Abstract
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.
Highlights
As the linear estimator of the mean and covariance, the Kalman filter has become the classic fusion algorithm in many fields [1, 2], and it is implemented as the basic fusion method in the data processing with multiple sensors [3, 4]
The Kalman filter is susceptible to outlying measurements, and it performs inadequately with the model errors and uncertain statistical information
The main superiority to the conventional Kalman filter lies on inflating the covariance matrix of the a priori state, namely, Pk/k‐1, and this indicates that the state estimation Xk/k relies more on the current observation information
Summary
As the linear estimator of the mean and covariance, the Kalman filter has become the classic fusion algorithm in many fields [1, 2], and it is implemented as the basic fusion method in the data processing with multiple sensors [3, 4]. For the data fusion of GNSS/INS integrated systems, the IAE strategy performs better than the MMAE strategy [11] Another type of adaptive-robust filter where both the adaptation and robustness were considered simultaneously was developed using the adaptive factors and the M-estimation, including four adaptive factors and four detective statistics [15]. The main superiority to the conventional Kalman filter lies on inflating the covariance matrix of the a priori state, namely, Pk/k‐1, and this indicates that the state estimation Xk/k relies more on the current observation information Both the single factor and the fading matrix are constructed based on the residual vector. The proposed algorithm is tested using the actual data obtained through the self-developed GNSS/INS integrated systems in actual environment Both the conventional fading filter and the proposed algorithm are implemented in the testing section of this paper.
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