Avoiding GNSS Kalman Filter Degradation in Urban Canyons with a Novel Process Noise Model

Abstract

Improving the accuracy of GNSS positioning in urban canyons is a challenging topic, especially for low-cost GNSS receivers. Although Non-Line-Of-Sight (NLOS) signals can be rejected by various methods, the number of satellites available in position calculation is reduced, and their geometric distribution is biased. In Kalman filter for GNSS positioning, the process noise covariance is often bumped up to avoid the filter divergence in the presence of unknown model errors, by assuming that there is a fictitious process noise in addition to the nominal process noise. In this paper, we first show that, if the process noise covariance is bumped up in a naïve manner for poor satellite geometry, the estimation-error covariance tends to become unintentionally large in a certain direction. This unintentional inflation of estimation-error covariance may cause the degradation of estimation accuracy. And then, we derive a fictitious process noise covariance based on an extension of a novel process noise model proposed in our previous work. The fictitious noise covariance is determined according to the observation matrix at each time step, and can reduce the estimation errors even for poor satellite geometry, without causing the unintentional inflation of estimation-error covariance. The effectiveness of the derived process noise model is demonstrated for the data sets that simulate GNSS signals from the antenna that moves from open sky areas to urban areas. The estimation errors with the derived process noise model are significantly reduced, compared to the ones with other two process noise models.