Gaoge Hu

A derivative UKF for tightly coupled INS/GPS integrated navigation.

The tightly coupled INS/GPS integration introduces nonlinearity to the measurement equation of the Kalman filter due to the use of raw GPS pseudorange measurements. The extended Kalman filter (EKF) is a typical method to address the nonlinearity by linearizing the pseudorange measurements. However, the linearization may cause large modeling error or even degraded navigation solution. To solve this problem, this paper constructs a nonlinear measurement equation by including the second-order term in the Taylor series of the pseudorange measurements. Nevertheless, when using the unscented Kalman filter (UKF) to the INS/GPS integration for navigation estimation, it causes a great amount of redundant computation in the prediction process due to the linear feature of system state equation, especially for the case with system state vector in much higher dimension than measurement vector. To overcome this drawback in computational burden, this paper further develops a derivative UKF based on the constructed nonlinear measurement equation. The derivative UKF adopts the concise form of the original Kalman filter (KF) to the prediction process and employs the unscented transformation technique to the update process. Theoretical analysis and simulation results demonstrate that the derivative UKF can achieve higher accuracy with a much smaller computational cost in comparison with the traditional UKF.

Matrix weighted multisensor data fusion for INS/GNSS/CNS integration

Inertial navigation system (INS)/global navigation satellite system (GNSS)/ celestial navigation system (CNS) integration is a promising solution to improve the performance of navigation due to the complementary characteristics of INS, GNSS, and CNS. Nevertheless, the information fusion involved in INS/GNSS/CNS integration is still an open issue. This paper presents a matrix weighted multisensor data fusion methodology with two-level structure for INS/GNSS/CNS integrated navigation system. On the first level, GNSS and CNS are integrated with INS by two local filters respectively to obtain local optimal state estimations. On the second level, two different matrix weighted data fusion algorithms, one based on generic weighting matrices and the other based on diagonal weighting matrices, are developed to fuse the local state estimations for generating the global optimal state estimation. These two algorithms are derived in the sense of linear minimum variance, which provide unbiased fusion results no matter whether the local state estimations are mutually independent or not. Thus, they overcome the limitations of the federated Kalman filter by refraining from the use of the upper bound technique. Compared with the data fusion algorithm based on generic weighting matrices, the computational load involved in the one based on diagonal weighting matrices is significantly reduced, even though its accuracy is slightly lower due to the disregard of the coupled relationship between the components of the local state estimations. The effectiveness of the proposed matrix weighted multisensor data fusion methodology is verified through Monte Carlo simulations and practical experiments in comparison with the federated Kalman filter.

Modified federated Kalman filter for INS/GNSS/CNS integration

This paper presents a modified version of federated Kalman filter (FKF) for INS/GNSS/CNS integration by improving the computational efficiency involved in the FKFs master filter. During the master filtering process, the modified federated Kalman filter (MFKF) firstly decomposes the global state vector into three sub-states according to the characteristics of INS/GNSS/CNS integration. Subsequently, it fuses the sub-state estimations from INS/GNSS and INS/CNS subsystems with the corresponding ones from the time-update solution of the master filter, respectively. Eventually, the fused sub-state estimations are recombined to yield the global state estimation. The proposed MFKF provides the capability of distributed and parallel data processing for the global state fusion to reduce the computational load involved in the master filtering process of the FKF. Experimental results and comparison analysis demonstrate the effectiveness of the proposed MFKF.

Stochastic stability of the derivative unscented Kalman filter

This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discrete-time system with linear system state equation. The first paper established a derivative unscented Kalman filter (DUKF) to eliminate the redundant computational load of the unscented Kalman filter (UKF) due to the use of unscented transformation (UT) in the prediction process. The present paper studies the error behavior of the DUKF using the boundedness property of stochastic processes. It is proved that the estimation error of the DUKF remains bounded if the system satisfies certain conditions. Furthermore, it is shown that the design of the measurement noise covariance matrix plays an important role in improvement of the algorithm stability. The DUKF can be significantly stabilized by adding small quantities to the measurement noise covariance matrix in the presence of large initial error. Simulation results demonstrate the effectiveness of the proposed technique.

Asymptotic Properties of Random Weighted Empirical Distribution Function

This article studies the asymptotic properties of the random weighted empirical distribution function of independent random variables. Suppose X1, X2, ⋅⋅⋅, Xn is a sequence of independent random variables, and this sequence is not required to be identically distributed. Denote the empirical distribution function of the sequence by Fn(x). Based on the random weighting method and Fn(x), the random weighted empirical distribution function Hn(x) is constructed and the asymptotic properties of Hn are discussed. Under weak conditions, the Glivenko–Cantelli theorem and the central limit theorem for the random weighted empirical distribution function are obtained. The obtained results have also been applied to study the distribution functions of random errors of multiple sensors.

Multi-Sensor Optimal Data Fusion Based on the Adaptive Fading Unscented Kalman Filter

This paper presents a new optimal data fusion methodology based on the adaptive fading unscented Kalman filter for multi-sensor nonlinear stochastic systems. This methodology has a two-level fusion structure: at the bottom level, an adaptive fading unscented Kalman filter based on the Mahalanobis distance is developed and serves as local filters to improve the adaptability and robustness of local state estimations against process-modeling error; at the top level, an unscented transformation-based multi-sensor optimal data fusion for the case of N local filters is established according to the principle of linear minimum variance to calculate globally optimal state estimation by fusion of local estimations. The proposed methodology effectively refrains from the influence of process-modeling error on the fusion solution, leading to improved adaptability and robustness of data fusion for multi-sensor nonlinear stochastic systems. It also achieves globally optimal fusion results based on the principle of linear minimum variance. Simulation and experimental results demonstrate the efficacy of the proposed methodology for INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integrated navigation.

Adaptive Square-Root Unscented Particle Filtering Algorithm for Dynamic Navigation

This paper presents a new adaptive square-root unscented particle filtering algorithm by combining the adaptive filtering and square-root filtering into the unscented particle filter to inhibit the disturbance of kinematic model noise and the instability of filtering data in the process of nonlinear filtering. To prevent particles from degeneracy, the proposed algorithm adaptively adjusts the adaptive factor, which is constructed from predicted residuals, to refrain from the disturbance of abnormal observation and the kinematic model noise. Cholesky factorization is also applied to suppress the negative definiteness of the covariance matrices of the predicted state vector and observation vector. Experiments and comparison analysis were conducted to comprehensively evaluate the performance of the proposed algorithm. The results demonstrate that the proposed algorithm exhibits a strong overall performance for integrated navigation systems.

An adaptive UKF for nonlinear state estimation via maximum likelihood principle

For the purpose of improving the performance of unscented Kalman filter (UKF) under the condition without accurate system noise statistics, this paper presents a new adaptive UKF based on the maximum likelihood principle. According to the maximum likelihood principle, the estimation of system noise statistics is determined by minimizing the negative of log likelihood function of innovation sequences. Subsequently, the estimated system noise statistics are fed back to the standard UKF to overcome its limitation. The proposed adaptive UKF can enhance the adaptive capability of standard UKF through the online estimation of system noise statistics. The effectiveness and advantage of the proposed algorithm are verified by the numerical simulations and comparison analysis.