Nonlinear Filtering Algorithm Research Articles

Sequential Monte Carlo methods for filtering of unobservable components of multidimensional diffusion Markov processes

AbstractThe problem of filtering of unobservable components x(t) of a multidimensional continuous diffusion Markov process zt=xt,yt, given the observations of the (multidimensional) process y(t) taken at discrete consecutive times with small time steps, is analytically investigated. On the base of that investigation the new algorithms for simulation of unobservable components, x(t), and the new algorithms of nonlinear filtering with the use of sequential Monte Carlo methods, or particle filters, are developed and suggested. The analytical investigation of observed quadratic variations is also developed. The new closed-form analytical formulae are obtained, which characterize dispersions of deviations of the observed quadratic variations and the accuracy of some estimates for x(t). As an illustrative example, estimation of volatility (for the problems of financial mathematics) is considered. The obtained new algorithms extend the range of applications of sequential Monte Carlo methods, or particle filters,...

The Nonsequential Fusion Method for Localization from Unscented Kalman Filter by Multistation Array Buoys

Based on special features of array buoy and the research field of location and tracking of underwater target, the research combines the highly adaptive nonlinear filtering algorithm unscented Kalman filter with the nonlinear programming of multistation array buoy positioning system. In accordance with the model of nonsequential target location, the research utilizes Unscented Transformation to update the measuring error and covariance matrix of state error, aiming at estimating the filtering of state variable and acquiring the object’s current state of motion. The research analyzes the positioning performance of algorithm, pursuit path, astringency, and other performance indexes of target-relevant parameter through numerical simulation experiment. From the result, the conclusion that multistation array buoy can complete the task of tracing target track very well can be reached, which provides theoretical foundation for putting the algorithm into engineering practice.

언센티드 칼만/FIR 하이브리드 필터를 이용한 실내 위치 추정

This paper proposes a new nonlinear filtering algorithm that combines the unscented Kalman filter (UKF) and the finite impulse response (FIR) filter. The proposed filter is called the unscented Kalman/FIR hybrid filter (UKFHF). In the UKFHF algorithm, the UKF is used as the main filter, which produces state estimates under ideal conditions. When failures of the UKF are detected, the FIR filter is operated. Using the output of the FIR filter, the UKF is reset and rebooted. In this way, the UKFHF recovers from failures. The proposed UKFHF is applied to indoor human localization using wireless sensor networks. Through simulations, the performance of the UKFHF is demonstrated in comparison with that of the UKF.

State Space Least Mean Fourth Algorithm for Dynamic State Estimation in Power Systems

Power system dynamic state estimation (DSE) has always been a critical problem in studying power systems. One of the essential parts of power systems are synchronous machines. In this work, we dealt with the problem of DSE of a synchronous machine by introducing a novel state space-based least mean fourth (SSLMF) algorithm. The rationale behind the proposed algorithm is the fact that a power system may encounter non-Gaussian disturbances/state errors and the least mean fourth algorithm is proven to be better in such environments. Moreover, we have also introduced a normalized version of the proposed algorithm, namely state space normalized least mean fourth (SSNLMF) algorithm to deal with the stability issue under Gaussian disturbances. Another motivation for developing the SSLMF algorithm is its simplicity as compared to other model-based nonlinear filtering algorithms such as Kalman filter, extended Kalman filter (EKF). Moreover, we also investigate the performance of the recently introduced state space least mean square (SSLMS). Performance of the SSLMF and the SSLMS is compared with existing EKF in both Gaussian and non-Gaussian noise environments. Extensive simulation results are presented which show superiority of the proposed algorithms, and hence, it verifies our rationale behind the work.

Design of real-time filter for the wheel force transducer

Purpose – Wheel force transducers (WFTs) have performance characteristics that make them attractive for applications in endurance evaluation of road vehicles, ride and handling optimization, tire development and vehicle dynamics. As a WFT is mounted on the the driven wheel, the loads on the wheel and the outputs of WFTs are usually nonlinearly related. Thus, a real-time filter is needed to measure the true loads on the wheel. Design/methodology/approach – In this paper, a new nonlinear filtering algorithm utilizing quadrature Kalman filter (QKF) is proposed to track the actual loads in real time through establishing the specific observation equations with Singer models. Findings – The simulation results show that the accuracy and the rapidity of QKF outperforms the capability of the unscented Kalman filter (UKF). Then, the dynamic tests on the MTS testing platform give the comparisons between the real-time QKF and the wavelet transform, where the former has superior dynamic accuracy. Finally, the practical tests of shifting and braking on a real vehicle confirm the effectiveness of QKF, which further validates the proposed method fitting reality. Originality/value – In this paper, a newly improved algorithm with QKF for WFT has been proposed and tested experimentally. As the wheel loads are always time-varying and complex, introducing Gaussian noise in the outputs of the transducer, WFT-suitable Singer model and WFT measurement equation base on a QKF are established. The experiment results show that QKF has advanced performance than the traditional UKF. Also, the road wheel test bed produced by MTS has been exploited as the test platform to demonstrate the dynamic efficiency of the proposed real-time filter under various operating conditions for a wide range of loads. And, the practical tests with the real vehicle are accomplished to verify the value and effectiveness of the proposed method.

Evaluation of nonlinear filtering for radar data tracking

Abstract Radar tracking plays an important role in the area of early warning and detection system, whose precision is closely connected with filtering algorithm. With the development of noise jamming technology in radar echo signal, linear filtering becomes more and more difficult to satisfy the demands of radar tracking, while nonlinear filtering can solve problems such as non-Gaussian noises. There exist a lot of nonlinear filtering algorithms at present, owning their particular characteristics. With this in mind, we provide a comprehensive overview of different nonlinear filtering algorithms in radar tracking, including basic ideas and concrete steps of them. For a more clear presentation, we also make comparisons of them from all sides. Through the analyses of different nonlinear data filters, we find that the unscented Kalman data filter (UKF) can achieve better performance than others. Therefore, we will simulate and show the performance of UKF, and performance of the extended Kalman data filter (EKF) under the same condition will be taken as comparison, whose accuracy was not ideal for radar tracking data filtering.

Two Second-Order Nonlinear Extended Kalman Particle Filter Algorithms

In algorithms of nonlinear Kalman filter, the so-called extended Kalman filter algorithm actually uses first-order Taylor expansion approach to transform a nonlinear system into a linear system. It is obvious that this algorithm will bring some systematic deviations because of ignoring nonlinearity of the system. This paper presents two extended Kalman filter algorithms for nonlinear systems, called second-order nonlinear Kalman particle filter algorithms, by means of second-order Taylor expansion and linearization approximation, and correspondingly two recursive formulas are derived. A simulation example is given to illustrate the effectiveness of two algorithms. It is shown that the extended Kalman particle filter algorithm based on second-order Taylor expansion has a more satisfactory performance in reducing systematic deviations and running time in comparison with the extended Kalman filter algorithm and the other second-order nonlinear Kalman particle filter algorithm.

Modified unscented Kalman Filter for nonlinear systems having linear subsystems

The Extended Kalman Filter (EKF) is the often used filtering algorithm for nonlinear systems. But it does not usually produce desirable results. Recently a new nonlinear filtering algorithm named as Unscented Kalman Filter (UKF) is introduced. In this paper, we propose a new modified Unscented Kalman Filter (MUKF) algorithm for nonlinear stochastic systems that are linear in some components. These nonlinear systems can be considered as having linear subsystems with parameters and aim is to estimate the system parameters. In simulation study, performance of the EKF, its known variant Modified Extended Kalman Filter (MEKF), UKF and the proposed MUKF is demonstrated for a nonlinear system that is linear in some components. The results show that MUKF gives the best solution for parameter identification problem

A robust fixed-lag smoothing algorithm for dynamic systems with correlated sensor malfunctions

Abstract A new robust fixed-lag smoothing algorithm for fault-tolerant signal processing in stochastic dynamic systems in the presence of correlated sensor malfunctions has been developed. The algorithm is developed using a state vector augmentation method and the Gaussian approximation of the current estimate probability density function. The algorithm can be used in the real-time fault-tolerant control systems as well as in radar tracking systems working in the complex interference environment. The performance of the developed algorithm are evaluated by simulations and compared with smoothing and nonlinear filtering algorithms.

Non-Gaussian Sensor Fusion Analysis with “Gaussian Mixture and Adaptive” Based Cubature Kalman Filtering for Unmanned Aerial Vehicle

In this paper, comparison of adaptive and robust non Gaussian sensor fusion INS/GNSS is proposed to solve specific problem of non linear non Gaussian time variant state space estimation with impulsive measurement noise, different algorithms are proposed based on the most recent approaches in non linear filtering during intentional and non intentional interferences caused by multiple sources, or by the GNSS receivers signal degradation. Non linear filters such as Extended Kalman filter EKF and the last developed Cubature based Kalman Filter are implemented to estimate the navigation flight states for UAV. A specific hypothesis assumes high non Gaussian scenario and low non Gaussian noise level. Especially, alpha stable impulsive noise is simulated and affects GNSS measurement. The modern non linear filter algorithm called Cubature Kalman Filter CKF which provides more accurate estimation with more stability in Tracking data fusion application is compared with conventional non linear filters under non Gaussian constraints as a first step, thus, additional hypothesis is introduced which consists on Gaussian measurement outliers of each non Gaussian densities. In our work, Gaussian sum filtering and adaptive fading algorithms are proposed to solve the problem of IMU/GNSS integration in denied environment. CKF is compared with EKF in ideal conditions and during GNSS impulsive interferences modeled as non Gaussian noises “Sum of Gaussian” supposed to occur during specific interval of time, during the same interval, we assume additional denied environment which consists on the vari\ation of the Gaussian sum noise covariance, then, innovation based adaptive fading approach is selected and used to modify the covariance calculation of the parallel non linear filters performed in this work. Two important results are carried out depending on the variation of the Gaussian mixture density modeled in this work. original results are observed, discussed with real perspectives in navigation data fusion for real time applications under multiple denied environment conditions.

The Application of Adaptive Square Root Cubature Particle Filtering Algorithm in Initial Alignment of Large Azimuth Misalignment in SINS

The error model of Strap-down Inertial Navigation System (SINS) initial alignment is nonlinear under large azimuth misalignment angle condition, and it could be processed by the Particle Filter (PF) algorithm. Because the importance density function of the standard particle filter algorithm is difficult to select, a new algorithm of the Cubature Particle Filter (CPF) is proposed in this paper. In the new algorithm, the importance density function of standard particle filter is obtained by Adaptive Square root Cubature Kalman Filter (ASCKF), square root decomposition is chosen to enhance the numerical robustness and ensure that the state covariance matrix is positive definite. To meet the realtime requirement, the adaptive factor is introduced to control system model error. As the computer simulation results are shown that this algorithm could reduce the effect of inaccurate noise statistical model and it is a very effective nonlinear filtering algorithm.

Solving the problem of structural stochastic identification of nonlinear discrete dynamic multistructural objects

Methods of structural stochastic identification of nonlinear discrete dynamic objects are shown to be a topical subject of study. The general structure of an identification algorithm leveraging nonlinear filtering algorithms is proposed. Synthesis of the structural identification algorithm that uses the criterion of the minimum of the autocorrelation residual function is considered. A numerical example that shows the proposed approach is efficient is considered.

Enhanced Modified Polar Coordinates Filter Applied to Bearing Only Tracking

Two new algorithms are presented in this paper to solve the bearing only tracking problem, by using the recently proposed algorithms for nonlinear filtering, which are the Unscented Kalman Filter (UKF) and the Cubature Kalman Filter (CKF). These filters are used to solve the high intrinsic nonlinearity in the modified polar coordinates dynamic model. The resulting filters, named the Modified Polar Unscented Kalman Filter (MPUKF) and the Modified Polar Cubature Kalman Filter (MPCKF) are applied to the two dimensional bearing-only tracking problem. The estimation performance of these nonlinear filters is assessed by means of the root mean square error (RMSE). The simulation results show that these new filters are more efficient than other similar filters, such as the Modified Polar Extended Kalman Filter (MPEKF). Compared to this filter, the MPUKF and the MPCKF are, in particular, non-sensitive to the initial range and more stable, by using a dedicated initialization procedure, proposed in this paper.

Multi‐moment statistical characterization and nonlinear filtering of chaos

PurposeThe purpose of this paper is to provide the results of investigation of multi‐moment statistical characteristics of chaos and apply them to improve the accuracy of nonlinear algorithms for chaos filtering for real‐time applications.Design/methodology/approachThe approach to find multi‐moment statistical properties of chaos‐multi‐moment cumulant (covariance) functions of higher order is a generalization of the previously proposed (by the authors) “degenerated cumulant equations” method. Those multi‐moment cumulants functions are applied in the generalization of the Stratonovich‐Kushner equations (SKE) for the optimum algorithm of nonlinear filtering of chaos as well as for synthesis of the quasi‐optimum algorithms.FindingsResults are presented to investigate the multi‐moment statistical properties of chaos and formulate the theoretical background for synthesis of multi‐moment optimum and quasi‐optimum algorithms for nonlinear filtering of chaos with the improved accuracy in the presence of additive white noise.Originality/valueThe paper presents new theoretical results of the statistical description of chaos, previously partially reported only from experimental studies. A novel approach for chaos filtering is also presented. The proposed approach is dedicated to further improvement of the filtering accuracy for the case of low (less than one) SNR scenarios and is important for implementation in real‐time processing. As an important practical example, the new modified EKF algorithm is proposed with the rather opportunistic characteristics of the filtering fidelity together with algorithm complexity – practically the same as the “classic” one‐moment EKF algorithm.

Square Root Receding Horizon Information Filters for Nonlinear Dynamic System Models

New nonlinear filtering algorithms are designed based on a receding horizon strategy, i.e., a finite impulse response (FIR) structure, and square root information filtering to achieve high accuracy and good performance in empirical error covariance tests. The new nonlinear receding horizon filters reduce approximation errors in nonlinear filtering by considering a set of recent observations with non-informative initial conditions. By applying information filtering, we are able to manage the non-informative initial conditions, and thus propose the square root version of the algorithm as a means of retaining the positive definiteness of the error covariance. Based on the proposed strategy, we then implement known nonlinear filtering frameworks. Simulation results confirm that the new nonlinear receding horizon filters outperform existing nonlinear filters in well-known nonlinear examples.

Rapid transfer alignment of laser SINS using quaternion based angular measurement

A novel rapid transfer alignment algorithm for laser strapdown inertial navigation system (SINS) is studied. Transfer alignment have typically relied on velocity measurements from the master SINS as the source of alignment information, but lever arm error must be compensated accurately while velocity information is utilized, all most every quaternion based error model is nonlinear, so nonlinear filtering algorithms are need, suffering from computational complex and large error. Aim at these problems, a novel improved rapid transfer alignment algorithm formulation is presented, applying quaternion to built the process and measurement models, the improvement employs a special manipulation of the measurement equation results in a linear pseudo-measurement equation, thus the classical linear Kalman filter is employed to estimate the state, need not lever arm error compensation, results in the reduce of computational burden. Observability analysis of this new transfer alignment algorithm has been done based on the piece-wise constant system (PWCS) method, results show that the presented algorithm can accomplish the initial alignment task perfectly. A transfer alignment simulation system is also developed for the evaluation and analysis of the presented algorithm, simulation results are confirmed with the theoretical conclusion, which can achieve the transfer alignment accuracy about 1mrad within 10s.

Infrared Imaging Inspection of Rare Bird Species Based on Nonlinear Filter Algorithm

According to the characteristics of infrared imaging and rare bird species, a infrared imaging inspection method for rare bird species based on nonlinear filter algorithm has been proposed. Firstly, the CCD(charge-coupled device) sensors are used to obtain infrared video-data for rare birds, and then the captured images of rare birds are preprocessed to obtain the body axis length. Secondly, nonlinear filter algorithm, combined with physiological characteristics of rare bird species, is used to detect and identify the high-speed flying birds. Finally, the capabilities of EKF(extended Kalman filter) and PF(particle filter), the two kinds of nonlinear filter algorithm in inspecting have been researched deeply. Theoretical analysis and experiments demonstrate that the performance of PF is much better than EKF to inspect high-speed flying non-rigid object in complex environment.

On a Real-Time First-Order Difference Evaluation

Abstract A subject of this paper is a real-time evaluation of the first-order backward difference of a measured signal with noise. It is wellknown that a difference evaluation strongly increase a noise amplitude so the signal prefiltering is necessary. A very short review of practically used filters is given. To perform the pre-filtering operation one mainly apply linear filters characterized by their impulse response shape: finite impulse response (FIR) and infinite impulse response (IIR). To enhance the filtering operation one successfully apply so called adaptive filters and these described by non-linear characteristics. In this paper a simple non-linear filtering algorithm is proposed and examined in the first-order backward difference of a measured signal.

Statistical, neural, and combined filtering algorithms for applicative image noise

Correlations for the lower limit of the estimate error variance of images distorted by additive and applicative noise are obtained. The potential and actual estimate error variances for linear and nonlinear filtering algorithms are analyzed. A combined filtering algorithm for images distorted by applicative noise is developed.

Novel adaptive high-performance and nonlinear filtering algorithm for mixed noise removal

A novel adaptive high-performance and nonlinear filtering algorithm (AHPNFA) is proposed for the removal of mixed noise from corrupted images. This algorithm contains two stages: noise determining and noise removing. In the first stage, for each filtering window of the processed image, the center pixel and its nearest neighbors are modeled as a statistical variable. By exploiting Chebyshev's theorem, the fuzzy mean process is used to estimate adaptively the detection parameters that are required in determining whether the current pixel is corrupted or not. In the second stage, the Radon transform is performed to determine the texture direction probability density distributions of local areas of images, then using the texture direction probability density distributions and the local features of the image remove the noisy pixels. To demonstrate the advantages, the proposed AHPNFA is compared with the other test filters both visually and quantitatively. Simulation results show that the proposed AHPNFA has better values in important evaluation metrics; in particular, the computational complexity of the AHPNFA is about five to 11 times lower than the other test filters used in the comparison, therefore, the proposed AHPNFA has better performances.