To solve the problem of unknown noise covariance matrices inherent in the cooperative localization of autonomous underwater vehicles, a new adaptive extended Kalman filter is proposed. The predicted error covariance matrix and measurement noise covariance matrix are adaptively estimated based on an online expectation-maximization approach. Experimental results illustrate that, under the circumstances that are detailed in the paper, the proposed algorithm has better localization accuracy than existing state-of-the-art algorithms.

A New Adaptive Extended Kalman Filter for Cooperative Localization

A robust Kalman filter scheme is proposed to resist the influence of the outliers in the observations. Two kinds of observation error are studied, i.e., the outliers in the actual observations and the heavy-tailed distribution of the observation noise. Either of the two kinds of errors can seriously degrade the performance of the standard Kalman filter. In the proposed method, a judging index is defined as the square of the Mahalanobis distance from the observation to its prediction. By assuming that the observation is Gaussian distributed with the mean and covariance being the observation prediction and its associate covariance, the judging index should be Chi-square distributed with the dimension of the observation vector as the degree of freedom. Hypothesis test is performed to the actual observation by treating the above Gaussian distribution as the null hypothesis and the judging index as the test statistic. If the null hypothesis should be rejected, it is concluded that outliers exist in the observations. In the presence of outliers scaling factors can be introduced to rescale the covariance of the observation noise or of the innovation vector, both resulting in a decreased filter gain. And the scaling factors can be solved using the Newton’s iterative method or in an analytical manner. The harmful influence of either of the two kinds of errors can be effectively resisted in the proposed method, so robustness can be achieved. Moreover, as the number of iterations needed in the iterative method may be rather large, the analytically calculated scaling factor should be preferred.

Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion

A new direct filtering approach to INS/GNSS integration

In this paper, we propose a novel localization methodology to enhance the accuracy from two aspects, i.e., adapting to the uncertain noise of microelectromechanical system-based inertial navigation system (MEMS-INS) and accurately predicting INS errors. First, an interacting multiple model (IMM)-based sequential two-stage Kalman filter is proposed to fuse the information of MEMS-INS, global positioning system (GPS), and in-vehicle sensors. Three bias filters are built with different covariance matrices to cover a wide range of noise characteristics. Then, IMM algorithm provides a soft switching among the three bias filters to adapt to the uncertain noise of MEMS-INS. Further, an elaborate predictor is developed to accurately predict INS errors during GPS outages. The elaborate predictor comprises an online trained autoregressive integrated moving average (ARIMA) model and an offline trained extreme learning machine (ELM) model. The ARIMA model is designed to predict the basic accumulation process of INS errors, while the ELM model is designed to correct the errors caused by the changes of noise characteristics. Thus, the INS errors can be properly compensated when GPS observations are not available. In all, the proposed localization methodology can achieve accurate performance when facing uncertain noises of MEMS-INS and GPS outages simultaneously. To verify the effectiveness of the proposed methodology, road test experiments with various driving scenarios were performed. The experimental results illustrate the feasibility and effectiveness of the proposed methodology.

Enhancing Localization Accuracy of MEMS-INS/GPS/In-Vehicle Sensors Integration During GPS Outages

The integration of the inertial navigation system and the global positioning system (INS/GPS) is a widely used procedure for position and attitude determination applications. The Kalman type filter (KTF) is the primary mechanism to perform the integration. In the KTF, the process noise is always assumed to be Gaussian distribution, which may be violated by the vehicle’s severe maneuver, resulting in a much degraded performance. In this paper, the Huber’s M-estimation methodology is investigated to suppress the process uncertainty, founded on the cascaded form of the M-estimation-based Kalman filter. An iterated algorithm is designed to construct the weighted matrix to rescale the prior state estimate covariance. The proposed process uncertainty robust algorithm is embedded into the newly derived modified unscented quaternion estimator to perform the standard inertial navigation equations-based INS/GPS integration. The car-mounted experiments are carried out to validate the proposed method against the process uncertainty.

Huber’s M-Estimation-Based Process Uncertainty Robust Filter for Integrated INS/GPS

The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has an unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of the unknown bias may be more pronounced on the extended Kalman filter (EKF), which is a nonlinear filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. Recently, the optimal two-stage Kalman filter (TKF) for linear stochastic systems with a constant bias or a random bias has been proposed by several researchers. A TEKF can also be similarly derived as the optimal TKF. In the case of a random bias, the TEKF assumes that the information of a random bias is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper proposes an adaptive two-stage extended Kalman filter (ATEKF) using an adaptive fading EKF. To verify the performance of the proposed ATEKF, the ATEKF is applied to the INS-GPS (inertial navigation system-Global Positioning System) loosely coupled system with an unknown fault bias. The proposed ATEKF tracked/estimated the unknown bias effectively although the information about the random bias was unknown.

Adaptive Two-Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System

The well-known conventional Kalman filter gives the optimal solution but requires an accurate system model and exact stochastic information. Thus, the Kalman filter with incomplete information may be degraded or even diverged. In a number of practical situations, the system model and the stochastic information are incomplete. To solve this problem, a new adaptive fading Kalman filter (AFKF) using the forgetting factor has recently been proposed. This paper extends the AFKF to nonlinear system models to obtain an adaptive fading extended Kalman filter (AFEKF). The forgetting factor is generated from the ratio between the calculated innovation covariance and the estimated innovation covariance. Based on the analysis result of Reif for the EKF, the stability of the AFEKF is also analyzed.

The Stability Analysis of the Adaptive Fading Extended Kalman Filter

In this paper, we propose a time delay compensation method for transfer alignment using a high-resolution buffer design. Time delay degrades the performance of transfer alignment, resulting in subsequent mission failure. The value of such a time delay may not be constant and varies indefinitely depending on the system configuration or operating environment, which reduces the time delay estimation performance using general Kalman filtering. Using a state buffer is one of the methods to solve this problem. This paper presents a new time delay estimation method using a time delay candidate buffer. The proposed scheme can finely set the interval of time delay candidates and does not require a separate memory. In addition, a method for designing an appropriate time delay candidate buffer interval according to the activation of a vehicle and the performance of the MINS is presented. Simulations verified that the proposed technique could reduce the memory requirement and improve the transfer alignment performance for finely changing the time delay. 

Kwang Hoon Kim

Papers

Adaptive Two-Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System

The Stability Analysis of the Adaptive Fading Extended Kalman Filter

High-Resolution Buffer Design for Measurement Time Delay Compensation of Transfer Alignment