Interacting Multiple Model Filter Research Articles

Vehicle Sideslip Angle estimation under critical road conditions via nonlinear Kalman filter-based state-dependent Interacting Multiple Model approach

The knowledge of Vehicle Sideslip Angle (VSA) can play an essential role in active safety vehicle control systems. However, due to the high costs of sensing instruments, this information is difficult to be directly measured onboard of series production vehicles, restricting de facto its application in practice. It follows that there is a need for online VSA estimation methods only based on available measurements from low-cost sensors. From this perspective, this work proposes a strategy based on Interacting Multiple Model (IMM) filters, which does not require tyre–road friction coefficient knowledge. By integrating the available onboard sensor data, the IMM estimates relevant information in different driving conditions leveraging a 2-Degrees Of Freedom (DOF) single-track vehicle model embedding a Dugoff tyre representation. Two alternative IMM algorithms based on the Extended (EKF) and Unscented Kalman filter (UKF) are developed. Moreover, while usually the transition probabilities among models in classical IMMs are fixed and set on prior information and/or dedicated analysis, here these conservative hypotheses are relaxed introducing a state-dependent Markov transition matrix based on a novel model switching algorithm. The effectiveness of the new proposed methods is evaluated on extensive non-trivial simulation scenarios through a Monte Carlo analysis exploiting an accurate 15-DOF vehicle model via a purposely designed high-fidelity co-simulation platform embedding the dSPACE software Automotive Simulation Model (ASM). Results provide a meaningful comparative performance analysis between the IMMEKF and IMMUKF solutions, as well as with respect to traditional IMM based on constant probabilities transition matrix, blue in both the EKF and UKF configuration. Finally, the developed IMM-based estimation strategy is tested in two realistic driving scenarios to assess the VSA estimation accuracy in case of abrupt changes in road surface conditions.

Multiple model estimation under perspective of random-fuzzy dual interpretation of unknown uncertainty

This study considered the problem of multiple model estimation from the perspective of sigma-max inference (probability - possibility inference), while focusing on discovering whether certain of the unknown quantities involved could be more faithfully modeled as fuzzy uncertainty. Two related key issues were addressed: 1) The random-fuzzy dual interpretation of unknown quantity being inferred. 2) The principle of selecting sigma-max operator for estimation and recognition. This study considered that any continuous unknown quantity involved in estimation should be more appropriately modeled as randomness and handled by sigma inference; whereas, a discrete unknown quantity involved in recognition could be better modeled as fuzziness and handled by max inference. Consequently, the interacting multiple model (IMM) filter was reformulated in the framework of sigma-max inference, where the Markovian jump system was reformulated as a hybrid uncertainty system, with continuous state evolution modeled as usual as model-conditioned stochastic systems and discrete mode transition modeled as a fuzzy system using a possibility transition matrix, and hypotheses mixing was conducted by using the operation of “max” instead of “sigma.” For our examples of time series prediction and maneuvering target tracking, the updated IMM filter exhibited remarkable improvement over the classic IMM filter.

Weighted Maximum Correntropy Criterion-Based Interacting Multiple-Model Filter for Maneuvering Target Tracking

During the process of maneuvering target tracking, the measurement may be disturbed by outliers, which leads to a decrease in the state estimation performance of the classic interacting multiple-model (IMM) filter. To solve this problem, a weighted maximum correntropy criterion (WMCC)-based IMM filter is proposed. In the proposed filter, the fusion state is used as the input of each sub-model to reduce the computational complexity of state interaction and the WMCC is adopted to derive the sub-model state update and state fusion to improve the state estimation performance under outlier interference. Through principal analysis, the superiority of the proposed filter over the classic IMM filter in fusion strategy is revealed. The specific form of the proposed filter in radar maneuvering target tracking is provided. Two experimental cases of maneuvering target tracking are tested to illustrate the effectiveness of the proposed filter.

Real-Time Power Tracking Control for Supercapacitor-Based Regenerative Braking System Using Interacting Multiple Model Filter

The mismatch between the charging power of the supercapacitor and the braking power of the motor will lead to redundant energy cycling. To accurately track the braking power, a real-time tracking control of braking power using interacting multiple model filter is proposed. Three supercapacitor models are established, and a novel interacting multiple model filter is developed accordingly. The main capacitor voltages of three supercapacitor models interact to obtain the terminal voltage of the supercapacitor. Then the loss function is established with power tracking as the objective. The reference current of the supercapacitor is obtained under the constraints. The comparative experimental results show that with the proposed control strategy, the redundant energy cycling of the system is reduced by 55% within one operating cycle.

Robust IMM Filtering Approach with Adaptive Estimation of Measurement Loss Probability for Surface Target Tracking

A suitable jump Markov system (JMS) filtering approach provides an efficient technique for tracking surface targets. In complex surface target tracking situations, due to the joint influences of lost measurements with an unknown probability and heavy-tailed measurement noise (HTMN), the estimation accuracy of conventional interacting multiple model (IMM) methods may be seriously degraded. Aiming to address the filtering issues in JMSs with HTMNs and random measurement losses, this paper presents an IMM filtering approach with the adaptive estimation of unknown measurement loss probability. In this study, we assumed that the measurement noises obey student’s t-distributions and then proposed Bernoulli random variables (BRVs) to characterize the random measurement loss. Notably, by converting the two likelihood functions from the weighted sum form to exponential multiplication, we established hierarchical Gaussian state space models to directly utilize the variational inference method. The system state vectors, unknown distribution parameters, BRVs, and unknown measurement loss probabilities were estimated simultaneously according to the variational Bayesian inference in the IMM framework. The results of maneuvering target tracking simulations verified that the presented filtering approach demonstrated superior estimation accuracy compared to existing IMM filters.

A Novel Robust IMM Filtering Method for Surface-Maneuvering Target Tracking with Random Measurement Delay

A proper filtering method for jump Markov system (JMS) is an effective approach for tracking a maneuvering target. Since the coexisting of heavy-tailed measurement noises (HTMNs) and one-step random measurement delay (OSRMD) in the complex scenarios of the surface maneuvering target tracking, the effectiveness of typical interacting multiple model (IMM) techniques may decline severely. To solve the state estimation problem in JMSs with HTMN and OSRMD simultaneously, this article designs a novel robust IMM filter utilizing the variational Bayesian (VB) inference framework. This algorithm models the HTMNs as student’s t-distribuitons, and presents a random Bernoulli variable to describe the OSRMD in JMSs. By transforming measurement likelihood function form from weighted summation to exponential product, this paper constructs hierarchical Gaussian state space models. Then, the state vectors, random Bernoulli vairable, and model probability are inferred jointly according to VB inference. The surface maneuvering target tracking simulation example result indicates that the presented IMM filter achieves superior target state estimation accuracy among existing IMM filters.

A novel robust IMM filter for jump Markov systems with heavy-tailed process and measurement noises

In some tracking application scenarios, the performances of the traditional interacting multiple model (IMM) approach may degrade dramatically since the presence of outliers in process and measurement noises. Aiming at solving the filtering problem for jump Markov systems containing heavy-tailed process and measurement noises, a new robust student's t-based Gaussian approximate filter utilizing the IMM filtering framework is presented in this paper. Firstly, the heavy-tailed process and measurement noises are assumed to obey student's t-distributions. Secondly, the degree of freedom parameters and the scale matrices are modeled as Gamma distributions and inverse-Wishart distributions respectively. Finally, the system state, degree of freedom parameters, scale matrices and the mode probabilities are inferred simultaneously by introducing the variational Bayesian (VB) theory. Maneuvering target tracking simulation verifies that the designed algorithm achieves superior estimation performances among the state-of-the-art filters.

Multiple User Intent Prediction Using Interacting Multiple Model Joint Probabilistic Data Association Filter

This paper presents a novel method for multi-user motion intent estimation when the motion is observed by a single sensor. A motion model is associated with each of the activities carried out by the operator and the end location of which is termed as a motion intent. Such modeling of intent is useful in human-robot collaborative tasks. The appropriate model selection is achieved via an interacting multiple model (IMM) filter. When the position measurements of multiple users originating from one sensor are close to each other, then the measurement to operator association becomes challenging. A joint probabilistic data association (JPDA) filter is employed to address this issue. The combined IMM and JPDA filter provides a way to infer the motion intent of each operator. Simulation results show that the IMM-JPDA filter tracks two target states reaching toward goal intent in the presence of clutter measurements originating from the Kinect sensor.

Sea current relative navigation using interacting multiple model filter with adaptive fading technique

AbstractIn this paper, we propose a sea current relative navigation method using an interacting multiple model (IMM) filter with adaptive fading technique that can compensate an inaccurate sea current dynamics model. Due to the marine environment, the underwater vehicles largely depend on inertial navigation. Unfortunately, since its performance deteriorates with time, it is usually aided by another sensor. An electromagnetic-log (EM-log) and a Doppler velocity log (DVL), which are mainly used in marine navigation, provide relative velocity measurements to the sea currents, and hence require an accurate sea current dynamics model to fully utilise them. However, it is difficult to reflect the actual sea current changes with just a single fixed model, resulting in degraded overall navigation performance. Therefore, this paper proposes an IMM filter that can use multiple sea current dynamics models and has sub-filters designed with adaptive fading extended Kalman filter (AFEKF) to compensate for the mismodelling of sea current dynamics. The method is verified by simulation and shows a performance improvement comparable to the optimal filter.

Innovative Interaction Approach in IMM Filtering for Vehicle Motion Models With Unequal States Dimension

Robust and adaptive vehicle state estimation and tracking algorithms have become a very important part within the autonomous driving field. The family of interacting multiple model (IMM) filters has shown to provide very effective and accurate state estimation in systems whose behavior patterns change significantly over time. The main reason for the improved performance of IMM filters compared to single model approaches is the mode mixing, which constantly aligns the different models. This paper proposes an innovative way for the mode mixing, when the state-vectors of the models are of different size. The proposed mixing approach consists of two parts: firstly mixing the common states and secondly weighting between original and mixed states based on the model probabilities. Results from artificial simulations and real world measurement setups are shown to demonstrate the validity of the approach. Compared to previously suggested solutions, the proposed approach is more general and the overall complexity of the mode mixing step is reduced, which is the main contribution of the presented paper.

An adaptive IMM filter for jump Markov systems with inaccurate noise covariances in the presence of missing measurements

This paper derives a Kullback-Leibler average (KLA) based adaptive interacting multiple model (IMM) filter for jump Markov systems with inaccurate noise covariances in the presence of missing measurements. Firstly, a switching error model (SEM) is constructed to model the probability density function of measurement likelihood. The SEM can automatically choose appropriate error model for the real measurement or pure measurement noise by estimating a binary indicator. Secondly, by assigning conjugate priors on inaccurate noise covariances and binary indicator, the state, noise covariances and binary indicator are jointly estimated based on variational Bayesian (VB) technique. Finally, by using the KLA fusion scheme to fuse the conditioned estimates from every mode in the mixing and output phase, an adaptive IMM filter is derived. Simulation results demonstrate that the proposed filter achieves better performance than existing typical algorithms.

Sequential linear filtering with non‐linear position and Doppler measurements for target tracking

For radar target tracking with non-linear measurements, a sequential linear filtering method is proposed in this study, which includes a linear filter based on the position measurements and a linear sequential filter based on the range rate measurement. The linear radar measurement equation in the sequential filter is estimated based on the position filtering result. Furthermore, the feedback information during tracking is adaptively selected according to the quality of the angle measurements. When tracking the manoeuvring target, the proposed sequential linear filtering with adaptive information feedback is combined with the interacting multiple model (IMM) framework, and the IMM filter based on sequential linear filtering with adaptive model probability selection is proposed. Simulation results demonstrate the effectiveness of the proposed algorithms in non-manoeuvring and manoeuvring target tracking. Compared with traditional algorithms, the tracking performance is improved by the proposed algorithms in both typical non-manoeuvring and manoeuvring scenes.

Virtual Target-Based Longitudinal Motion Planning of Autonomous Vehicles at Urban Intersections: Determining Control Inputs of Acceleration With Human Driving Characteristic-Based Constraints

This article describes the development and implementation of virtual target-based longitudinal motion planning of autonomous vehicles at urban intersections ensuring safety and ride comfort. In this study, virtual targets are designed to cope with oncoming vehicles in the blind zone at the intersection for safety. The true field of view (FOV) of cognitive sensors and the virtual target states are constructed based on the sensor specification and intersection road information from a high-definition (HD) map. The future states and intention of sensor-detected targets are inferred and predicted with an interacting multiple model (IMM) filter. The local IMM filters are employed with an intelligent driver model (IDM). Based on predicted target states, two driving modes-"cross" and "stop"-under three different intersection stages-"approach," "intersection in," and "intersection out"-are determined. The model predictive control (MPC) is formulated to determine the control inputs of acceleration with human driving characteristics-based constraints. The proposed algorithm is evaluated through simulation to indicate the effectiveness of the virtual target. The suggested motion planning has been implemented on an autonomous driving vehicle and tested on urban roads.

An adaptive approach for estimation of transition probability matrix in the interacting multiple model filter

The traditional Interacting Multiple Model (IMM) filters usually consider that the Transition Probability Matrix (TPM) is known, however, when the IMM is associated with time-varying or inaccurate transition probabilities the estimation of system states may not be predicted adequately. The main methodological contribution of this paper is an approach based on the IMM filter and retention models to determine the TPM adaptively and automatically with relatively low computational cost and no need for complex operations or storing the measurement history. The proposed method is compared to the traditional IMM filter, IMM with Bayesian Network (BNs) and a state-of-the-art Adaptive TPM-based parallel IMM (ATPM-PIMM) algorithm. The experiments were carried out in an artificial numerical example as well as in two real-world health monitoring applications: the PRONOSTIA platform and the Li-ion batteries data set provided by NASA. The Retention Interacting Multiple Model (R-IMM) results indicate that a better prediction performance can be obtained when the TPM is not properly adjusted or not precisely known.

The Interacting Multiple Model Filter and Smoother on Boxplus-Manifolds.

Hybrid systems are subject to multiple dynamic models, or so-called modes. To estimate the state, the sequence of modes has to be estimated, which results in an exponential growth of possible sequences. The most prominent solution to handle this is the interacting multiple model filter, which can be extended to smoothing. In this paper, we derive a novel generalization of the interacting multiple filter and smoother to manifold state spaces, e.g., quaternions, based on the boxplus-method. As part thereof, we propose a linear approximation to the mixing of Gaussians and a Rauch–Tung–Striebel smoother for single models on boxplus-manifolds. The derivation of the smoother equations is based on a generalized definition of Gaussians on boxplus-manifolds. The three, novel algorithms are evaluated in a simulation and perform comparable to specialized solutions for quaternions. So far, the benefit of the more principled approach is the generality towards manifold state spaces. The evaluation and generic implementations are published open source.

Variable structure Human Intention Estimator with mobility and vision constraints as model selection criteria

In this paper, a novel method for early estimation of a human’s action intention is presented. Human intention, modeled as a goal location associated with a hand motion and eye gaze dynamics, is inferred by fusing information from collected hand motion and gaze motion data. The algorithm, called Human Intention Estimator with Variable Structure (HIEVS), uses two variable structure Interacting Multiple Model (VS-IMM) filters in parallel to process the hand motion and gaze data and generate posterior model probabilities associated with a finite set of action models. The posterior model probabilities from each filter are then fused at the end of each iteration and the current intention is estimated as the model, which has the highest fused posterior model probability. Two model set augmentation (MSA) algorithms are presented to select the active models for each VS-IMM during each iteration. For the hand motion filter, an MSA algorithm which computes the human’s reachable workspace is used. The MSA algorithm for the gaze filter utilizes the human’s visual span to determine the active models. This method allows for accurate early prediction of the human’s intention even when the total model set is large. A real world experiment is performed to validate the proposed method.

IMM/EKF filter based classification of real-time freeway video traffic without learning

ABSTRACT This paper addresses the problem of traffic variable estimation and traffic state classification of highway traffic, from video. To solve this problem, we propose to use the Interactive Multiple Model (IMM) filter with a multi-class macroscopic model. This filter runs two Extended Kalman Filters (EKF) to smooth the measured traffic parameters. In addition, the models’ probabilities that it provides are exploited to simply classify the traffic state as either free or congested, without the need for a training phase. The evaluation of the proposed system using simulated traffic parameters shows that it achieves a very accurate traffic state classification. The system was also tested in the real world, using video data acquired on a freeway by camera sensors. The obtained classification rates are comparable to those obtained by SVM classification, but at a significantly lower computational load.

Target Vehicle Motion Prediction-Based Motion Planning Framework for Autonomous Driving in Uncontrolled Intersections

This paper presents a motion-planning framework for urban autonomous driving at uncontrolled intersections. The intention and future state of the target vehicles are predicted using information obtained from the environment sensors. The target state prediction module employs an Interacting Multiple Model (IMM) filter to infer the intention of targets. The prediction results of each model of the IMM filter are fused to predict the future state of targets. The proposed predictor uses the intelligent driver model based-driver behavior model to construct the local filter of IMM. The driving mode decision is realized as a state machine consisting of two phases, ‘Approach’ and ‘Risk Management’. The risk management phase is composed of two sub-modes, ‘Cross’ and ‘Yield’. The state transition conditions between phases and modes are defined by introducing the concepts of ‘Critical gap’ and ‘Follow-up gap’. Based on the determined driving mode, the motion planning module consists of two sub-modules for each phase. The required deceleration determination for the approach phase is proposed to consider the occluded region in order to prevent inevitable collisions caused by fast approaches. The model predictive controller for the risk management phase is designed to determine the desired acceleration to guarantee safety and prevent unnecessary deceleration simultaneously. Both computer simulation studies and vehicle tests are conducted to evaluate the proposed framework. The results indicate that the proposed framework ensures the safety at uncontrolled intersections with a driving pattern similar to that of a driver.

Low Temperature, Current Dependent Battery State Estimation Using Interacting Multiple Model Strategy

Lithium-ion battery State of Charge (SoC) estimation for Electric Vehicle (EV) applications must be robust and as accurate as possible to maximize battery utilization and ensure safe operation over a wide range of operating conditions. SoC estimation commonly utilizes filters such as the Extended Kalman Filter (EKF) which rely on battery models, usually in the form of Equivalent Circuit Models (ECM). At low temperatures the battery response to current draw becomes increasingly non-linear, resulting in amplified SoC estimation errors. In this study, current dependent SoC estimation at low temperature is proposed using an Interacting Multiple Model (IMM) filter with three ECMs covering a range of C-rates. The IMM is combined with the Smooth Variable Structure Filter (SVSF) to obtain robust SoC estimates within a SoC estimation error of 2%.

Observability-Constrained VINS for MAVs Using Interacting Multiple Model Algorithm

This article presents the design of an interacting multiple model (IMM) filter for visual-inertial navigation (VIN) of MAVs. VIN of MAVs in practice typically uses a single system model for its state estimator design. However, microaerial vehicles (MAVs) can operate in different scenarios such as aggressive flights, hovering flights, and under high external disturbance requiring changing constraints imposed on the estimator model. This article proposes the use of a conventional VIN and a drag force VIN in an error-state IMM filtering framework to address the need for multiple models in the estimator. The work uses an epipolar geometry constraint for the design of the measurement model for both filters to realize computationally efficient state updates. Observability of the proposed modifications to VIN filters (drag force model and epipolar measurement model) are analyzed, and observability-based consistency rules are derived for the two filters of the IMM. Monte Carlo numerical simulations validate the performance of the observability constrained IMM, which improved the accuracy and consistency of the visual-inertial navigation system (VINS) for changing flight conditions and external wind disturbance scenarios. Experimental validation is performed using the EuRoC dataset to evaluate the performance of the proposed IMM filter design. The results show that the IMM outperforms stand-alone filters used in the IMM filtering bank by switching between the filters based on the residual likelihood of the models.