ION GNSS 2012
Session D2: GPS & GLONASS Modernization

Title: GNSS Guaranteed OD&TS Performance Optimisation by the Innovative MiniMax Approach
Author(s): V.V. Bobrov, Thales Alenia Space, Italy
Date/Time: Wednesday, September 19, 2012, 2:35 p.m.
Room: Grand Ballroom West (Renaissance)

As well known, the Least Square Algorithm (LSQ) and his modification Kalman Filter are from one side, the optimal filters for the SV ODTS by a real tracking data processing. But, from other side, they have a lot of drawbacks for a priory ODTS accuracy estimation (Gaussian random model of errors, simulator manager arbitrariness, only partial Ranging Error estimation instead of the total URE and oth.). To resolve the above Problem, the innovative MiniMax (MMX) Estimated Approach was proposed in 1964 by M.Lidov in Russia and developed by him and other Russian scientist as an alternative to traditional LSQ and Kalman Filters for a priory ODTS accuracy estimation without disadvantages of the last filters. The MMX Approach is based on the arbitrary (worst) correlated models of the measurement errors and perturbed factors and on the Linear Programming Theory, which, in combination, are provided an optimal and guaranteed a priory accuracy of the SV ODTS performance estimation and also optimal measurement strategy planning. The additional advantage of the MMX Approach with respect to the LSQ and Kalman Filters are as following:  the MMX estimator manager arbitrariness is cancelled because the MMX Algorithm is optimised not a mean square parameter value, but non-average absolute one;  the MMX Algorithm is estimated a total URE (URET) without of the reference orbit calculation and also it is allowed to determine separately the contribution of the each PR error and SV acceleration uncertainties to URET;  the number of the PR-measurements in optimal strategy is equal to the system state vector dimension and essentially smaller with respect to the total amount of measurements in each scenario. This one could be used for radically reduction amount of the processed PR-observations in real operations by the real observation strategy optimisation without of the ODTS accuracy reduction. On the system level, the first application of the MMX Approach have been realised by V. Bobrov for Russian TDRSS OD&TS performance optimisation in 1975-85. For SARSAT-KOSPAS performance optimisation, MMX Approach was applied by V. Krupen and L. Belousov in 1980-th. The first attempt, of the MMX Approach application for Russian GLONASS ODTS accuracy optimisation have been done in Russia by L. Belousov before 2003. The paper presents the results of the renew original MMX Approach application for the future European GNSS GALILEO and modernised GPS IIF&III Systems guaranteed OD&TS accuracy optimisation with new models of PR errors and perturbed factors and, also, with NAV message uploads and upload cutover accounting. The PR error model is included a biases and systematic errors, which are a drivers in GNSS. The integrated affect of the perturbed factors was simulated by so-named SV Acceleration Uncertainties (non-modelled accelerations). The SIS URE optimal components have been estimated with accounting of the common affect of the all PR errors and SV Acceleration Uncertainties. Validation of the MMX Estimator performance have been performed by GPS PPS Standard and real data. As shown the results, the relative variations of the GPS MMX URE magnitude versus GPS PPS Standard and real data for different operation modes in average consist of about 20%. The Galileo MMX accuracy estimation analysis shown, for example, that if Galileo sensor stations (GSS) will be equipped by Rubidium frequency standard (RAFS), GAL FOC SIS URE will be worst versus GPS IIR/F one, nevertheless on two time bigger measurement Arc. To reach the same as GPS IIF and better GAL SIS URE, ESA shall reequipped GAL GSS by more accurate Caesium Clocks (CsAFS). The analysis of the future Galileo and GPS IIF/III Systems MMX ODTS accuracy estimation shown that now the problem of the developed and modernised GNSS ODTS performance cost/effective optimisation can be resolved most effectively by the renovated MMX Estimate Approach application for a priory GNSS ODTS guaranteed accuracy optimisation, instead of the classic, but not effective in this case LSQ and Kalman Filters.

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