Systematic multi-frequency positioning algorithms and performance analysis for GNSS receivers

The known multi-frequency positioning algorithms neglected the correlations of the measurement errors and were lack of performance analysis. This paper introduces systematic dual-frequency and triple-frequency positioning algorithms, concerning the correlations of the multi-frequency signals, and defines multi-frequency dilution of precision parameters to compare the positioning accuracies. The variance of the multipath error and receiver measurement error is the key factor for multi-frequency positioning accuracy. Under normal conditions, dual-frequency accuracy is worse than single-frequency accuracy with the variance larger than 3.18m(2), and triple-frequency accuracy is worse than single-frequency accuracy with the variance larger than 4.56m(2). Multi-frequency GNSS receivers should be designed and used to reduce multipath effect as much as possible.