Global navigation satellite system (GNSS) signal reflection over buildings degrades positioning performance in urban canyons. Different three-dimensional (3D) mapping-aided (3DMA) GNSS algorithms have been proposed, which utilize 3D building models to aid in positioning. Recently, the candidate-based 3DMA GNSS framework has been applied to examine evenly spaced distributed particles. The particles that best match the observed measurements, that is, with the minimum cost, are identified as the receiver location. However, such particle sampling approaches incur a high computational load and are not robust. In this study, a Kriging-based interpolation method is applied to model the cost function of a 3DMA GNSS based on sampled particles, and the modeled cost function is then integrated with Doppler measurements through factor graph optimization. The regressed model can reduce the computational load by sparsely distributing the particles. Designed experiments with smartphone and commercial-level GNSS receivers demonstrate that the positioning performance can achieve a root mean square error of less than 10 m in Hong Kong and New York City urban canyons.
Global navigation satellite system (GNSS) signal reflection over buildings degrades positioning performance in urban canyons. Different three-dimensional (3D) mapping-aided (3DMA) GNSS algorithms have been proposed, which utilize 3D building models to aid in positioning. Recently, the candidate-based 3DMA GNSS framework has been applied to examine evenly spaced distributed particles. The particles that best match the observed measurements, that is, with the minimum cost, are identified as the receiver location. However, such particle sampling approaches incur a high computational load and are not robust. In this study, a Kriging-based interpolation method is applied to model the cost function of a 3DMA GNSS based on sampled particles, and the modeled cost function is then integrated with Doppler measurements through factor graph optimization. The regressed model can reduce the computational load by sparsely distributing the particles. Designed experiments with smartphone and commercial-level GNSS receivers demonstrate that the positioning performance can achieve a root mean square error of less than 10 m in Hong Kong and New York City urban canyons.