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Aiming at cooperative navigation of multi‐aircrafts, an adaptive EKF‐SLAM algorithm for non‐fixed landmark is proposed. First, the aircraft motion model and angle measurement model are established. Second, the fixed landmark cooperative EKF‐SLAM algorithm is established. Furthermore, a distributed EKF‐SLAM algorithm is designed. Then, the adaptive EKF‐SLAM algorithm with non‐fixed landmark is proposed. Finally, simulation results verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

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.

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 FROM AUTHOR]

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 FROM AUTHOR]

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.

This study addresses the state estimation problem of discrete‐time non‐linear stochastic systems with non‐Gaussian noises, particularly impulsive noises. Instead of minimizing the mean square error of the state estimate, which tends to excessively focus on outliers caused by non‐Gaussian noises, the ℓ1${\ell }_1$ norm‐based non‐linear recursive filter (L1KF) is put forward in this paper. Here, minimizing the ℓ1${\ell }_1$ norm of model errors is actually to pursue the minimum sum of absolute values of all errors, which is equitable to all model errors rather than paying much attention on outliers. To further improve estimation accuracy, a recursive nonlinear smoother (L1KS) is proposed, based on minimizing the ℓ1${\ell }_1$ norm of model errors. The proposed ℓ1${\ell }_1$ norm‐based filter and smoother are implemented using unscented transformation for statistical linear regression applied to nonlinear models. Additionally, the computational complexity of the proposed method is analysed. Simulation results of tracking a radar target with impulsive noises demonstrate the effectiveness and robustness of the proposed estimator. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

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.

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 FROM AUTHOR]

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.

One of the main issues in inertial navigation systems is attitude determination, which means estimating the level angles (i.e., roll and pitch). This paper investigates the attitude estimation problem for an accelerated rigid body using three gyros and three accelerometers. The most critical challenges in attitude determination systems are external accelerations and gyroscope drift errors. Thus, a novel method based on the adaptive filter-Kalman algorithm is proposed to estimate and compensate for these errors. Linearization was performed around a general work point, and the covariance matrix's adaptive values were obtained so that leveling angles were accurately determined despite external accelerations. The simulation results, along with the car test, which was performed in different dynamic conditions with external accelerations, showed that the introduced algorithm has a high capability in accurately estimating leveling angles. This approach can be used for GPS-less navigation Algorithms. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

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 FROM AUTHOR]

Adaptive Kalman filtering method is based on generating a separable Variational model for estimating joint posterior distribution of states in dynamical system and noise parameters on each time step separately. In this article we present a Gaussian approximation based framework for optimal smoothing of non-linear stochastic state space models, and also time-varying noisy measurements of the system are obtained at discrete instances of time. It is also shown how the method can be applied to a class of models. The result is a recursive algorithm, where on each step the state is estimated with Kalman filter and the sufficient statistics of the noise variances are estimated. We also numerically compare accuracies and error performance of the algorithm with different simulated data. [ABSTRACT FROM AUTHOR]

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.

In this study, full adaptive Kalman filters are designed for continuous-time nonlinear fractional-order systems (FOSs) containing unknown parameters and fractional-orders. First, the estimated FOS is discretized using the Grünwald–Letnikov difference method to transform the fractional-order differential equation into a difference equation. Then, in terms of the nonlinear function contained in the investigated system, the Taylor expansion formula is adopted to linearize the discretized equation. Based on the method of augmented vector, an augmented state equation is established by state equations, unknown parameter equations, and fractional-order equation to achieve the state estimation. Besides, the sigmoid function is brought to ensure that the estimation of the fractional-order is performed in a suitable range. Because the covariance matrices of noises are difficult to be measured in physical systems, we also concern the problems on the state estimation, parameter estimation, and fractional-order estimation under the cases that the covariance matrix of process noise is unknown or the covariance matrix of measurement noise is unknown. Considering that the initial value can produce an error of state estimation and parameter identification for the FOS defined under the Caputo sense, the augmented vector method is used to achieve the initial value compensation. Finally, the effectiveness of the proposed algorithms is validated by four examples. [ABSTRACT FROM AUTHOR]

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.

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 FROM AUTHOR]

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 FROM AUTHOR]

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 FROM AUTHOR]

The characteristics of subsynchronous oscillation (SSO) in series‐compensated wind power systems are significantly affected by the system's operating condition. Besides the variation in the magnitude and frequency of the SSO during an SSO event, the fundamental frequency may also deviate from its nominal value. This study aims at capturing the dynamics of both subsynchronous and fundamental frequency components simultaneously. This work first explores the strengths and weaknesses of various Kalman filtering based frequency tracking algorithms for joint tracking of the fundamental and SSO components. Then, it proposes a novel adaptive extended Kalman filtering (AEKF) algorithm, in which the process noise covariance is updated online by maximising the probability density function of the predicted error. The process noise covariance factor changes to positive non‐zero value whenever the frequency of the fundamental component deviates. Thus, the proposed AEKF extracts the time‐varying subsynchronous component while also tracking the small variations in the fundamental frequency. The tracking performance of the AEKF is validated on computer‐generated test signals as well as on the electromagnetic transient simulation model of an actual wind power system facing SSO. The captured fundamental and subsynchronous dynamics can be used for designing monitoring, protection, and control schemes for the SSO. [ABSTRACT FROM AUTHOR]

Current target tracking algorithms for wireless sensor networks in noise environments have large positioning errors. Owing to the environmental noise, Kalman filters (KFs) are used to estimate the target position. To reduce the adverse effect of unknown or time‐varying noise on KFs, adaptive KFs (AKFs) are developed. However, the present AKFs can only achieve second‐order estimation accuracy. To improve the existing target tracking algorithm's positioning accuracy under unknown and time‐varying noise environments, the authors propose a noise‐aware algorithm based on a novel third‐order adaptive cubature KF (ACKF) with higher estimation accuracy, which improves the accuracy of the existing algorithm by up to 63%. The innovative ACKF contains a new third‐order noise statistic estimator and a traditional cubature KF without noise perception. A large number of numerical simulations and practical experiments show that the proposed noise‐aware target tracking algorithm based on the novel ACKF is always more accurate than the target tracking algorithms based on the current KFs, no matter whether the moving target is manoeuvring or not, whether the strength of the noise is small or large, whether the number of anchor nodes is many or few, and whether the noise is time‐varying or constant. [ABSTRACT FROM AUTHOR]

This study is intended to design a novel adaptive Kalman filter (KF) that can solve the filtering problem with unknown noise statistics. The proposed method named as measurement sequence adaptive KF (MSAKF) can adaptively estimate the unknown parameters of noise statistics via the information from measurement sequences. In order to enhance the computational efficiency, algorithm optimisation via recursive covariance estimation is introduced. In addition, stability analysis of the MSAKF is also made under some given conditions. The estimation process is proved to be stable and its filtering results converge to the ones of the ideal KF with exact system parameters. To demonstrate the effectiveness of the MSAKF algorithm, the simulation based on a navigation signal‐tracking model is presented, and the results show that the MSAKF algorithm possesses low calculation complexity, fast convergence, high‐precision and adaptability in complex application environments. [ABSTRACT FROM AUTHOR]

Model validation is an essential task to determine whether a model can accurately describe the actual behaviours of a power system. Currently, major commercial software tools are equipped with an 'event playback' function to validate dynamic models using testing data from phasor measurement units (PMUs). Due to their limited bandwidth and low sampling rates, PMUs cannot capture the fast‐transient dynamics. As such, the playback function using the conventional approach may mistakenly invalidate an accurate model during the high‐frequency responses. To overcome the deficiency, a batch state estimation approach is proposed in this study to improve the performance of the 'event playback' function by focusing on low‐frequency responses in model validation. The proposed approach consists of three major steps. First, a multi‐model adaptive Kalman filter approach is used to estimate the dynamic states of the system. Second, the singular spectrum analysis (SSA) is used to detect the fault clearance time. Finally, the estimated states after the fault are used as the initial states of the 'event playback' to validate the dynamic model during the low‐frequency responses. The analytical basis of the proposed method is also provided by showing the existence and uniqueness of the trajectory of the underlying model. The effectiveness of the proposed approach is demonstrated using the PSS/E. [ABSTRACT FROM AUTHOR]

In order to use a stand‐alone global navigation satellite system (GNSS) receiver to determine the stable instantaneous velocity, a new hybrid GNSS velocimetry approach combining carrier phase and Doppler measurements is proposed. This is a data fusion problem. The problem is expressed as a state‐space model, in which the deviation between the average velocity determined by the time difference carrier phase approach and the instantaneous velocity is represented by the uncertainty of the state model. In kinematic applications, this uncertainty is often variant and hard to be known in advance, a predefined process noise level of the state model is often not sufficiently accurate in the whole working time. Here, an adaptive Kalman filtering approach is employed to fix this problem. To verify the proposed approach, one static experiment and two dynamic experiments with different sampling intervals are performed, separately. All results demonstrate the validity and stability of the proposed approach. [ABSTRACT FROM AUTHOR]

During the recursive calculate process of the cubature Kalman filter (CKF), the covariance matrix tends to lose positive definiteness and noise statistical characteristics are inaccurate, which results in inaccurate filtering or even filter divergence. This study presents an improved algorithm based on the CKF. The algorithm combines the square root filter algorithm and the Sage–Husa maximum a posterior noise estimator, which can ensure the non‐negative determination and symmetry of the covariance matrix and has the ability to deal with unknown and time‐varying noise statistical characteristics in the filtering process adaptively. In the multi‐dimension system, the noise covariance matrix may dissatisfy non‐negative definiteness and result in filter divergence, and then the noise covariance matrix estimator is improved. The analysis is verified by state estimation example of the non‐linear system, compared with the standard CKF, the accuracy of the adaptive square root CKF (ASRCKF) state estimation is increased by 63.13, 63.88, and 42.71%, respectively. Finally, the effectiveness of the ASRCKF is verified by the state estimation of the permanent magnet linear synchronous motor. [ABSTRACT FROM AUTHOR]

A hybrid particle swarm optimisation (PSO) and genetic algorithm (GA) aided Kalman filter (PSO‐GA‐KF) method for dynamic harmonic state estimation in the power system is investigated. The initial choice of states and KF's parameters, such as process and measurement error covariance matrices significantly affects the estimation precision. Aiming at this problem, a combination of PSO and GA (PSO‐GA) is proposed to optimise KF's parameters. In this hybrid algorithm, by replacing the gene mutation operator of GA, the PS algorithm mutation operator is constructed, which can adjust the evolution direction and range based on historical records and swarm records, leading to avoiding the blindness of GA mutation and reducing the probability of devious mutation and enhancing the velocity of evolution. Thus, the global search ability of the hybrid PSO‐GA can ensure KF has more accurate estimation of harmonics. To test the effectiveness of the algorithm, several time‐varying signals are simulated with harmonics and decaying DC components in the presence of amplitude drift and white noise. Simulation results show that the proposed hybrid algorithm has more accurate estimation, faster convergence and better robustness against noise in comparison with the conventional Kalman filter (KF), KF based on the maximum likelihood and PSO aided KF (PSO‐KF). [ABSTRACT FROM AUTHOR]

The objective of this paper presents a novel trajectory estimation (TE) system for mitigating the measurement noise and the undulation for the implementation of the touch interface. The methodology is based on an adaptive Kalman filter with a fuzzy neural network (FNN). The FNN is implemented as an artificial intelligence decision maker to regulate the smoothness of the output estimation. In real time, the FNN adaptively configures the filtering performance of the Kalman filter by analyzing the trajectory using the Fourier spectrum and the kinematic data. The result of this research is demonstrated on the touch interface that is implemented using the IR camera sensing method, and the proposed TE system is embedded to a coordinate processing module that converts the raw touch coordinates into the USB human interface device multi-touch protocol. A 70-inch projector screen is set up for the experiment, and the touch trajectories are tested with various magnitudes of measurement noise. The significance of the proposed TE system is demonstrated by showing the tracking delay and the distortion of the filtered trajectory are adaptively reduced. As the magnitude of the measurement noise increases, the proposed TE system detects the unwanted high-frequency component and decreases the filtering gain to stabilize the smoothness of the output trajectory. In conclusion, when compared to the recent researches, the proposed TE system shows lower tracking error and tolerates high magnitude of randomly appeared noise on the touch interface. [ABSTRACT FROM AUTHOR]

In this study, an improved square root adaptive cubature Kalman filter (ISRACKF) is proposed to improve the filter performance in terms of accuracy, computation efficiency, and robustness. Through the evaluated measure of non‐linearity value, the cubature rule under different accuracy levels can be adaptively selected in the dynamic process or measurement model. In this way, high accuracy can be maintained without sacrificing computation efficiency. Furthermore, the maximum correntropy criterion cost function can help improve the robustness of ISRACKF. The measure of non‐Gaussianity value is utilised to control the computation complexity of the robust iterative process as well. The stability proof of estimated state error and covariance is given. The comparison results of the target tracking problem and integrated navigation system demonstrate the superior performance of the proposed ISRACKF in this study. [ABSTRACT FROM AUTHOR]

To obtain an effective state estimator for industrial processes, estimator needs to be designed to match the characteristics of noise. In this study, a new filter is proposed focusing on asymmetric measurement noise with probable outliers. By learning a time‐varying skew t distribution using the variational Bayesian technique, the authors' method can estimate the system state and update the noise statistics simultaneously. A numerical simulation, as well as an experiment on the hybrid tank system, is conducted to demonstrate the performance. It shows that the proposed filter is superior to the existing solutions, especially when the statistics of measurements noise are unknown. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive Kalman filter (AKF) control algorithm for capacitive touch panels under the radiation effect of a commercial fluorescent lamp. The predicted covariance matrix of the proposed algorithm is timely updated by two-dimensional gesture compensation. It adaptively adjusts the filter correction manner between fast tracking and smoothing modes. The trajectory area and velocity concept builds up the compensation method and proves in real-time practice by a microprocessor unit. The electromagnetic radiation effect is investigated to obtain the lamp emission noise level. A comprehensive system structure provides the flexibility and efficiency in competing with different algorithms for comparison. A microprocessor unit completed the AKF method calculation in 8.23 ms under fluorescent lamp lightening condition in real time. All Python environments are implemented in the merit of hardware peripheral support, rich programming environments, and open source modules. [ABSTRACT FROM AUTHOR]

This study considers the dynamic state estimation of power systems with model uncertainties that might be caused by the unknown noise statistics or unpredicted changes to the model parameters. To deal with these issues, an innovation‐based estimator that is able to dynamically revise the statistics of system and measurement noise is proposed firstly. Then, based on the H∞ criteria for bounding the adverse influences on the estimation error of model uncertainties and unscented transform technique, an adaptive strategy is developed to adjust the estimation error covariance matrix under various conditions. Finally, by incorporating the proposed approaches and H∞ filter theory, a novel adaptive unscented H∞ filter is established to realise dynamic state estimation of power system against model uncertainties. Extensive simulation results obtained from the IEEE‐39 bus test system are presented to illustrate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract This study considers an asynchronous multirate data integration problem in the linear state space model with unknown and time-varying statistical parameters of the measurement noises. To improve performance of the multirate adaptive Kalman filter algorithm, a multi-sensor adaptive Kalman filtering algorithm based on variational Bayesian approximations has been developed in an asynchronous multirate multi-sensor integrated navigation system. The proposed filtering algorithm estimates measurement noise variances of the sensors adaptively and also it is robust to anomalous measurements of sensors and however, multirate adaptive Kalman filter is required to use an appropriate algorithm for outlier rejection to achieve a reliable and optimal estimation of position, velocity, and orientation. A navigation system composed of a strapdown inertial navigation system along with Doppler velocity log, inclinometer and depth meter with different sampling rates is designed to evaluate performance of multirate error state Kalman filter (MESKF) and multirate adaptive error state Kalman filter (MAESKF) algorithms and the proposed algorithm. Results of two experimental tests show that the average relative root mean square error (RMSE) of the position estimated by the proposed filtering algorithm can be decreased approximately 57% and 36% when compared to that of MESKF and MAESKF algorithms, respectively. Highlights • A multisensor adaptive Kalman filtering based on variational Bayesian is developed. • Asynchronous multirate multisensor integrated navigation improves performance of MAKF. • Proposed algorithm estimates measurement noise variances of the sensors adaptively. • Experimental results showed that the proposed algorithm is robust to outliers. [ABSTRACT FROM AUTHOR]

In order to incorporate the time smoothness of ionospheric delay to aid the cycle slip detection, an adaptive Kalman filter is developed based on variance component estimation. The correlations between measurements at neighboring epochs are fully considered in developing a filtering algorithm for colored measurement noise. Within this filtering framework, epoch-differenced ionospheric delays are predicted. Using this prediction, the potential cycle slips are repaired for triple-frequency signals of global navigation satellite systems. Cycle slips are repaired in a stepwise manner; i.e., for two extra wide lane combinations firstly and then for the third frequency. In the estimation for the third frequency, a stochastic model is followed in which the correlations between the ionospheric delay prediction errors and the errors in the epoch-differenced phase measurements are considered. The implementing details of the proposed method are tabulated. A real BeiDou Navigation Satellite System data set is used to check the performance of the proposed method. Most cycle slips, no matter trivial or nontrivial, can be estimated in float values with satisfactorily high accuracy and their integer values can hence be correctly obtained by simple rounding. To be more specific, all manually introduced nontrivial cycle slips are correctly repaired. [ABSTRACT FROM AUTHOR]

The paper presents a novel adaptive stator ground fault protection scheme with fault location capability for high-impedance grounded synchronous generators. The protection scheme uses already available neutral grounding signals in the existing subharmonic injection protection to obtain a Kalman adaptive filter (KAF) for real-time stator insulation parameter estimation. The KAF estimator yields a method of continuous tracking of stator insulation condition during healthy operations. This information is then used for real-time stator ground fault detection as well as fault location. The effectiveness of the proposed method is verified using extensive experiments performed on a lab-scale unit-connected generating station. [ABSTRACT FROM AUTHOR]

During the tracking, kernelized correlation filters may fail as the target is occluded seriously and goes out of view. To solve this problem, a long-term visual tracking algorithm based on adaptive correlation filters is proposed. First, we learn two correlation filters to locate the target and estimate the target scale, respectively. Meanwhile, we learn an independent target appearance correlation filter conservatively updated to know the occlusion degree of the target. Second, we combine the Kalman filter to predict and the support vector machine detector to redetect when tracking failure occurs, caused by the target undergoing severe occlusion or disappearing in the camera view. Third, to solve model drifts due to serious appearance changes of the target, we apply an adaptive model updating strategy to update the correlation filters and classifier. Extensive experimental results on the OTB2013 benchmark dataset demonstrate that our proposed method achieves the excellent overall performance against the nine state-of-the-art methods while running efficiently in real time. © 2018 SPIE and IS&T [DOI: 10.1117/1.JEI.27.5.053018] [ABSTRACT FROM AUTHOR]

This paper concerns the application of Huber-based robust unscented Kalman filter (HRUKF) in nonlinear system with non-Gaussian measurement noise. The tuning factor γ is key factor in determining the form of Huber cost function. Traditionally, γ is mainly determined by experience and/or experiments. It is hard to acquire optimal parameter or achieve an optimal filtering. To solve this problem, the influence of tuning factor γ on the performance of HRUKF is analyzed, and then, an adaptive strategy based on projection statistics algorithm for this parameter is proposed to improve filtering performance under the conditions that the measurement noise is contaminated by heavier tails and/or outliers. Simulation results for the problem of Reentry Vehicle Tracking demonstrate the superiority of the proposed method over the traditional ones. [ABSTRACT FROM AUTHOR]

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The broadband Kalman filter (BKF) and general Kalman filter (GKF) have been proposed for the application of acoustic system identification. Here, the authors present a multiband‐structured Kalman filter (MSKF) to speed up the convergence rate of BKF and GKF for highly correlated signal. A simplified version of MSKF (SMSKF) is also provided at the aim of reducing the complexity. It is shown that the BKF and GKF are the special cases of the proposed MSKF, and the SMSKF can be treated as the improved multiband‐structured subband adaptive filter algorithm with a variable regularisation matrix. The low‐complexity implementation of SMSKF, both in the fast filtering and matrix inversion operation, is discussed. Computer simulations confirm the performance advantage of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an approach to railway track fault monitoring using signal processing techniques based on signal separation. The measured vibration signal is detected by sensors during the movement of the train on tracks at various speeds. The detected signal can be processed by using digital signal processing techniques. The signal consists of information about the tracks along with noise by various other sources. This noise is estimated by variance and mean values. Initially, the noise is eliminated using an adaptive Kalman filter. Further, to extract a specific frequency band where the peaks of the peaks of the signal are exited, a Finite Impulse Response (FIR) filter is applied. Later the peaks are compared subsequently and the peaks above the threshold of vibrations are detected by using the null space search (NSP) method, which decompose the signal into a series of subcomponents and wastes according to their characteristics. Experimental studies of the signals observed from the railroad during the movement of the train have verified the effectiveness of the current approach for the railway fault monitoring system. [ABSTRACT FROM AUTHOR]

This paper focuses on the application of low-cost sensors for autonomous underwater vehicle (AUV). We propose an intelligent assistance positioning methodology by combining the modified incremental smoothing and mapping (iSAM) and constrained optimally pruned extreme learning machine (OP-ELM) for low-cost sensors, which makes full use of GPS data and produce a variety of correction models. Compared to relinearizing and variable reordering by period batch step in the original iSAM, modified iSAM is implemented variable reordering alone and conducted adaptive relinearization when the value of local Chi-square exceeded a certain threshold. Meanwhile, a novel constrained OP-ELM is presented by mapping the output to the constraint space, which provides full guarantee for generating reliable correction model. When GPS is valid, the constrained OP-ELM is applied to the low-cost sensors to generate correction model. Simultaneous, the correction model of measurement for modified iSAM is also given by this way. Once GPS becomes invalid, the correction models are used to amend the low-cost sensors data and measurement model for getting more accurate location information. Experimental results and analysis show that the proposed method outperforms the traditional algorithm, which RMSE can improve by at most 83.8% than Extended Kalman Filter's (EKF). [ABSTRACT FROM AUTHOR]

An motor torque fault diagnosis for four wheel independent motor-drive vehicle is presented in this paper. Focusing on the fault that the actual motor torques differ from the motor torques commanded by vehicle control unit, the fault parameters are introduced to represent the differences and a nonlinear vehicle dynamics model is built. This model considers vehicle body nonlinear dynamics, wheel dynamics, and tire nonlinear characteristics, and the fault parameters are set to be the coefficients of motor torque commands. Then the motor fault diagnosis problem is converted to these fault parameters identification problem, and unscented Kalman filter is implemented to identify them in real time. With the road test data of a four wheel independent motor-drive vehicle, the fault diagnosis method is testified to be effective both in normal and extreme handling situations. [ABSTRACT FROM AUTHOR]

Information fusion method of INS/GPS navigation system based on filtering technology is a research focus at present. In order to improve the precision of navigation information, a navigation technology based on Adaptive Kalman Filter with attenuation factor is proposed to restrain noise in this paper. The algorithm continuously updates the measurement noise variance and processes noise variance of the system by collecting the estimated and measured values, and this method can suppress white noise. Because a measured value closer to the current time would more accurately reflect the characteristics of the noise, an attenuation factor is introduced to increase the weight of the current value, in order to deal with the noise variance caused by environment disturbance. To validate the effectiveness of the proposed algorithm, a series of road tests are carried out in urban environment. The GPS and IMU data of the experiments were collected and processed by dSPACE and MATLAB/Simulink. Based on the test results, the accuracy of the proposed algorithm is 20% higher than that of a traditional Adaptive Kalman Filter. It also shows that the precision of the integrated navigation can be improved due to the reduction of the influence of environment noise. [ABSTRACT FROM AUTHOR]