Search

Abstract The problem of dynamic attitude alignment for strapdown inertial navigation system (SINS) and Doppler velocity log (DVL) integrated navigation has become a research hotspot. Underwater complex environment makes DVL output vulnerable to non‐Gaussian noise pollution, which makes it difficult to converge the SINS misalignment angle to within 1° based on analytical coarse alignment. This is to say, the performance of SINS fine alignment via Kalman filter will be degraded because the model of initial alignment exhibits non‐linearity. The inaccurate and/or unknown prior information of measurement noise statistical characteristics will also degrade the filtering performance. To ensure the SINS/DVL alignment accuracy under non‐linear, non‐Gaussian and uncertain conditions, this paper proposed a robust adaptive unscented Kalman filter (UKF) based on Variational Bayesian (VB) method (VBRAUKF). The proposed VBRAUKF improves the adaptability and robustness of UKF from the following two main aspects. Firstly, an adaptive estimation strategy for the measurement noise covariance is designed based on the VB algorithm, which can restrain the effect of inaccurate observation model and improve the adaptive ability of the filtering method. Secondly, an expansion factor is designed based on Mahalanobis distance algorithm, which can restrain the effect of non‐Gaussian noise and improve the robustness of the filtering method. The experimental results for the problem of the SINS/DVL dynamic alignment under mixed Gaussian noise and/or outlier conditions demonstrate the superiority of the proposed VBRAUKF over the traditional ones.

Abstract This article presents a novel approach for adaptive nonlinear state estimation in a modified autoregressive time series with fixed coefficients, leveraging an adaptive polynomial Kalman filter (APKF). The proposed APKF dynamically adjusts the evolving system dynamics by selecting an appropriate autoregressive time‐series model corresponding to the optimal polynomial order, based on the minimum residual error. This dynamic selection enhances the robustness of the state estimation process, ensuring accurate predictions, even in the presence of varying system complexities and noise. The proposed methodology involves predicting the next state using polynomial extrapolation. Extensive simulations were conducted to validate the performance of the APKF, demonstrating its superiority in accurately estimating the true system state compared with traditional Kalman filtering methods. The root‐mean‐square error was evaluated for various combinations of standard deviations of sensor noise and process noise for different sample sizes. On average, the root‐mean‐square error value, which represents the disparity between the true sensor reading and estimate derived from the adaptive Kalman filter, was 35.31% more accurate than that of the traditional Kalman filter. The comparative analysis highlights the efficacy of the APKF, showing significant improvements in state estimation accuracy and noise resilience.

Abstract The application of the hybrid extended Kalman filter (HEKF), hybrid unscented Kalman filter (HUKF), hybrid particle filter (HPF), and hybrid extended Kalman particle filter (HEKPF) is discussed for hybrid non‐linear filter problems, when prediction equations are continuous‐time and the update equations are discrete‐time, and also the discrete extended Kalman filter (DEKF), discrete unscented Kalman filter (DUKF), discrete particle filter (DPF), and discrete extended Kalman particle filter (DEKPF) for discrete‐time non‐linear filter problems, when prediction equations and update equations are discrete‐time. In order to assess the performance of the filters, the authors consider the non‐linear dynamics for a re‐entry vehicle. The filters are used in two hybrid and discrete states to estimate the position, velocity, and drag parameter associated with the re‐entry vehicle. Theoretical topics concerning estimating the drag parameter of a vehicle in re‐entry phase have been dealt with. Drag parameter estimation is carried out using a combination of hybrid filters and discrete filters as an effective estimator and fixed value, forgetting factor, and Robbins‐Monro stochastic approximation methods as the noise covariance matrix adjuster of the parameter.

Abstract Due to the federal Kalman filter is used to directly fuse the measurement information into the main filter without processing, resulting in the problem of reduced filtering accuracy. An adaptive weighted federated Kalman filtering based on Mahalanobis distance was proposed in this paper. By calculating the Mahalanobis distance between the predicted value and the measurements of the system, the random fluctuation of the measurements is detected. The statistical characteristics of the system measurement noise are adjusted at any time according to random fluctuations in the measurements. And then by using a adaptive amplification factor to dynamically adjust the measurement noise in the subsystems, and reduce the impact of measurement information contamination in subfilters on the main filter. The adaptive federated information distribution coefficient is used to realize the global information fusion of the federal Kalman filter method, to reduce the influence of inaccurate estimation of subfilters on the main filter.Simulation results and comparison analysis prove that the filtering performance of the proposed is better than the traditional federated Kalman filter (FKF) and adaptive FKF, which can improve the accuracy of the integrated navigation system.

Abstract This paper proposes a novel variational Bayesian (VB) adaptive Kalman filter with mismatched process noise covariance matrix (PNCM). Firstly, this paper explains the reason why the predicted error covariance matrix (PECM) is chosen for variational inference. Secondly, compared with the earlier VB adaptive Kalman filter (VB‐AKF‐Q), the proposed filter calculate the dynamic model of the PECM with its historical estimation information. Therefore, the proposed filter can overcome the influence of mismatched PNCM on the initial value setting of PECM in the VB‐AKF‐Q. Finally, we use the evidence lower bound for the proposed filter and give the convergence criterion on this basis. Some examples with a target tracking simulation are carried out to demonstrate the superiority of the proposed filter.

Abstract In this study, a distributed fuzzy filter is proposed for a non‐linear state estimation problem on the possibilistic framework. Firstly, instead of Gaussian distribution on the probability framework, the process and observation noises are modelled as fuzzy random variables with trapezoidal possibility distributions. Secondly, a novel square root fuzzy cubature information filtering (SRFCIF) algorithm is proposed to deal with non‐linear state estimation with fuzzy noise; a fuzzy variable fusion (FVF) algorithm is used for fuzzy random variables fusion. Consequently, a distributed square root fuzzy cubature information filter (DSRFCIF) is proposed by embedding SRFCF and FVF into the consensus frame. Finally, consistency analysis and simulation demonstration are executed for the proposed filter.

Abstract In order to establish a unified spatial reference for the whole ship, inertial matching measurement of hull deformation is widely used because of its continuity and concealment. However, the vibration‐shock signal of shipborne equipment often brings short‐time output disturbance to the user‐side fibre gyroscope unit (FGU), and the disturbance will bring great challenges to the accuracy and convergence of inertial matching measurement. To solve these problems, the authors put forward a new algorithm named as attitude quaternion matching method‐improved double factor adaptive Kalman filter‐parameter adaptive Kalman filter (AQM‐IDFAKF‐PAKF). (1) The AQM established the FGU attitude as observation to build the basic model for hull deformation inertial matching method. (2) The authors introduced IDFAKF to track the trend of dynamic hull deformation in vibration interference by using historical data. (3) After judging the anti‐vibration‐shock calculation stop node, PAKF was utilised to adaptively adjust the parameters of hull deformation matching after vibration‐shock, so as to quickly calculate the static hull deformation angle after shock interference. Numerical simulation results illustrated that the AQM‐IDFAKF‐PAKF can quickly converge the calculation of hull deformation angle with a small steady‐state error under the condition of vibration‐shock signal interference.

Abstract For radar target tracking with non‐linear measurements, a sequential linear filtering method is proposed in this study, which includes a linear filter based on the position measurements and a linear sequential filter based on the range rate measurement. The linear radar measurement equation in the sequential filter is estimated based on the position filtering result. Furthermore, the feedback information during tracking is adaptively selected according to the quality of the angle measurements. When tracking the manoeuvring target, the proposed sequential linear filtering with adaptive information feedback is combined with the interacting multiple model (IMM) framework, and the IMM filter based on sequential linear filtering with adaptive model probability selection is proposed. Simulation results demonstrate the effectiveness of the proposed algorithms in non‐manoeuvring and manoeuvring target tracking. Compared with traditional algorithms, the tracking performance is improved by the proposed algorithms in both typical non‐manoeuvring and manoeuvring scenes.

Abstract Bearing‐only tracking of an underwater uncooperative target is essential to defend the sea territory. Considering the influences by uncertain underwater environment, the purpose of this work is to estimate 2‐D locations and velocities of an interested underwater target for non‐Gaussian environment. In this work, a fast particle filter (FPF) based on the traditional particle filter (PF) with novel jet transport (JT) technique is proposed to deal with this problem. Aiming to overcome the heavy computation burden of the traditional PF that limits most of its practical applications, the JT technique can dramatically reduce the computation time and complexity in the particle evolution process, which contributes huge computational complexities to the traditional PF. Then, the proposed FPF is tested through simulations in the 2‐D underwater uncooperative target tracking scenario. Finally, the Monte Carlo simulation results demonstrate that the proposed FPF can track the underwater uncooperative target with the similar accuracies as the traditional PF but only occupies less than 20% of the computational resources.

Abstract The measurement noise covariance R plays a vital role in the Kalman filter (KF) algorithm. Traditionally, a constant R is obtained by experience or experiments. However, the KF cannot achieve optimal estimation using constant R under non‐Gaussian conditions. A robust strategy for adaptive estimation of R is proposed to suppress the influence of non‐Gaussian noise on the in‐motion alignment performance of the Doppler velocity log (DVL) velocity‐aided strapdown inertial navigation system (SINS). Furthermore, an improved Sage–Husa robust adaptive KF algorithm (SHRAKF) based on the Mahalanobis distance (MD) algorithm is proposed to handle the outliers that frequently occur within the complicated underwater environment. The contributions of this work are twofold—the SHRAKF (1) designs a robust strategy to adaptively estimate R in real time and (2) further improves filtering robustness and adaptability with the MD algorithm, conditional on the DVL outputs being contaminated by non‐Gaussian noise. A semi‐physical simulation experiment for SINS/DVL in‐motion alignment based on the test data is carried out, and the experimental results show that the SHRAKF adaptively estimates R in real time and effectively suppresses observational outliers. For non‐Gaussian noise pollution, including outliers and heavy‐tailed noise, the SHRAKF performs better than traditional methods.

Abstract State estimation and dynamical model identification from observed data has been an attractive research area with a wide range of applications such as communication, navigation, radar target tracking, and system control. A method of Adaptive Fuzzy Unscented Kalman/H∞ Filter (AFUKH∞) to estimate non‐linear systems is presented using a combination of the Unscented Kalman Filter (UKF) and Unscented H∞ Filter (UH∞F). The proposed filter does not need linearisation and is based on a combination of gain, a priori state estimation, and a priori measurement estimation in each time step. The performance of the filter is adaptively adjustable. Thus, its efficiency is better than the other two filters. Two fuzzy logic systems are proposed that determine the weight of the UKF and UH∞F filters at each step. These two fuzzy systems are designed to be independent of the dynamics of the system (problem). The proposed filter is referred to as a hybrid AFUKH∞‐II. In the proposed method, the state of the feedback is used as input that improves the efficiency of the filter. The challenge of reentry vehicle tracking and the state estimation of a magnetic motor as two non‐linear high‐order problems are used as benchmarks, and the results are compared with the UKF, UH∞F, and AFUKH∞ filters. The experiments show that an estimation of the proposed hybrid filter (AFUKH∞‐II) is improved against state‐of‐the‐art filters. Also, estimation error and variance values of the proposed filter in the presence of Gaussian noise is decreased by 270% and 370%, respectively, compared with the AFUKH∞ filter.