Multiple Update Particle Filter: Position Estimation by Combining GNSS Pseudorange and Carrier Phase Observations

TL;DR

The paper tackles the problem of particle filter degeneracy when multiple GNSS observations with sharp-peaked likelihoods are used for position estimation. It introduces the Multiple Update Particle Filter (MU-PF), which updates particle weights in multiple steps in the order of the likelihood spread, using intermediate distributions to progressively concentrate particles toward the true state. By applying pseudorange first and carrier-phase likelihoods (including wide-lane AFV variants) in decreasing spread, MU-PF avoids zero-weights and achieves rapid, centimeter-level convergence with fewer particles than traditional or annealed PF methods. Experimental results in static and urban-kinematic settings demonstrate superior convergence speed and accuracy, and improved robustness in environments with limited satellites, indicating practical benefits for GNSS-based localization in challenging conditions.

Abstract

This paper presents an efficient method for updating particles in a particle filter (PF) to address the position estimation problem when dealing with sharp-peaked likelihood functions derived from multiple observations. Sharp-peaked likelihood functions commonly arise from millimeter-accurate distance observations of carrier phases in the global navigation satellite system (GNSS). However, when such likelihood functions are used for particle weight updates, the absence of particles within the peaks leads to all particle weights becoming zero. To overcome this problem, in this study, a straightforward and effective approach is introduced for updating particles when dealing with sharp-peaked likelihood functions obtained from multiple observations. The proposed method, termed as the multiple update PF, leverages prior knowledge regarding the spread of distribution for each likelihood function and conducts weight updates and resampling iteratively in the particle update process, prioritizing the likelihood function spreads. Experimental results demonstrate the efficacy of our proposed method, particularly when applied to position estimation utilizing GNSS pseudorange and carrier phase observations. The multiple update PF exhibits faster convergence with fewer particles when compared to the conventional PF. Moreover, vehicle position estimation experiments conducted in urban environments reveal that the proposed method outperforms conventional GNSS positioning techniques, yielding more accurate position estimates.

Figures (8)

• Figure 1: Illustration of the normal particle filter (PF) in the presence of multiple observations with sharp peaks. When the initial particle distribution is widely spread and the number of particles is limited, the weights of particles at their true positions are not evaluated.
• Figure 2: Illustration of the proposed multiple update PF. By repeating weight updates and resampling in the order of the spread of the distribution of the likelihood function of multiple observations, the particles are gradually moved to the correct state.
• Figure 3: Examples of likelihood computed from GNSS observations. (1) DD-pseudorange, (2) DD-WL AFV, (3) DD-L2 AFV, and (4) DD-L1 AFV. The distributions exhibit sharp peaks in this order. The likelihood from the L1 and L2 AFVs has many local maxima in the ±1 m range.
• Figure 4: Comparison of 3D position estimation errors over 100 trials using different GNSS observations. The proposed method converges to within 10 cm of the 3D position estimation error after almost one observation when compared to other methods.
• Figure 5: Percentage of 3D position estimation within 10 cm for each method when the number of particles is varied.