In the literature, the fading factor was constructed to overcome the shortage of model uncertainties in the Kalman filter. However, the a priori covariance matrix might be inflated abnormally by the fading factor once the measurement is unreliable. Thus, the fading factor may become invalid, and this problem is rarely discussed and tested. In this paper, squares of the Mahalanobis distance are introduced as the judging index, and the fading factor or the covariance inflation factor is adopted conditionally according to the hypothesis testing result. Therefore, an adaptive filtering scheme based on the Mahalanobis distance is put forward for the systems with model uncertainties. The proposed algorithm is implemented with the actual data collected by the integration of the global navigation satellite system (GNSS) and the inertial navigation system and INS (inertial navigation system) integrated systems (INS). For the systems with model uncertainties, experimental results demonstrate that the influences of both the outlying measurements and model errors are controlled effectively with the proposed scheme.
As a typical application of geodesy, the GNSS/INS (Global Navigation Satellite System and Inertial Navigation System) integrated navigation technique was developed and has been applied for decades. For the integrated systems with multiple sensors, data fusion is one of the key problems. As a well-known data fusion algorithm, the Kalman filter can provide optimal estimates with known parameters of the models and noises. In the literature, however, the data fusion algorithm of the GNSS/INS integrated navigation and positioning systems is performed under a certain norm, and performance of the conventional filtering algorithms are improved only under this fixed and limited frame. The mixed norm-based data fusion algorithm is rarely discussed. In this paper, a mixed norm-based data fusion algorithm is proposed, and the hypothesis test statistics are constructed and adopted based on the chi-square distribution. Using the land vehicle data collected through the multi-GNSS and the IMU (Inertial Measurement Unit), the proposed algorithm is tested and compared with the conventional filtering algorithms. Results show that the influences of the outlying measurements and the uncertain noises are weakened with the proposed data fusion algorithm, and the precision of the estimates is further improved. Meanwhile, the proposed algorithm provides an open issue for geodetic applications with mixed norms.
Due to expansive soils and high slopes, the deep excavated channel section of the China South–North Water-Diversion Middle-Route Project has a certain risk of landslide disaster. Therefore, examining the deformation law and mechanism of the channel slope in the middle-route section of the project is an extreme necessity for safe operation. However, the outdated monitoring method limits research on the surface deformation law and mechanism of the entire deep excavation channel section. For these reasons, we introduced a novel approach that combines SBAS-InSAR and GNSS, enabling the surface domain monitoring of the study area at a regional scale as well as real-time monitoring of specific target regions. By using SBAS-InSAR technology and leveraging 11-view high-resolution TerraSAR-X data, we revealed the spatiotemporal evolution law of surface deformations in the channel slopes within the study area. The results demonstrate that the predominant deformation in the study area was uplifted, with limited evidence of subsidence deformation. Moreover, there is a distinct region of significant uplift deformation, with the highest annual uplift rate reaching 19 mm/y. Incorporating GNSS and soil-moisture-monitoring timeseries data, we conducted a study on the correlation between soil moisture and the three-dimensional deformation of the ground surface, revealing a positive correlation between the soil moisture content and vertical displacement of the channel slope. Furthermore, combining field investigations on surface uplift deformation characteristics, we identified that the main cause of surface deformation in the study area was attributed to the expansion of the soil due to water absorption in expansive soils. The research results not only revealed the spatiotemporal evolution law and mechanism of the channel slope deformation in the studied section of the deep excavation channel but also provide successful guidance for the prevention and control of channel slope-deformation disasters in the study area. Furthermore, they offer effective technical means for the safe monitoring of the entire South–North Water-Diversion Middle-Route Project and similar long-distance water-conveyance canal projects.
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