Nonlinear Filtering Algorithm Research Articles

Boosted Fourier nonlinear filter and boosted even mirror Fourier nonlinear filter for active control of machinery noises

To overcome the limitations of the Fourier nonlinear filter and even mirror Fourier nonlinear filter-based adaptive algorithms for active noise control, this paper introduces boosted Fourier nonlinear filter and boosted even mirror Fourier nonlinear filter algorithms. Weight updating equations for the proposed algorithms are derived. Their performance is compared with Fourier nonlinear filter and even mirror Fourier nonlinear filter. Experimentally recorded bandsawand compressor noises are utilized for the analysis. The analysis is carried out for (a) linear primary and linear secondary paths, and (b) nonlinear primary path and linear secondary path. Visual inspection of residual noises after control and dB values of residual noises are utilized to understand the performance of the developed algorithms.

Integration of airborne magnetic and geological data for mineral prospectivity mapping in the Ambam-Amvom rainforest area, Archean Ntem Complex, southern Cameroon

The accurate mapping of mineral resources in rainforest areas is challenging due to dense vegetation and thick lateritic cover obscuring rock outcrops. This study utilized airborne magnetic survey data to map geological features and target mineral resources in the Ambam-Amvom area at the NW margin of the Congo craton. Linear and non-linear filtering algorithms were used, including reduction to the equator (RTE), upward continuation (UC) at 1000 m and 2000 m, first vertical derivative (FVD), and analytic signal (AS). Field surveys were carried out for sampling and petrographic investigations. The TMI map showed magnetic signals varying from -4489 nT to 2317 nT, while the RTE map displayed magnetic signals varying from -2984 nT to 3528 nT. The RTE-Reg map exhibited anomaly signal variations ranging between -2704 nT and +3637 nT and between -2829 and +3864 nT, respectively for UC at 1000 m and 2000 m. Geological structures were interpreted from the FVD, AS, and TMI-RTE images, and linear structures of regional extend mainly trend NW-SE, E-W, and NE-SW. Field investigations revealed that the study area comprises iron formations, amphibolite, gneiss, gabbro, biotite granite, and charnockite. The bulk chemical composition of iron formations showed a high content of TFe, averaging 39.80 wt.% for itabirite, 53.79 wt.% for hematite-geothite ore and 59.63 wt.% for quartz-hematite ore. The zones of peak magnetic anomalies coincided with the occurrence of the greenstone belt, and the integration of aeromagnetic and geological data led to the identification of three main target zones for iron ore minimization. High fracture density zones within the research were identified as high prospective targets for gold mineralization. The study's findings highlight the high potential of the Ntem Complex for mineral resources and provide valuable information for future research and development.

Probing robustness of nonlinear filter stability numerically using Sinkhorn divergence

Using the recently developed Sinkhorn algorithm for approximating the Wasserstein distance between probability distributions represented by Monte Carlo samples, we demonstrate exponential filter stability of two commonly used nonlinear filtering algorithms, namely, the particle filter and the ensemble Kalman filter, for deterministic dynamical systems. We also establish numerically a relation between filter stability and filter convergence by showing that the Wasserstein distance between filters with two different initial conditions is proportional to the bias or the RMSE of the filter.

Nonlinear Spline Versoria Prioritization Optimization Adaptive Filter for Alpha-Stable Clutter

The increasing demand for a better quality of service in radar and wireless communications has attracted research on interference suppression. Nonlinear filtering methods based on spline architecture have been widely utilized in signal processing due to their effectiveness against alpha-stable interference. However, existing nonlinear spline adaptive filter algorithms suffer from high steady-state misalignment. To achieve lower steady-state misalignment along with having comparable computational complexity, we propose a nonlinear spline Versoria prioritization optimization adaptive filter (SPOAF-MVC) for alpha-stable clutter in this article. Furthermore, we study the bound on learning rate and computational complexity for the proposed algorithm. Numerical simulations confirm the effectiveness and efficiency of the proposed SPOAF-MVC algorithm for alpha-stable clutter under the Wiener system identification.

Implementation of a C Library of Kalman Filters for Application on Embedded Systems

Having knowledge about the states of a system is an important component in most control systems. However, an exact measurement of the states cannot always be provided because it is either not technically possible or only possible with a significant effort. Therefore, state estimation plays an important role in control applications. The well-known and widely used Kalman filter is often employed for this purpose. This paper describes the implementation of nonlinear Kalman filter algorithms, the extended and the unscented Kalman filter with square-rooting, in the programming language C, that are suitable for the use on embedded systems. The implementations deal with single or double precision data types depending on the application. The newly implemented filters are demonstrated in the context of semi-active vehicle damper control and the estimation of the tire–road friction coefficient as application examples, providing real-time capability. Their per-formances were evaluated in tests on an electronic control unit and a rapid-prototyping platform.

Multi-AUV Cooperative Navigation Algorithm Based on Temporal Difference Method

To reduce the cooperative positioning error and improve the navigation accuracy, a single master–slave AUV cooperative navigation method is proposed in this paper, which mainly focuses on planning the optimal path of the master AUV by the time difference (TD) method, under the premise that the path of the slave AUV has been planned. First, the model of multi-AUV cooperative navigation is established, and the observable problem of the system is analyzed. Second, for the single master–slave AUV cooperative navigation system, a Markov decision process (MDP)-based multi-AUV cooperative navigation model is established, and the master AUV path planning method is designed based on the TD method. Finally, the extended Kalman filter (EKF) and unscented Kalman filter (UKF) nonlinear filtering algorithms are applied to simulate and verify the algorithm that is proposed in this paper. The results show that the theoretical positioning error of the slave AUV can be controlled to about 3.2m by planning the path of the master AUV using the TD method. This method can not only reduce the observation error and positioning error of the slave AUV during the whole cooperative navigation process, but also keep the relative measurement distance between the master AUV and the slave AUV within an appropriate range.

A Switched Variational Estimation Algorithm for Continuous Discrete Measurement Information Loss in Underwater Navigation: Linear versus Nonlinear

In various applications of automatic underwater vehicles (AUVs), it is necessary to acquire the real-time location and speed information of the AUV. However, the complicated and fluctuating marine environment leads to measurement information loss. The accuracy of noise measurement is vital for accurate state estimation, but it is difficult for traditional algorithms to acquire time-varying noise measurements. Due to inaccurate process models and measurement noise, the filtering performance becomes poor or even diverges. To address the problems above, a switched variational estimation filtering (SVEF) algorithm, which combines the advantages of both Gaussian filtering and the variational estimation (VE) method, is proposed. In SVEF, VE is embedded into a linear or nonlinear filtering algorithm. Owing to the continuous discrete underwater navigation model, the state vector is estimated by the SVEF in the case of measurement information loss, and the accurate position and velocity of the AUV are determined. The experimental results prove that the SVEF achieves better positioning precision and is more robust than other conventional algorithms for AUV applications.

Implementation of ensemble Kalman filter algorithm for underwater target tracking

ABSTRACT Surveillance of underwater for maritime warfare is traditionally being carried out by bearings-only tracking from many decades. The measurements used for state estimation here are nonlinear. Also the noise in the measurements and the process cannot be always Gaussian. The traditional nonlinear filtering algorithms like extended Kalman filter and modified gain extended Kalman filter use the linearisation of the system. The unscented Kalman filter (UKF) uses the sigma point approach based on Gaussian distribution to deal with nonlinearity. The particle filter (PF) uses the randomly generated particles based on the pdf of the state. PF is highly complex to implement and it also suffers from sample impoverishment. Hence, ensemble Kalman filter (EnKF) which is a simplified form of PF will be tried out for bearings-only tracking in this research work. The performance of EnKF is compared with PF and UKF and the results obtained using these filters in Matlab are presented.

Nonlinear Gaussian Filter with Multi-Step Colored Noise

Color noise is a special kind of noise often occurring in localization systems, and it is more suitable than the general Gaussian white noise to model time dependence due to time delay or high-frequency sampling. This paper derives a nonlinear Gaussian filtering framework for multi-step colored noise systems using noise whitening techniques and Bayes rule. Meanwhile, the cubature rule is used to solve the Gaussian-weighted integral in the proposed Gaussian filtering framework, resulting in an analytic form of posterior state estimate. Compared with the existing nonlinear filtering algorithms, the proposed method has obvious advantages in colored noise systems because it fully takes into account the time dependence of colored noise. Finally, the effectiveness and advantages of the proposed algorithm are verified with a classical target tracking system.

Real-time parameter identification of ship maneuvering response model based on nonlinear Gaussian Filter

In order to solve the problem of parameter identification of nonlinear ship motion model in ship autonomous navigation control, a real-time parameter identification method based on nonlinear Gaussian filtering algorithm and nonlinear ship response model is proposed. It is proved theoretically that the influence of parameter drift on parameter identification can be reduced by increasing the number of observers and filters, and the system identification accuracy can be improved. The validity of the proposed method is verified by parameter identification experiments based on Zig-zag motion simulation data of Mariner standard ship model. Simulation results show that compared with EKF, the nonlinear Gaussian filter algorithm can effectively improve the parameter identification accuracy and reduce the computational complexity. The application of parallel structure is helpful to improve the identification accuracy and convergence rate of nonlinear Gaussian filter algorithm.

Embedded real-time state observer implementation for lithium-ion cells using an electrochemical model and extended Kalman filter

Accurate knowledge of the current state of lithium-ion battery cells is crucial for enhanced operational management of battery electric vehicles. Electrochemistry-based models provide the unique ability to predict cell internal states for advanced state monitoring, such as the anode potential, being of great interest for preventing lithium plating during fast charging. Furthermore, they are extendable by electrochemistry-based descriptions of cell degradation mechanisms. However, unlike the widely used equivalent circuit models, they are more computationally expensive and therefore have been scarcely used in embedded systems for online applications. This work addresses an efficient implementation of the popular pseudo-two-dimensional (p2D) electrochemical model in combination with a nonlinear filtering algorithm on a state-of-the-art microcontroller for automotive applications. For the first time, it is shown that with a suitable discretization scheme for the finite-difference approximation, a state observer convergence duration below 40 ms can be achieved for constant current, constant voltage charging at a current rate of 2C, with fast recovery of even local states. The mean relative error of the model internal states is less than 2% compared to an about 15 times slower implementation. This works therefore contributes valuably to demonstrating fast and robust performance of online state estimation using electrochemical models.

Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise. Based on the cubature Kalman filter, we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise. The system states and the statistics of skew t noise distribution, including the shape matrix, the scale matrix, and the degree of freedom (DOF) are estimated jointly by employing variational Bayesian (VB) inference. The proposed method is validated in a target tracking example. Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.

Application of Transformed Cubature Quadrature Information Filtering in Distributed POS

For aerial earth observation system, the accuracy of motion parameters provided by airborne distributed position and orientation system (POS) is crucial to the observation load imaging quality. According to the working principle, slave systems of distributed POS rely on the master node information to realize error estimation and correction, and then to achieve multiple node high accuracy measurement. Due to the nonlinearity of the error model, nonlinear filtering algorithm is used to the estimation process. Then in order to achieve higher estimation performance, a transformed cubature quadrature information filtering algorithm is developed for distributed POS estimation. In this method, the contributions are located that: (1) spherical radial cubature rule and Gauss-Laguerre quadrature rule are used to generate sigma points; (2) orthogonal transformation is conducted on the sampling points to deal with nonlocal sampling; (3) information filtering framework is adopted to simplify filtering update process, then the algorithm is applied in distributed POS nonlinear transfer alignment estimation. By the flight test validation, the outcomes are found that the developed algorithm can enhance the distributed POS estimation accuracy effectively, including attitude, velocity, position accuracy, then can be used to loads imaging quality improvement.

Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation

For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.

Prevalence of shifted Rayleigh filter for passive surveillance in underwater

PurposeFrom many decades, bearings-only tracking (BOT) is the interested problem for researchers. This utilises nonlinear filtering methods for state estimation as there is only information about the target, i.e. bearing is a nonlinear measurement. The measurement bearing is tangentially related to the target state vector. There are many nonlinear filtering algorithms developed so far in the literature.Design/methodology/approachIn this research work, the recently developed nonlinear filtering algorithm, i.e. shifted Rayleigh filter (SRF), is applied to BOT.FindingsThe SRF is tested for two-dimensional BOT against various scenarios. The simulation results emphasise that the SRF performs well when compared to the standard nonlinear filtering algorithm, unscented Kalman filter (UKF).Originality/valueSRF utilises the nonlinearities present in the bearing measurement through the use of moment matching. The SRF is able to produce the solution in highly noisy environment, long ranges and high dimension tracking.

Nonlinear Filter for Simultaneous Localization and Mapping on a Matrix Lie Group Using IMU and Feature Measurements

Simultaneous localization and mapping (SLAM) is a process of concurrent estimation of the vehicle&#x2019;s pose and feature locations with respect to a frame of reference. This article proposes a computationally cheap geometric nonlinear SLAM filter algorithm structured to mimic the nonlinear motion dynamics of the true SLAM problem posed on the matrix Lie group of <inline-formula> <tex-math notation="LaTeX">$\mathbb {SLAM}_{n}(3)$ </tex-math></inline-formula>. The nonlinear filter on manifold is proposed in continuous form and it utilizes available measurements obtained from group velocity vectors, feature measurements, and an inertial measurement unit (IMU). The unknown bias attached to velocity measurements is successfully handled by the proposed estimator. Simulation results illustrate the robustness of the proposed filter in discrete form, demonstrating its utility for the six-degrees-of-freedom (6 DoF) pose estimation as well as feature estimation in three-dimensional (3-D) space. In addition, the quaternion representation of the nonlinear filter for SLAM is provided.

Research on underwater target tracking based on Gaussian Hermitian Kalman Particle filter algorithm

The underwater target tracking environment usually has the characteristics of strong nonlinearity and non-Gaussian. The target tracking problem usually uses the nonlinear filtering algorithm, which combines the nonlinear measurement model with the linear system dynamics. The primary goal of target tracking is to extract accurate information about the real-time state of the target from the noise nonlinear observation obtained by the sensor. A new Gaussian Hermitt Kalman particle filter algorithm (GHKF-PF) is used to improve the tracking accuracy of the particle filter algorithm (PF). GHKF-PF uses the GHKF sampling method to sample particles from the posterior distribution of the target, calculates the mean and covariance for each particle, and uses the mean and variance to guide sampling. In the simulation experiment, the uniform linear motion model of underwater 3D target in the environment of Gaussian mixture noise (GMN) is established, and the application of GHKF-PF algorithm in 3D space is realized, and the accuracy is higher than that of PF. In order to further verify the effectiveness of the algorithm, a six-dimensional uniform acceleration motion model is established and compared with the extended particle filter (EPF) algorithm and the unscented particle filter (UPF) algorithm. The simulation results show that the performance of the GHKF-PF algorithm is similar to that of the UPF algorithm and better than the EPF algorithm.

Locality-Sensitive Non-Linear Kalman Filter for Target Tracking

Target tracking (TT) with non-linear kalman filtering (NLKF) has recently become a very popular research area, particularly in the field of marine engineering and air traffic control. Contemporary NLKF algorithms have been very effective, in particular, with extensions and merging with a reduced root mean square error (RMSE) value. However, there are a number of issues that confront NLKF approaches, notably weakness in robustness, convergence speed, and tracking accuracy due to large initial error and weak observability. Furthermore, NLKF algorithms significantly results in error for high non-linear systems (NLS) because of the propagation of uncertainty. Again, there is a problem of estimating future states as a result of white noise. To handle these issues, the authors propose a novel non-linear filtering algorithm, called locality-sensitive NLKF (LSNLKF) that incorporates locality-sensitive adaptors into the structure of an integrated NLKF. They are the extended kalman filter (EKF) and the unscented kalman filter (UKF) for TT.

A Robust Unscented Kalman Filter applied to Ultra-wideband Positioning

ABSTRACT Ultra-wideband (UWB) is well suited for indoor positioning due to its high resolution and good penetration through objects. As one of nonlinear filter algorithms, unscented Kalman filter (UKF) is widely used to estimate the position. However, UKF cannot resist the effect of outliers. The performance of the filter algorithm will be inevitably influenced. In this study, a robust UKF (RUKF) method accompanied by hypothesis test and robust estimation is proposed. Furthermore, the simulation and measurement experiments are performed to verify the effectiveness and feasibility of the proposed RUKF. Simulation experiment results are given to demonstrate that the RUKF can effectively control the influences of the outliers being treated as systematic errors and large variance random errors. When the outliers come from the thick-tailed distribution, the robust estimation does not play a role, and the RUKF does not work well. The measured experiment results show that the outliers will be generated in the non-line-of-sight environment whose impact is abnormally serious. The robust estimation can provide relatively reliable optimised residuals and control the influences of the outliers caused by gross errors. We can believe that the proposed RUKF is effective to resist the effects of outliers and improves the positioning accuracy.

Guaranteed Performance Nonlinear Observer for Simultaneous Localization and Mapping

A geometric nonlinear observer algorithm for Simultaneous Localization and Mapping (SLAM) developed on the Lie group of \mathbb{SLAM}_{n}\left(3\right) is proposed. The presented novel solution estimates the vehicle's pose (i.e. attitude and position) with respect to landmarks simultaneously positioning the reference features in the global frame. The proposed estimator on manifold is characterized by predefined measures of transient and steady-state performance. Dynamically reducing boundaries guide the error function of the system to reduce asymptotically to the origin from its starting position within a large given set. The proposed observer has the ability to use the available velocity and feature measurements directly. Also, it compensates for unknown constant bias attached to velocity measurements. Unit-qauternion of the proposed observer is presented. Numerical results reveal effectiveness of the proposed observer. Keywords: Nonlinear filter algorithm, Nonlinear observer for Simultaneous Localization and Mapping, Nonlinear estimator, nonlinear SLAM observer on manifold, nonlinear SLAM filter on matrix Lie Group, observer design, asymptotic stability, systematic convergence, Prescribed performance function, pose estimation, attitude filter, position filter, feature filter, landmark filter, gradient based SLAM observer, gradient based observer for SLAM, adaptive estimate, SLAM observer, observer SLAM framework, equivariant observer, inertial vision unit, visual, SLAM filter, SE(3), SO(3).