Multiple Model Extended Kalman Filter Research Articles

Intelligent Bayesian regularization backpropagation neuro computing paradigm for state features estimation of underwater passive object

In underwater environments, the accurate estimation of state features for passive object is a critical aspect of various applications, including underwater robotics, surveillance, and environmental monitoring. This study presents an innovative neuro computing approach for instantaneous state features reckoning of passive marine object following dynamic Markov chains. This paper introduces the potential of intelligent Bayesian regularization backpropagation neuro computing (IBRBNC) for the precise estimation of state features of underwater passive object. The proposed paradigm combines the power of artificial neural network with Bayesian regularization technique to address the challenges associated with noisy and limited underwater sensor data. The IBRBNC paradigm leverages deep neural networks with a focus on backpropagation to model complex relationships in the underwater environment. Furthermore, Bayesian regularization is introduced to incorporate prior knowledge and mitigate overfitting, enhancing the model’s robustness and generalization capabilities. This dual approach results in a highly adaptive and intelligent system capable of accurately estimating the state features of passive object in real-time. To evaluate the efficacy of this intelligent computing approach, a controlled supervised maneuvering trajectory for underwater passive object is constructed. Real-time estimations of location, velocity, and turn rate for dynamic target are scrutinized across five distinct scenarios by varying the Gaussian observed noise’s standard deviation, aiming to minimize mean square errors (MSEs) between real and estimated values. The effectiveness of the proposed IBRBNC paradigm is demonstrated through extensive simulations and experimental trials. Results showcase its superiority over traditional nonlinear filtering methods like interacting multiple model extended Kalman filter (IMMEKF) and interacting multiple model unscented Kalman filter (IMMUKF), especially in the presence of noise, incomplete measurements and sparse data.

Vehicular Connectivity on Complex Trajectories: Roadway-Geometry Aware ISAC Beam-Tracking

In this paper, we propose sensing-assisted beamforming designs for vehicles on arbitrarily shaped roads by relying on integrated sensing and communication (ISAC) signalling. Specifically, we aim to address the limitations of conventional ISAC beam-tracking schemes that do not apply to complex road geometries. To improve the tracking accuracy and communication quality of service (QoS) in vehicle to infrastructure (V2I) networks, it is essential to model the complicated roadway geometry. To that end, we impose the curvilinear coordinate system (CCS) in an interacting multiple model extended Kalman filter (IMM-EKF) framework. By doing so, both the position and the motion of the vehicle on a complicated road can be explicitly modeled and precisely tracked attributing to the benefits from the CCS. Furthermore, an optimization problem is formulated to maximize the array gain by dynamically adjusting the array size and thereby controlling the beamwidth, which takes the performance loss caused by beam misalignment into account. Numerical simulations demonstrate that the roadway geometry-aware ISAC beamforming approach outperforms the communication-only-based and ISAC kinematic-only-based technique in tracking performance. Moreover, the effectiveness of the dynamic beamwidth design is also verified by our numerical results.

Water quality evolution mechanism modeling and health risk assessment based on stochastic hybrid dynamic systems

Water quality assessment analysis is an important technical means for water pollution prevention and control. In this research area, mechanism models and real observation data of water quality evolution are always used to perform water quality assessment. However, the existing water quality evolution mechanism modeling researches commonly use a single time-invariant model to model the water quality evolution process. It is inappropriate to directly describe the complex behavior of long-term water quality evolution with the existing models, since the evolution process contain different feature states, and the water quality evolution characteristics under these states are different. In addition, the existing water quality assessment methods are mostly methods for directly processing and calculating the observation data of water quality. This makes the existing methods difficult to effectively compensate for the contingency and randomness in the water quality evolution process, which leads to deviations and errors in performing the water quality assessment. Considering these deficiencies, this paper proposes a water quality evolution mechanism modeling and health risk assessment method based on stochastic hybrid dynamic systems (SHDS). Firstly, a hybrid water quality evolution mechanism (H-WQEM) model is established based on SHDS, and a hybrid improved fruit fly optimization algorithm (H-IFFOA) is proposed to identify the unknown parameters of the H-WQEM model. Then, an improved interacting multiple model extended Kalman filter algorithm (IIMM-EKF) is employed to estimate the probability distribution of the hybrid state of the H-WQEM model, including the probability distribution of different feature states of water bodies and the probability distribution of water quality indexes under these states. Finally, the health degree of water quality is proposed as an indicator to achieve a quantitative assessment of the water health risk status. Real observation data from a monitoring station at Baiyangwan in China is used to validate the effectiveness of the proposed method. The results show that the method can effectively describe the complex water quality evolution process, and reasonably assess the water quality health risk status.

State Estimation of an Underwater Markov Chain Maneuvering Target Using Intelligent Computing.

In this study, an application of deep learning-based neural computing is proposed for efficient real-time state estimation of the Markov chain underwater maneuvering object. The designed intelligent strategy is exploiting the strength of nonlinear autoregressive with an exogenous input (NARX) network model, which has the capability for estimating the dynamics of the systems that follow the discrete-time Markov chain. Nonlinear Bayesian filtering techniques are often applied for underwater maneuvering state estimation applications by following state-space methodology. The robustness and precision of NARX neural network are efficiently investigated for accurate state prediction of the passive Markov chain highly maneuvering underwater target. A continuous coordinated turning trajectory of an underwater maneuvering object is modeled for analyzing the performance of the neural computing paradigm. State estimation modeling is developed in the context of bearings only tracking technology in which the efficiency of the NARX neural network is investigated for ideal and complex ocean environments. Real-time position and velocity of maneuvering object are computed for five different cases by varying standard deviations of white Gaussian measured noise. Sufficient Monte Carlo simulation results validate the competence of NARX neural computing over conventional generalized pseudo-Bayesian filtering algorithms like an interacting multiple model extended Kalman filter and an interacting multiple model unscented Kalman filter.

Interacting multiple model cubature Kalman filter for geomagnetic/ infrared projectile attitude measurement

When GPS signals are interrupted artificially or by environmental interferences, it is impossible to determine the attitude of a spinning projectile using the conventional method. The geomagnetic field and atmospheric infrared radiation field are inherent physical properties of the Earth; in this study, corresponding geomagnetic and infrared attitude measurement models are established to improve reliability. Anticipating sensor output failure in the flight process, the interacting multiple model cubature Kalman filter (IMMCKF) algorithm is designed to improve the adaptability of the system. The effectiveness of the algorithm is verified by semi-physical experiments, which showed that the IMMCKF algorithm, with high accuracy and strong anti-interference, is significantly better than the cubature Kalman filter (CKF) and the interacting multiple model extended Kalman filter (IMMEKF).

Multiple model extended continuous ant colony filter applied to real-time wind estimation in a fixed-wing UAV

In this study, a new heuristic multiple model filter, called Multiple Model Extended Continuous Ant Colony Filter, is proposed to solve a nonlinear multiple model state estimation problem. In this filter, a bank of extended continuous ant colony filters are run in parallel to solve the multiple model estimation problem. The probability of each model is continually updated and consequently both the true model and the states of the nonlinear system are updated based on the weighted sum of the filters. The new multiple model filter is tested on an engineering problem. The problem is to estimate simultaneously the states of a fixed-wing unmanned aerial vehicle as well as the wind model, applied to the system. Four different wind models are considered and the proposed filter is unaware of the wind type. Then, observability of the states and the wind components are analyzed. Four new propositions are introduced and proved for unknown input observability, state and unknown input observability, the effect of time-varying unknown input matrix on the unknown input observability, and the effect of linearization errors on the state observability. Moreover, observability of the wind parameters is analyzed based on the nonlinear systems observability theory. Performance of the proposed filter is also evaluated in maneuvering flight and compared to a single extended continuous ant colony filter and a multiple model extended Kalman filter. A hardware-in-the-loop experiment is also performed to verify the real-time implementation capability of the suggested architecture.

Continuous Tracking of Targets for Stereoscopic HFSWR Based on IMM Filtering Combined with ELM

High frequency surface wave radar (HFSWR) plays an important role in marine surveillance on account of its ability to provide wide-range early warning detection. However, vessel target track breakages are common in large-scale marine monitoring, which limits the continuous tracking ability of HFSWR. The following are the possible reasons for track fracture: highly maneuverable vessels, dense channels, target occlusion, strong clutter/interference, long sampling intervals, and low detection probabilities. To solve this problem, we propose a long-term continuous tracking method for multiple targets with stereoscopic HFSWR based on an interacting multiple model extended Kalman filter (IMMEKF) combined with an extreme learning machine (ELM). When the trajectory obtained by IMMEKF breaks, a new section of the track will start on the basis of the observation data. For multiple-target tracking, a number of broken tracks can be obtained by IMMEKF tracking. Then the ELM classifies the segments from the same vessel by extracting different features including average velocity, average curvature, ratio of the arc length to the chord length, and wavelet coefficient. Both the simulation and the field experiment results validate the method presented here, showing that this method can achieve long-term continuous tracking for multiple vessels, with an average correct track segment association rate of over 91.2%, which is better than the tracking performance of conventional algorithms, especially when the vessels are in dense channels and strong clutter/interference area.

Kinematic and Dynamic Vehicle Model-Assisted Global Positioning Method for Autonomous Vehicles with Low-Cost GPS/Camera/In-Vehicle Sensors.

Real-time, precise and low-cost vehicular positioning systems associated with global continuous coordinates are needed for path planning and motion control in autonomous vehicles. However, existing positioning systems do not perform well in urban canyons, tunnels and indoor parking lots. To address this issue, this paper proposes a multi-sensor positioning system that combines a global positioning system (GPS), a camera and in-vehicle sensors assisted by kinematic and dynamic vehicle models. First, the system eliminates image blurring and removes false feature correspondences to ensure the local accuracy and stability of the visual simultaneous localisation and mapping (SLAM) algorithm. Next, the global GPS coordinates are transferred to a local coordinate system that is consistent with the visual SLAM process, and the GPS and visual SLAM tracks are calibrated with the improved weighted iterative closest point and least absolute deviation methods. Finally, an inverse coordinate system conversion is conducted to obtain the position in the global coordinate system. To improve the positioning accuracy, information from the in-vehicle sensors is fused with the interacting multiple-model extended Kalman filter based on kinematic and dynamic vehicle models. The developed algorithm was verified via intensive simulations and evaluated through experiments using KITTI benchmarks (A project of Karlsruhe Institute of Technology and Toyota Technological Institute at Chicago) and data captured using our autonomous vehicle platform. The results show that the proposed positioning system improves the accuracy and reliability of positioning in environments in which the Global Navigation Satellite System is not available. The developed system is suitable for the positioning and navigation of autonomous vehicles.

A Novel FEM Based T-S Fuzzy Particle Filtering for Bearings-Only Maneuvering Target Tracking.

In this paper, we propose a novel fuzzy expectation maximization (FEM) based Takagi-Sugeno (T-S) fuzzy particle filtering (FEMTS-PF) algorithm for a passive sensor system. In order to incorporate target spatial-temporal information into particle filtering, we introduce a T-S fuzzy modeling algorithm, in which an improved FEM approach is proposed to adaptively identify the premise parameters, and the model probability is adjusted by the premise membership functions. In the proposed FEM, the fuzzy parameter is derived by the fuzzy C-regressive model clustering method based on entropy and spatial-temporal characteristics, which can avoid the subjective influence caused by the artificial setting of the initial value when compared to the traditional FEM. Furthermore, using the proposed T-S fuzzy model, the algorithm samples particles, which can effectively reduce the particle degradation phenomenon and the parallel filtering, can realize the real-time performance of the algorithm. Finally, the results of the proposed algorithm are evaluated and compared to several existing filtering algorithms through a series of Monte Carlo simulations. The simulation results demonstrate that the proposed algorithm is more precise, robust and that it even has a faster convergence rate than the interacting multiple model unscented Kalman filter (IMMUKF), interacting multiple model extended Kalman filter (IMMEKF) and interacting multiple model Rao-Blackwellized particle filter (IMMRBPF).

A Speed and Flux Observer of Induction Motor Based on Extended Kalman Filter and Markov Chain

To improve the performance of sensorless induction motor (IM) drives, an adaptive speed and flux estimation method based on the multiple-model extended Kalman filter (EKF) with Markov chain for IMs is proposed in this paper. In this algorithm, the multiple model EKF for speed and flux estimation is established, and the transition of the models obeys the Markov chain and the estimation value is obtained by mixing the outputs of different models in different weightings, and the calculation of the weighting is researched. Simultaneously, the transition probability can be continuously self-tuned by the residual sequence, the prior information is modified by the posterior information, and the more accurate transition among the models is obtained. Therefore, the proposed method improves the model adaptability to the actual systems and the environmental variations, and reduces the speed estimation error. The correctness and the effectiveness of the proposed method are verified by the simulation and experimental results.

Received signal strength–based indoor localization using a robust interacting multiple model–extended Kalman filter algorithm

Due to the vast increase in location-based services, currently there exists an actual need of robust and reliable indoor localization solutions. Received signal strength localization is widely used due to its simplicity and availability in most mobile devices. The received signal strength channel model is defined by the propagation losses and the shadow fading. In real-life applications, these parameters might vary over time because of changes in the environment. Thus, to obtain a reliable localization solution, they have to be sequentially estimated. In this article, the problem of tracking a mobile node by received signal strength measurements is addressed, simultaneously estimating the model parameters. Particularly, a two-slope path loss model is assumed for the received signal strength observations, which provides a more realistic representation of the propagation channel. The proposed methodology considers a parallel interacting multiple model–based architecture for distance estimation, which is coupled with the on-line estimation of the model parameters and the final position determination via Kalman filtering. Numerical simulation results in realistic scenarios are provided to support the theoretical discussion and to show the enhanced performance of the new robust indoor localization approach. Additionally, experimental results using real data are reported to validate the technique.

Enhancement in Li-Ion Battery Cell State-of-Charge Estimation Under Uncertain Model Statistics

Accurate battery state-of-charge (SOC) estimation in real time is desired in many applications. Among other methods, the extended Kalman filter (EKF) allows for high-accuracy real-time tracking of the SOC. However, an accurate SOC model is needed to guarantee convergence. Additionally, knowledge of the statistics of the process noise and the measurement noise is needed for high-accuracy SOC estimation. In this paper, two methods, namely, the multiple-model EKF (MM-EKF) and the autocovariance least squares technique, are proposed for estimating the SOC of lithium-ion (Li-ion) battery cells. The first method has the advantage of minimizing the EKF algorithm's dependence on the correct assumptions of the measurement's noise statistics, thus, minimizing the impact of model mismatch. The MM-EKF assumes a number of hypotheses for the unknown measurement noise covariance. An EKF is assigned for each assumed measurement noise covariance. The SOC estimate is then obtained by probabilistically summing up the estimates of the hypothesized EKFs. On the other hand, the second method assumes that the measurement noise is unknown and determines its value from the statistics of the EKF. Given an initial and possibly wrong assumption of the measurement noise covariance, the method accounts for possible correlation in the measurement innovations. The estimated measurement noise covariance is subsequently used to obtain an optimal SOC estimate. The proposed methods are evaluated and compared with the conventional EKF method on experimental test data obtained from a 3.6-V Li-ion battery cell.

Adaptive Parameter Estimation of Blood Pressure Dynamics Subject to Vasoactive Drug Infusion

Dynamic modeling of arterial blood pressure change subject to vasoactive drug infusion can be a valuable tool for computerized decision support of drug administration as well as for automated closed-loop drug delivery to treat hypotension in emergency trauma care. A time-varying time-delayed first-order dynamic model is considered to describe blood pressure response due to continuous injection of the vasorestrictive drug phenylephrine (PHP). The patient-to-patient as well as intrapatient variability of the dynamic response is taken into account by online identification of the varying model parameters. A multiple-model extended Kalman filter (MMEKF) structure is developed for the real-time estimation of mean arterial pressure and the dynamic blood pressure response model to PHP infusion to assist treatment. Convergence analysis is carried out, along with comparison with offline identification methods. Static drug-response curves for dosage recommendation are obtained from the estimation of the model sensitivity parameter. Finally, a detection algorithm is proposed to identify abrupt model variations caused by sudden physiological changes, such as hemorrhage. The proposed MMEKF parameter estimation method and the hemorrhage detection algorithm are tested and validated using data from animal experiments on anesthetized healthy and hemorrhagic swine that are subject to PHP infusion.

Constrained state estimation for individual localization in wireless body sensor networks.

Wireless body sensor networks based on ultra-wideband radio have recently received much research attention due to its wide applications in health-care, security, sports and entertainment. Accurate localization is a fundamental problem to realize the development of effective location-aware applications above. In this paper the problem of constrained state estimation for individual localization in wireless body sensor networks is addressed. Priori knowledge about geometry among the on-body nodes as additional constraint is incorporated into the traditional filtering system. The analytical expression of state estimation with linear constraint to exploit the additional information is derived. Furthermore, for nonlinear constraint, first-order and second-order linearizations via Taylor series expansion are proposed to transform the nonlinear constraint to the linear case. Examples between the first-order and second-order nonlinear constrained filters based on interacting multiple model extended kalman filter (IMM-EKF) show that the second-order solution for higher order nonlinearity as present in this paper outperforms the first-order solution, and constrained IMM-EKF obtains superior estimation than IMM-EKF without constraint. Another brownian motion individual localization example also illustrates the effectiveness of constrained nonlinear iterative least square (NILS), which gets better filtering performance than NILS without constraint.

Bearings-only maneuvering target tracking based on truncated quadrature Kalman filtering

In this paper, a novel bearings-only maneuvering target tracking algorithm based on truncated quadrature Kalman filtering (TQKF) is proposed. In the proposed method, when the target maneuvers, in order to reduce the effect on performance duo to the increasing variance of the prior distribution, a modified prior distribution based on the current measurement is proposed. In the update step, the first two moments of the modified prior distribution is approximately estimated based on the least square estimation method and Gauss–Hermite quadrature rule, and the posterior distribution is jointly updated by using the prior distribution and the modified prior distribution. Moreover, in order to adaptively choose the estimated results obtained by the prior PDF and the truncated prior PDF, a fuzzy logic approach in which a Gaussian membership function is employed is proposed to determine the weight α. Finally, the experiment results show that the proposed algorithm results in more accurate tracking than the existing one, namely, the unscented Kalman filter (UKF), the quadrature Kalman filter (QKF), interact multiple model extended Kalman filter (IMMEKF) and multiple model Rao–Blackwellized particle filter (MMRBPF).

Research on Robust Performance of Speed-Sensorless Vector Control for the Induction Motor Using an Interfacing Multiple-Model Extended Kalman Filter

The interfacing multiple-model extended Kalman filter (IMM-EKF) is proposed here as a modification of the extended Kalman filter (EKF). In this algorithm, two multiple-model EKF groups are built, one group is the optimum model, and the other is the noise model. Each model group is created by multiple models, and it will get good performance at stable state and robust ability when disturbance occurred. The algorithm gets the estimation value by mixing the outputs of the different model in different weightings, and the calculation of weightings is researched. Whether the IMM-EKF can give better estimation performances and robust ability than the EKF for speed estimation of induction machines is explored in this paper. Via simulations and experiments, estimated error and the change of flux linkage by disturbance based on the IMM-EKF and EKF is compared. The simulation results show that the IMM-EKF has the better estimation performance of antigross error than the EKF.

Estimation of lateral tire–road forces and sideslip angle for electric vehicles using interacting multiple model filter approach

Vehicle control systems require certain vehicle information (e.g., tire–road forces and vehicle sideslip angle) concerning vehicle-dynamic parameters and vehicle–road interaction, which is difficult to measure directly for both technical and economedic reasons. This paper proposes a novel method to estimate lateral tire–road forces and vehicle sideslip angle by utilizing real-time measurements. The estimation method is based on an interacting multiple model (IMM) filter that integrates in-vehicle sensors of in-wheel-motor-driven electric vehicles to adapt multiple vehicle–road system models to variable driving conditions. Based on a four-wheel nonlinear vehicle dynamics model (NVDM) considering extended roll dynamics and load transfer, the vehicle–road system model set of the IMM filter is consists of a linear tire model based NVDM and a nonlinear Dugoff tire model based NVDM. Therefore, the IMM filter can integrate the estimates from two kinds of different vehicle–road system models to improve estimation accuracy. To address system nonlinearities and un-modeled dynamics, the interacting multiple model-unscented Kalman filter (IMM-UKF) and the interacting multiple model-extended Kalman filter (IMM-EKF) are investigated and compared simultaneously. Simulation using Matlab/Simulink-Carsim is carried out to verify the effectiveness of the proposed estimation methods. The results show that the developed estimation methods can accurately estimate lateral tire–road forces and the vehicle sideslip angle.

Bearing-Only Maneuvering Mobile Tracking With Nonlinear Filtering Algorithms in Wireless Sensor Networks

Mobile node localization is important to offer wireless services in vehicular communication applications. Some typical methods realize the mobile node tracking through data fusion from time of arrival (TOA) and received signal strength (RSS) measurements provided by sensor nodes or base stations (BSs). Although the TOA/RSS method is not expensive under a concern of cost, it is very sensitive to multipath signal propagation effects. As the technology of angle of arrival (AOA) antennas is showing a rapid progress, we turn to consider AOA estimation. In this paper, the nonlinear extended Kalman filter (EKF) and the particle filter (PF) along with a three-model interacting multiple model (IMM) algorithm are utilized and compared for maneuvering mobile station (MS) tracking with bearing-only measurements. A coordinated turn model is used to improve the tracking performance since the MS frequently turns in the streets. We also propose an efficient method for resampling particles to alleviate the degeneracy effect of particle propagation in the interacting multiple model particle filter (IMMPF) algorithm. Moreover, a BS sensor selection scheme is also exploited for the long-haul MS tracking case which often changes BSs in a wireless vehicular sensor network. Numerical simulations show that the three-model IMMPF algorithm outperforms the interacting multiple model extended Kalman filter algorithm and achieves a root-mean-square tracking performance which is quite close to the posterior Cramer-Rao lower bound.

Moving target localization in indoor wireless sensor networks mixed with LOS/NLOS situations

Indoor target localization is an essential and fundamental issue for wireless sensor networks (WSN). However, it is rather difficult for WSN to maintain the localization accuracy in line-of-sight (LOS) and non-line-of-sight (NLOS) mixed environment. NLOS propagation always leads to larger ranging error than LOS does. When the target moves in the rooms and corridors, the signal transmission state will switch frequently between LOS and NLOS. It is a challenging task to deal with this situation because the ranging error characteristics under LOS and NLOS conditions are quite different. In this paper, we propose an interacting multiple model-extended Kalman filter (IMM-EKF) algorithm to improve the localization accuracy for moving target in indoor environment. In the IMM structure, two Kalman filters (KF) are adopted in parallel to accurately smoothen the distance measurement. The proposed algorithm can adapt to the dynamically changing condition between LOS and NLOS due to the two KFs' interaction so that large NLOS ranging errors are further reduced. Once the estimated ranges are obtained, the EKF is employed to estimate the target's location. Empirical measurement results are obtained from typical office environment to verify the effectiveness of the proposed algorithm. Experimental results illustrate that the IMM smoother can efficiently mitigate the NLOS effects on ranging errors and achieve high localization accuracy.

Comparison of Ballistic-Coefficient-Based Estimation Algorithms for Precise Tracking of a Re-Entry Vehicle and its Impact Point Prediction

This paper studies the problem of tracking a re-entry vehicle (RV) in order to predict its impact point on the ground. Re-entry target dynamics combined with super-high speed has a complex non-linearity due to ballistic coefficient variations. However, it is difficult to construct a database for the ballistic coefficient of a unknown vehicle for a wide range of variations, thus the reliability of target tracking performance cannot be guaranteed if accurate ballistic coefficient estimation is not achieved. Various techniques for ballistic coefficient estimation have been previously proposed, but limitations exist for the estimation of non-linear parts accurately without obtaining prior information. In this paper we propose the ballistic coefficient <TEX>${\beta}$</TEX> model-based interacting multiple model-extended Kalman filter (<TEX>${\beta}$</TEX>-IMM-EKF) for precise tracking of an RV. To evaluate the performance, other ballistic coefficient model based filters, which are gamma augmented filter, gamma bootstrapped filter were compared and assessed with the proposed <TEX>${\beta}$</TEX>-IMM-EKF for precise tracking of an RV.