Measurement Noise Statistics Research Articles

Artificial bee colony–based Kalman filter hybridization for three–dimensional position estimation of a quadrotor

Purpose The purpose of this paper is to introduce an artificial bee colony-based Kalman filter algorithm along with an extended objective function to ensure the optimality of the estimator of the quadrotor in the presence of unknown measurement noise statistics. Design/methodology/approach Six degree-of-freedom mathematical model of the quadrotor is derived. Position controller for the quadrotor is designed. Kalman filter-based estimation algorithm is implemented in the sensor feedback loop. Artificial bee colony-based hybrid algorithm is used as an optimization method to handle the unknown noise statistics. Existing objective function is extended with a penalty term. Mathematical proof of the extended objective function is derived. Results of the proposed algorithm is compared with de facto genetic algorithm-based Kalman filter. Findings Artificial bee colony algorithm-based Kalman filter and extended objective function duo are able to optimize the measurement noise covariance matrix with an absolute error as low as 0.001 [m2]. Proposed method and function is capable of reducing the noise from 2 to 0.09 [m] for x-axis, 3.4 to 0.14 [m] for y-axis and 3.7 to 0.2 [m] for z-axis, respectively. Originality/value The motivation behind this paper is to bring a novel optimization-based solution for the estimation problem of the quadrotor when the measurement noise statistics are unknown along with an extended objective function to prevent the infeasible solutions with mathematical convergence analysis.

Model set adaptive filtering algorithm using variational Bayesian approximations and R\xe9nyi information divergence

The paper presents a model set adaptive filtering algorithm based on variational Bayesian approximation (MSA-VB) for the target tracking system with the model and noise uncertainties. The Rényi information divergence, as a criterion, is to choose the best match model that has the minimum divergence between candidate models and true mode. Subsequently, the model-conditioned estimation based on variational Bayesian approximation is proposed to estimate system state and measurement noise variances. To deal with the coupled noise intractability, the moments matching technique is used to obtain the mixed statistics of measurement noise at the fusion stage. The proposed algorithm is compared with the interacting multiple models (IMM) algorithm and the variational Bayesian-interacting multiple models (IMM-VB) algorithm via two scenarios for maneuvering target tracking, and simulation results show that the MSA-VB has improved estimation and tracking performance.

Real-Time Nonlinear Characterization of Soft Tissue Mechanical Properties

Online soft tissue characterization is important for robotic-assisted minimally invasive surgery to achieve precise and stable robotic control with haptic feedback. This paper presents a new nonlinear recursive adaptive filtering methodology for online nonlinear soft tissue characterization. An adaptive unscented Kalman filter is developed based on the Hunt-Crossley model by windowing approximation to online estimate system and measurement noise covariances. To improve the accuracy of noise covariance estimations, a recursive formulation is subsequently developed for estimation of system and measurement noise covariances by introducing a weighting factor. This weighting factor is further modified to accommodate noise statistics of large variation which could be caused by rupture events and geometric discontinuities in robotic-assisted surgery. Simulations, experiments, and comparison analyses demonstrate that the proposed nonlinear recursive adaptive filtering methodology can characterize soft tissue parameters in the presence of system or measurement noise statistics in both small and large variations for robotic-assisted surgery. The proposed methodology can effectively estimate soft tissue parameters under system and measurement noises in both small and large variations, leading to improved filtering accuracy and robustness in comparison with UKF.

Robust adaptive filter using fuzzy logic for tightly‐coupled visual inertial odometry navigation system

In this study, a robust adaptive filter using fuzzy logic for tightly-coupled visual-inertial odometry (VIO) navigation system is proposed. First, the authors use the epipolar geometry and trifocal tensor geometry as the measurement models of the VIO navigation system, which can avoid calculating the three-dimensional position of feature points. Second, the camera poses corresponding to the three images are corrected in the filter to form a multi-state constraint Kalman filter. Finally, when the measurement noise statistics changes or the erroneous measurement occurs in practical applications, the proposed method utilises Takagi–Sugeno (T–S) fuzzy logic to determine a scalar factor according to the divergence degree parameter. Then, the scalar factor is applied to the innovation covariance matrix and the filter gain, which improves the navigation accuracy and robustness of the VIO navigation system. The experimental results testing with the publicly available real-world KITTI dataset demonstrate the effectiveness of the proposed method.

Multiple-Step Randomly Delayed Adaptive Robust Filter With Application to INS/VNS Integrated Navigation on Asteroid Missions

This paper develops a novel nonlinear adaptive robust filter called the multiple-step randomly delayed variational Bayesian adaptive high-degree cubature Huber-based filter (MRD-VBAHCHF) for a class of nonlinear stochastic systems whose measurements are randomly delayed by multiple sampling times and corrupted by contaminated Gaussian noise with unknown covariance. First, a system with randomly delayed measurement is modeled in terms of multiple Bernoulli random variables. Then, the multiple-step randomly delayed high-degree cubature Kalman filter (MRD-HCKF) is derived by employing the fifth-degree cubature rule to compute the mean and covariance of the nonlinear equations in the system model. Next, the MRD-HCKF is modified to the MRD-VBAHCHF by incorporating the variational Bayesian theory and Huber technique for estimating the measurement noise covariance online and suppressing the influence of non-Gaussian noise. Consequently, the proposed filter is not only adaptive to unknown measurement noise statistics but also robust to random measurement delays and non-Gaussian noise. Finally, the MRD-VBAHCHF is verified for use in inertial navigation system/visual navigation system (INS/VNS) integrated navigation on asteroid missions, and the results of Monte Carlo simulations demonstrate that the MRD-VBAHCHF outperforms the high-degree cubature Kalman filter (HCKF), the MRD-HCKF and the variational Bayesian adaptive high-degree cubature Huber-based filter (VBAHCHF), thus showing the superiority of the proposed filter.

An Adaptive Gaussian Sum Kalman Filter Based on a Partial Variational Bayesian Method

In this article, we address the online state estimation problem of linear discrete-time systems in the presence of inaccurate and slowly time-varying non-Gaussian measurement noise (NGMN). Recently, the variational Bayesian (VB) method has been successfully used to jointly estimate the system state along with the statistics of the unknown Gaussian measurement noise. However, we prove that the original VB method for the non-Gaussian state-space models, modeled by the Gaussian mixture distributions, is analytically intractable. To overcome this problem, we propose a partial VB-based adaptive Gaussian sum Kalman filter, which uses a feedback-based filtering framework to independently calculate the posterior distribution of the state and posterior distribution of the NGMN. Experimental results demonstrate the effectiveness of the proposed filter.

Data-Driven Modeling and UFIR-Based Outlet NO$_{x}$ Estimation for Diesel-Engine SCR Systems

An accurate and efficient model for selective catalytic reduction (SCR) systems plays an important role in diagnosis and control of diesel-engine after-treatment systems. In this paper, we investigate the data-driven modeling of SCR systems and outlet NO $_{x}$ concentration estimation based on the developed data-driven model and the algorithm of unbiased finite impulse response (UFIR) filtering. The structure used for the data-driven model is an autoregressive exogenous (ARX) model and the method of partial least square is utilized to identify the parameters of the corresponding ARX model. Moreover, the approach of fuzzy c-means is employed to partition the data and derive multiple local linear models with a better performance on approximating the system nonlinearities. Finally, the algorithm of UFIR filtering is adopted to estimate the outlet NO $_{x}$ concentration due to its strong robustness without the statistics of process and measurement noises. The performance of proposed approaches on SCR systems is validated with simulations based on experimental data. In addition, comparisons show the improvement of the adopted algorithm on the estimation accuracy.

Robust dynamic state estimation of power systems with model uncertainties based on adaptive unscented filter

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.

Adaptive Dual Extended Kalman Filter Based on Variational Bayesian Approximation for Joint Estimation of Lithium-Ion Battery State of Charge and Model Parameters

An accurate state of charge (SOC) estimation is vital for the safe operation and efficient management of lithium-ion batteries. At present, the extended Kalman filter (EKF) can accurately estimate the SOC under the condition of a precise battery model and deterministic noise statistics. However, in practical applications, the battery characteristics change with different operating conditions and the measurement noise statistics may vary with time, resulting in nonoptimal and even unreliable estimation of SOC by EKF. To improve the SOC estimation accuracy under uncertain measurement noise statistics, a variational Bayesian approximation-based adaptive dual extended Kalman filter (VB-ADEKF) is proposed in this paper. The variational Bayesian inference is integrated with the dual EKF (DEKF) to jointly estimate the lithium-ion battery parameters and SOC. Meanwhile, the measurement noise variances are simultaneously estimated in the SOC estimation process to compensate for the model uncertainties, so that the adaptability of the proposed algorithm to dynamic changes in battery characteristics is greatly improved. A constant current discharge test, a pulse current discharge test, and an urban dynamometer driving schedule (UDDS) test are performed to verify the effectiveness and superiority of the proposed algorithm by comparison with the DEKF algorithm. The experimental results show that the proposed VB-ADEKF algorithm outperforms the traditional DEKF algorithm in terms of SOC estimation accuracy, convergence rate, and robustness.

WiFi/PDR-integrated indoor localization using unconstrained smartphones

In this paper, we propose a WiFi/pedestrian dead reckoning (PDR)-integrated localization approach based on unscented Kalman filters (UKF). The UKF integrating WiFi localization with PDR is used for ultimate location estimation. Instead of setting process and measurement noise-related parameters empirically as previous works, the error covariance of user heading estimation in PDR state model can be accurately estimated by developing another UKF, while the measurement noise statistics in WiFi localization are estimated by deploying a kernel density estimation-based model. Another developed UKF is used for device attitude tracking in user heading estimation of PDR. Besides, in order to adapt the unconstrained carrying positions and orientations of smartphones, we propose a robust carrying position recognition method based on orientation invariant features. Experimental results show that the proposed WiFi/PDR-integrated localization approach may improve traditional approaches in terms of reliability and localization accuracy.

An ASVSF‐SLAM Algorithm with Time‐Varying Noise Statistics Based on MAP Creation and Weighted Exponent

The probability‐based filtering method has been extensively used for solving the simultaneous localization and mapping (SLAM) problem. Generally, the standard filter utilizes the system model and prior stochastic information to approximate the posterior state. However, in the real‐time situation, the noise statistics properties are relatively unknown, and the system is inaccurately modeled. Thus the filter divergence might occur in the integration system. Moreover, the expected accuracy might be challenging to be reached due to the absence of the responsive time‐varying of both the process and measurement noise statistic which naturally can enlarge the uncertainty in the continuous system. Consequently, the traditional strategy needs to be improved aiming to provide an ability to estimate those properties. In order to accomplish this issue, the new adaptive filter is proposed in this paper, termed as an adaptive smooth variable structure filter (ASVSF). Sequentially, the improved SVSF is derived and implemented; the process and measurement noise statistics are estimated by utilizing the maximum a posteriori (MAP) creation and the weighted exponent concept, and the covariance correction step is added based on the divergence suppression concept. In this paper the ASVSF is applied to overcome the SLAM problem of an autonomous mobile robot; henceforth it is abbreviated as an ASVSF‐SLAM algorithm. It is simulated and compared to the classical algorithm. The simulation results demonstrated that the proposed algorithm has better performance, stability, and effectiveness.

Robust Cubature Kalman Filter for Dynamic State Estimation of Synchronous Machines Under Unknown Measurement Noise Statistics

Kalman-type filtering techniques including cubature Kalman filter (CKF) does not work well in non-Gaussian environments, especially in the presence of outliers. To solve this problem, Huber's M-estimation based robust CKF (RCKF) is proposed for synchronous machines by combining the Huber's M-estimation theory with the classical CKF, which is capable of coping with the deterioration in performance and discretization of tracking curves when measurement noise statistics deviatefrom the prior noise statistics. The proposed RCKF algorithm has good adaptability to unknown measurement noise statistics characteristics including non-Gaussian measurement noise and outliers. The simulation results on the WSCC 3-machine 9-bus system and New England 16-machine 68-bus system verify the effectiveness of the proposed method and its advantage over the classical CKF.

An Advanced Cubature Information Filtering for Indoor Multiple Wideband Source Tracking With a Distributed Noise Statistics Estimator

Acoustic vector sensor (AVS) is an effective tool to tracking acoustic sources. However, for the problem of tracking multiple wideband sources using distributed AVS array (DAVS), there are still unsolved issues which include measurements-to-targets association and targets tracking under incorrect or unknown statistics of measurement noise. Joint probabilistic data association (JPDA) is an effective algorithm to solve data association between measurements and targets and JPDA based cubature information filter (MTCIF) is designed for nonlinear system. Meanwhile, noise statistics estimator (NSE) based on modified Sage-Husa maximum posterior (SHMP) is constructed to cope with incorrect or unknown statistics of measurement noise. Then, a two-step distributed information fusion based on weighted average consensus (WAC) is built for DAVS to improve the stability and accuracy of state estimator and NSE. Numerical simulations demonstrate the effectiveness of the proposed algorithms.

Application of improved fifth-degree cubature Kalman filter in the nonlinear initial alignment of strapdown inertial navigation system.

This paper addresses the state estimation of the nonlinear initial alignment of the strapdown inertial navigation system (SINS), which mainly focuses on the initial alignment on the swaying base and under the in-motion condition with the measurement uncertainties. In order to achieve a higher alignment precision, stronger numerical stability, and lower computational cost for the initial alignment of SINS on the swaying base, a new discrete large azimuth misalignment error model of SINS is established, and an improved fifth-degree cubature Kalman filter (5th-CKF) algorithm is proposed, which combines the 5th-CKF and a simplified dimensionality reduction filtering algorithm. The 5th-CKF is introduced to solve the nonlinear filtering problem, a simplified dimensionality reduction algorithm is derived to reduce the large calculation values of 5th-CKF. Furthermore, under the Bayesian framework, a novel filtering approach named the fifth-degree variational Bayesian (VB) adaptive cubature Kalman filter is deduced for the in-motion alignment with a large azimuth misalignment angle and unknown and time-varying measurement noise statistics, which combines the iterative VB approach and 5th-CKF. The 5th-CKF is exploited to handle the nonlinear initial alignment model, and the VB approach is utilized to iteratively estimate the sufficient statistics of the measurement noise. Mathematical simulation, turntable, and vehicle experiments are performed to demonstrate the effectiveness and the superiority of the proposed approaches.

Automatic EKF Tuning for UAS Path Following in Turbulent Air

By using two simultaneously working Extended Kalman Filters, a procedure is implemented in order to perform in a fully autonomous way the path following in turbulent air. To guarantee the robustness of the proposed algorithm, an automatic tuning procedure is proposed to determine optimal values of Process and Measurement Noise statistics. Such a procedure is based on both the characteristics of the disturbances and the desired flight path; in particular, a specific performance index is applied to tune filters. In this way control laws are adapted to the flight condition and these lead to an optimal path-following. This research represents an upload of previous papers. It allows eliminating the time expensive trial and error procedure usually employed to tune Extended Kalman Filters. Obviously, procedure results are optimal for ever flight condition.

Parallel model adaptive Kalman filtering for autonomous navigation with line-of-sight measurements

In this paper, a parallel model adaptive Kalman filtering algorithm is presented for multiple sensors estimation fusion when the measurement noise statistics are uncertain. As a typical adaptive filtering algorithm, the multiple model adaptive estimation tries to reduce the dependency of the filter on the noise parameters. It utilizes multiple models with different noise levels to estimate the state and combines the model-dependent estimates with model probability. However, with the increase in the number of active sensors, a large number of models are required to cover the entire range of the possible noise parameter values, which can become computationally infeasible. The main goal of this work is to incorporate the noise statistic estimator in the framework of the multiple model adaptive estimation, such that only two models are required for each sensor, which significantly reduce the complexity of the estimator. The advantage of the presented algorithm to deal with the model uncertainty is studied analytically. The high performance of the parallel model adaptive Kalman filtering for autonomous satellite navigation using inter-satellite line-of-sight measurements is illustrated in comparison with a robust Kalman filter, an intrinsically Bayesian robust Kalman filter, and the traditional multiple model adaptive estimation.

A Modified Extended Kalman Filter for a Two-Antenna GPS/INS Vehicular Navigation System

Recently, the integration of an inertial navigation system (INS) and the Global Positioning System (GPS) with a two-antenna GPS receiver has been suggested to improve the stability and accuracy in harsh environments. As is well known, the statistics of state process noise and measurement noise are critical factors to avoid numerical problems and obtain stable and accurate estimates. In this paper, a modified extended Kalman filter (EKF) is proposed by properly adapting the statistics of state process and observation noises through the innovation-based adaptive estimation (IAE) method. The impact of innovation perturbation produced by measurement outliers is found to account for positive feedback and numerical issues. Measurement noise covariance is updated based on a remodification algorithm according to measurement reliability specifications. An experimental field test was performed to demonstrate the robustness of the proposed state estimation method against dynamic model errors and measurement outliers.

Experimental Validation of an Unscented Kalman Filter for Estimating Transient Engine Exhaust Composition with Fourier Transform Infrared Spectroscopy

Fourier transform infrared (FTIR) spectroscopy is a prevalent technique for measuring the comprehensive chemical composition of engine emissions. However, its applicability to transient emissions is limited due to recirculation of exhaust from past engine cycles within a FTIR gas cell and nonstationarity of the infrared beam intensity. An unscented Kalman filter is developed to overcome these limitations and obtain accurate, time-resolved estimations of engine exhaust composition from FTIR measurements. Residence time distribution within the FTIR gas cell is modeled using the well-mixed assumption, while the Fourier transform of an interferogram generated from a linearly evolving, uniformly broadened absorption line is used to deduce transient gas cell composition values from FTIR measurements. The filter utilizes both models, as well as measurement noise statistics, to infer the composition of sample entering the FTIR gas cell during a measurement period. To validate the filter, FTIR measurements of air ...

A Consensus Nonlinear Filter With Measurement Uncertainty in Distributed Sensor Networks

This letter addresses the consensus-based nonlinear state estimation in distributed sensor networks with unknown measurement noise statistics. The existence of naive nodes and the communication constraint in sensor networks requires a hybrid consensus filtering method. In the frame of consensus filtering, a novel consensus nonlinear filtering approach named variational Bayesian consensus cubature Kalman filter (VB-CCKF) is proposed, in which the CKF is employed to handle the nonlinear state estimation and the VB approximation is adopted to iteratively estimate the sufficient statistics of the measurement noise covariance on each step. Simulations are performed in order to demonstrate the effectiveness of the proposed approach.

Unbiased Finite Impluse Response Filtering: An Iterative Alternative to Kalman Filtering Ignoring Noise and Initial Conditions

If a system and its observation are both represented in state space with linear equations, the system noise and the measurement noise are white, Gaussian, and mutually uncorrelated, and the system and measurement noise statistics are known exactly; then, a Kalman filter (KF) [1] with the same order as the system provides optimal state estimates in a way that is simple and fast and uses little memory. Because such estimators are of interest for designers, numerous linear and nonlinear problems have been solved using the KF, and many articles about KF applications appear every year. However, the KF is an infinite impulse response (IIR) filter [2]. Therefore, the KF performance may be poor if operational conditions are far from ideal [3]. Researchers working in the field of statistical signal processing and control are aware of the numerous issues facing the use of the KF in practice: insufficient robustness against mismodeling [4] and temporary uncertainties [2], the strong effect of the initial values [1], and high vulnerability to errors in the noise statistics [5]-[7].