZB). The procedure is akin to that found in the literature to obtain the so-called Modified Cramér-Rao Bound (MCRB) for the well known Cramér-Rao Bound (CRB). Application of the (M)ZZB and numerical results are shown for multicarrier modulations like those envisaged in next-generation, possibly regional, GNSSs.