This paper presents a hypothesis test-constrained robust Kalman filter for INS/GNSS (inertial navigation system/global navigation satellite system) integrated navigation in the presence of measurement outliers. This method estimates measurement noise covariance by combining hypothesis test with the maximum likelihood theory to handle measurement outliers. A chi square test and an improved sequential probability ratio test are established to characterize abrupt and slow-growing measurement outliers, respectively. Subsequently, these two hypothesis tests are used to constrain the maximum likelihood estimation of measurement noise covariance to accommodate measurement outliers. Based on the hypothesis test-constrained maximum likelihood estimation of measurement noise covariance, a robust Kalman filter is developed for INS/GNSS integrated navigation in the presence of measurement outliers. Simulation and experimental results demonstrate that the proposed method can effectively deal with measurement outliers. The resultant navigation accuracy is about 46% and 30% higher than that of the Kalman filter and maximum likelihood-based robust Kalman filter for INS/GNSS integrated navigation.

This article proposes a double-channel sequential probability ratio test (DCSPRT) failure detection algorithm for improving the fault-tolerant ability of the multisensor system. It develops a horizon-based sequential probability ratio test (HSPRT) using the horizon technique for the detection of slowing-growing failures and a current sample-based probability ratio test (CSPRT) for the detection of abrupt failures. Subsequently, the DCSPRT is established by combining HSPRT with CSPRT for the detection of both slow-growing and abrupt failures. Simulation and experimental results together with comparison analysis demonstrate that the proposed DCSPRT can effectively detect both slow-growing failures and abrupt failures to improve the capability of failure tolerance for multisensor integrated systems.

In order to achieve a highly autonomous and reliable navigation system for aerial vehicles that involves the spectral redshift navigation system (SRS), the inertial navigation (INS)/spectral redshift navigation (SRS)/celestial navigation (CNS) integrated system is designed and the spectral-redshift-based velocity measurement equation in the INS/SRS/CNS system is derived. Furthermore, a new chi-square test-based robust Kalman filter (CSTRKF) is also proposed in order to improve the robustness of the INS/SRS/CNS navigation system. In the CSTRKF, the chi-square test (CST) not only detects measurements with outliers and in non-Gaussian distributions, but also estimates the statistical characteristics of measurement noise. Finally, the results of our simulations indicate that the INS/SRS/CNS integrated navigation system with the CSTRKF possesses strong robustness and high reliability.

This paper investigates a novel robust Kalman filter by incorporating kernel density estimation in the Kalman filtering framework to address the disturbance of measurement outliers on system state estimation. It establishes a logarithmic Gaussian kernel function to approximate the unknown probability density function of abrupt-change measurement noise covariance caused by measurement outliers. Based on the logarithmic Gaussian kernel function, a state estimation equation is derived according to the Bayesian estimation theory in the presence of measurement outliers. Upon the above, a novel robust Kalman filter is established for system state estimation against measurement outliers. Simulation and experiment results demonstrate the superiority of the proposed robust Kalman filter for integrated vehicle navigation in the presence of measurement outliers.

This paper presents a maximum correntropy method of redshift estimation for spectral redshift navigation (SRN). It converts the problem of spectral redshift estimation to a problem of maximum correntropy. A wavelet transform technique is established to denoise spectral signals and fit spectral continuous portions for spectral line extraction and further construction of a candidate redshift set. Subsequently, the joint correntropy is established by using the correntropy based on the redshift predicted from the SRN system equations to correct the correntropy based on the candidate redshift set. According to the maximum correntropy criterion, the spectral redshift estimation is acquired as the candidate redshift with the maximum joint correntropy. Simulations and comparative analysis demonstrate that in addition to the possessed real-time performance, the proposed method can also improve the accuracy of redshift estimation, leading to the improved accuracy for spectral redshift navigation.

This paper develops an enhanced fault-tolerant strap-down inertial navigation (SINS)/spectral redshift navigation (SRS)/celestial navigation (CNS) integration system. In the developed system, a new SRS observation equation based on Doppler shift is established to improve the accuracy and anti-interference performance of SINS/SRS/CNS integration. Subsequently, an adaptive fault-tolerant cubature Kalman filter (AFTCKF) is proposed to inhibit the effect of noise uncertainty and outliers in observations on state estimation. The AFTCKF promotes the robustness of the cubature Kalman filter, in which the maximum likelihood method is adopted for the online estimation of observation noise statistics, and the sequential probability ratio test and the chi-square test are employed in the determination of Kalman gain to further resist the outliers in the filtering procedure. The developed SINS/SRS/CNS integration system not only has the capability to maintain the stability of the navigation system in high-dynamic circumstances, but also is robust against the observation uncertainty. Simulations and comprehensive analysis have been conducted to verify the effectiveness of developed SINS/SRS/CNS integration.