The Kalman filter is an optimal estimator with numerous applications in technology, especially in systems with Gaussian distributed noise. Moreover, the adaptive Kalman filtering algorithms, based on the Kalman filter, can control the influence of dynamic model errors. In contrast to the adaptive Kalman filtering algorithms, the H-infinity filter is able to address the interference of the stochastic model by minimization of the worst-case estimation error. In this paper, a novel adaptive H-infinity filtering algorithm, which integrates the adaptive Kalman filter and the H-infinity filter in order to perform a comprehensive filtering algorithm, is presented. In the proposed algorithm, a robust estimation method is employed to control the influence of outliers. In order to verify the proposed algorithm, experiments with real data of the Global Positioning System (GPS) and Inertial Navigation System (INS) integrated navigation, were conducted. The experimental results have shown that the proposed algorithm has multiple advantages compared to the other filtering algorithms.

The Kalman filter has been widely applied in the field of dynamic navigation and positioning. However, its performance will be degraded in the presence of significant model errors and uncertain interferences. In the literature, the fading filter was proposed to control the influences of the model errors, and the H-infinity filter can be adopted to address the uncertainties by minimizing the estimation error in the worst case. In this paper, a new multiple fading factor, suitable for the Global Positioning System (GPS) and the Inertial Navigation System (INS) integrated navigation system, is proposed based on the optimization of the filter, and a comprehensive filtering algorithm is constructed by integrating the advantages of the H-infinity filter and the proposed multiple fading filter. Measurement data of the GPS/INS integrated navigation system are collected under actual conditions. Stability and robustness of the proposed filtering algorithm are tested with various experiments and contrastive analysis are performed with the measurement data. Results demonstrate that both the filter divergence and the influences of outliers are restrained effectively with the proposed filtering algorithm, and precision of the filtering results are improved simultaneously.

As an optimal estimation method, the Kalman filter is the most frequently-used data fusion strategy in the field of dynamic navigation and positioning. Nevertheless, the abnormal model errors seriously degrade performance of the conventional Kalman filter. The adaptive Kalman filter was put forward to control the influences of model errors. However, the adaptive Kalman filter based on the predicted residuals (innovation vector) requires reliable observation information, and its performance is significantly affected by outliers in the measurements. In this paper, a novel adaptively-robust strategy based on the Mahalanobis distance is proposed to weaken the effects of abnormal model deviations and outliers in the measurements. In the proposed scheme, the judging index is defined based on the Mahalanobis distance, and the adaptively-robust filtering is performed when the observations are reliable, otherwise, the robust filtering is performed based on the robust estimation method. Various experiments with the actual data of GPS/INS integrated navigation systems are implemented to examine validity of the proposed scheme. Results show that both the influences of model deviations and outliers are weakened effectively by using the proposed adaptive robust filtering scheme. Moreover, the proposed scheme is easy to implement with a reasonable calculation burden.

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.

Kalman filter is widely applied in data fusion of dynamic systems under the assumption that the system and measurement noises are Gaussian distributed. In literature, the interval Kalman filter was proposed aiming at controlling the influences of the system model uncertainties. The robust Kalman filter has also been proposed to control the effects of outliers. In this paper, a new interval Kalman filter algorithm is proposed by integrating the robust estimation and the interval Kalman filter in which the system noise and the observation noise terms are considered simultaneously. The noise data reduction and the robust estimation methods are both introduced into the proposed interval Kalman filter algorithm. The new algorithm is equal to the standard Kalman filter in terms of computation, but superior for managing with outliers. The advantage of the proposed algorithm is demonstrated experimentally using the integrated navigation of Global Positioning System (GPS) and the Inertial Navigation System (INS).