On the Use of Multi-correlator Values as Sufficient Statistics as Basis for Flexible Ultra-tight GNSS/INS Integration Developments

Within an ultra-tightly (or deeply) integrated global navigation satellite system (GNSS) and inertial navigation system (INS) GNSS/INS, GNSS signal correlation delivers correlator values as input to the integration filter. On the other side, the integration filter controls the correlation process by determining the numerically controlled oscillator (NCO) values. As GNSS signal correlation is a computational trivial but a time-consuming process, we propose for R&D in this area an alternative approach to first generate for each GNSS signal multi-correlator values and store them for the later GNSS/INS filter development work. Once the filter runs, it interpolates from the multi-correlator values the actual needed correlation values. The multi-correlator values thus act like a data compression for the GNSS signals. This paper discusses the mathematical framework for this data compression, which is loosely described as a sufficient statistic. This statistic consists of the correlation values themselves plus the NCO values that have been used during the correlation process. The generation and interpolation process will be described in this contribution with all mathematical details, as well as interpolation limits in code phase and Doppler direction. Finally, this approach is validated by comparison of global positioning system (GPS) C/A code pseudorange and carrier phase data from direct tracking to results originate from a MATLAB-based receiver which uses the multi-correlator values as sufficient statistics.