Interacting Multiple Model Estimator Research Articles

The Interacting Multiple Model Smooth Variable Structure Filter for Trajectory Prediction

An autonomous vehicle would benefit from being able to predict trajectories of other vehicles in its vicinity for improved safety. In order for the self-driving car to plan safe trajectories, paths of nearby vehicles are required to be predicted for risk assessment, decision making, and motion planning. In this study, a trajectory prediction algorithm based on the Interacting Multiple Model (IMM) estimation strategy is proposed to predict paths involving lane-changing, lane-keeping, and turning motion. More specifically, the Interacting Multiple Model estimation technique is used with models defined in curvi-linear coordinates to predict a vehicle’s trajectory based on prior behavioral maneuvers. The road geometry is used to help facilitate behavior identification and prediction. Moreover, the combination of a more recently developed estimation technique known as the Generalized Variable Boundary Layer-Smooth Variable Structure Filter and the Interacting Multiple Model Estimator is applied to track, identify behaviors, and predict trajectories of a vehicle. The performance of this technique is compared with a Kalman Filter based formulation using synthetic and experimental data. This model-based strategy is also compared with machine learning-based strategies for trajectory prediction.

Long Distance Moving Vehicle Tracking with a Multirotor Based on IMM-Directional Track Association

The multirotor has the capability to capture distant objects. Because the computing resources of the multirotor are limited, efficiency is an important factor to consider. In this paper, multiple target tracking with a multirotor at a long distance (~400 m) is addressed; the interacting multiple model (IMM) estimator combined with the directional track-to-track association (abbreviated as track association) is proposed. The previous work of the Kalman estimator with the track association approach is extended to the IMM estimator with the directional track association. The IMM estimator can handle multiple targets with various maneuvers. The track association scheme is modified in consideration of the direction of the target movement. The overall system is composed of moving object detection for measurement generation and multiple target tracking for state estimation. The moving object detection consists of frame-to-frame subtraction of three-color layers and thresholding, morphological operation, and false alarm removing based on the object size and shape properties. The centroid of the detected object is input into the next tracking stage. The track is initialized using the difference between two nearest points measured in consecutive frames. The measurement nearest to the state prediction is used to update the state of the target for measurement-to-track association. The directional track association tests both the hypothesis and the maximum deviation between the displacement and directions of two tracks followed by track selection, fusion, and termination. In the experiment, a multirotor flying at an altitude of 400 m captured 55 moving vehicles around a highway interchange for about 20 s. The tracking performance is evaluated for the IMMs using constant velocity (CV) and constant acceleration (CA) motion models. The IMM-CA with the directional track association scheme outperforms other methods with an average total track life of 91.7% and an average mean track life of 84.2%.

Estimation of a Human-Maneuvered Target Incorporating Human Intention.

This paper presents a new approach for estimating the motion state of a target that is maneuvered by an unknown human from observations. To improve the estimation accuracy, the proposed approach associates the recurring motion behaviors with human intentions, and models the association as an intention-pattern model. The human intentions relate to labels of continuous states; the motion patterns characterize the change of continuous states. In the preprocessing, an Interacting Multiple Model (IMM) estimation technique is used to infer the intentions and extract motions, which eventually construct the intention-pattern model. Once the intention-pattern model has been constructed, the proposed approach incorporate the intention-pattern model to estimation using any state estimator including Kalman filter. The proposed approach not only estimates the mean using the human intention more accurately but also updates the covariance using the human intention more precisely. The performance of the proposed approach was investigated through the estimation of a human-maneuvered multirotor. The result of the application has first indicated the effectiveness of the proposed approach for constructing the intention-pattern model. The ability of the proposed approach in state estimation over the conventional technique without intention incorporation has then been demonstrated.

Interacting Multiple Model Estimation for Helicopter Regime Recognition

Regime recognition (RR) is an important aspect of condition-based maintenance for modern helicopters. RR involves the postflight classification of flight data into regime categories. These classifications are then used to predict fatigue damage and vehicle usage spectra. Although several RR algorithms have been proposed to date, many suffer from an overreliance on training data or poor accuracy when presented with flight data that do not precisely match one of the defined regimes. This paper introduces a new type of RR algorithm based on interacting multiple model (IMM) estimators. IMM estimators use a bank of dynamic models to evaluate the probability of the system existing in one of various possible dynamic modes. In the RR context, each of the dynamic modes corresponds to a particular regime. The proposed recognition algorithm offers advantages over other methods in that it provides a probabilistic classification of flight data, thereby explicitly acknowledging uncertainty in the recognition process. Furthermore, the algorithm is model based, reducing reliance on training data. Following a detailed description of the methodology, results are provided by applying the algorithm to both simulated and actual flight test data. Results show significant performance improvements compared with a typical rule-based recognition scheme.

An Interacting Multiple-Model-Based Algorithm for Driver Behavior Characterization Using Handling Risk

Performance of vehicle control systems, such as active safety systems and driver assistance systems, can be significantly improved by taking driver behavior information into consideration. This paper implements a handling limit-based algorithm for driver behavior characterization by introducing stochastic perspective with the interacting multiple model (IMM) estimation theory. The proposed algorithm constructs mathematical models for four vehicle dynamics categories. The IMM estimator is designed for each vehicle dynamics category to evaluate driver scores. The proposed algorithm is compared with an existing handling limit-based algorithm through experimental tests, and the results illustrate advantages of the proposed algorithm.

Interacting Multiple Model Estimator for Networked Control Systems: Stability, Convergence, and Performance

In this paper, we study the interacting multiple model (IMM) estimator for networked control systems with packet loss but without packet acknowledgment (ACK). The ACK is a signal sent by the actuator to inform the estimator of whether control packets are lost or not. A system with ACK is usually called a transmission control protocol (TCP) like system; otherwise, it is called a user datagram protocol (UDP) like system. We show that the stability of the IMM estimator for UDP-like systems is determined by the observation packet arrival rate (p.a.r.) and is independent of the control p.a.r. and control inputs. The IMM estimator is stable if the observation p.a.r. is greater than a critical value. We show that this critical value is the same as the critical value for the stability of the optimal estimator for its corresponding TCP-like system. If control inputs eventually tend to zero, the error covariance of the IMM estimator converges to that of the optimal estimator for TCP-like systems. We characterize the impact of the control/observation p.a.r. and the control input on estimation performance. Finally, we prove that the average estimation performance of the IMM estimator approximates that of the optimal estimator within a finite bound, and is superior to that of the linear minimum mean square error estimator.

Deep feature tracking based on interactive multiple model

Existing convolutional neural network (CNN) based trackers have limited tracking performance in some challenging scenarios such as deformation, background clutter and illumination variation, because the features extracted from a single layer or from a linear combination of multiple layers are insufficient to describe the target appearance. To overcome this problem, we propose a novel tracking algorithm based on interactive multiple model (IMM) framework for better exploring deep features from different layers (IMM_DFT). In this method, we first build measurement models from convolutional layers by applying correlation filters on hierarchical features. Then, to effectively estimate the target state for each layer, we design a hybrid system which consists of the foregoing measurement model and an online learning motion model. Finally, in order to achieve the optimal fusion of the systems for adapting diverse appearance variation of the target and background, an IMM estimator is developed to dynamically adjust the weight of each system using likelihood function and transition probabilities. Extensive experiments on OTB-2013, OTB-2015 and VOT-2016 benchmark databases demonstrate that the proposed algorithm achieves more favorable performance than several state-of-the-art methods.

Adaptive state estimation for tracking of civilian aircraft

Tracking of manoeuvring subsonic aerospace vehicles has traditionally been handled by state estimators. Ordinary state estimators perform poorly as the concerned process model can only be defined imprecisely. This contribution evaluates and compares the performance of adaptive single mode non-linear estimators against several versions of other estimators. The primary comparison is with the recently introduced smooth variable structure filter (SVSF) which is claimed to inherit the robustness of variable structure approach. Both the above types of estimators are then benchmarked with a well-known version of interacting multiple model (IMM) estimator which treats the manoeuvring aircraft as a hybrid system consisting of multiple modes. Monte Carlo simulation has been used and several descriptors have been used for comparison. The comparison demonstrates that a version of non-linear adaptive estimators incorporating sigma points and a single constant turn model performs substantially better than the SVSF and its tracking performance approaches that obtainable by the IMM estimator. Novelty of this contribution lies in providing a detailed comparison of the above three families of estimators, which provides adequate insight for selecting tracking estimators by trading off estimation accuracy, algorithm complexity, tuning requirement, and computational load.

Multiple-Model Estimators for Tracking Sharply Maneuvering Ground Targets

This paper presents algorithms that can be used to track the state of kinematic point targets, moving in two dimensions, that are capable of making very sharp heading maneuvers over short periods of time. Ground vehicles with continuous wheel tracks moving in an open held may perform such maneuvers. These targets are capable of 60°/s turn rates, whereas measurements are received at only 1 Hz. We describe how an interacting multiple model estimator (IMM) should be designed to accommodate such maneuvers, and we introduce the nonzero mean, white noise turn-rate model to quickly detect sharp turns by modeling a multimode process noise probability density function. Results show that including such modes in an IMM achieves significant improvement in accuracy and consistency, as compared to conventional coordinated-turn IMM filters.

Interacting multiple model estimation-based adaptive robust unscented Kalman filter

The unscented Kalman filter (UKF) is a promising approach for the state estimation of nonlinear dynamic systems due to its simple calculation process and superior performance in highly nonlinear systems. However, its solution will be degraded or even divergent when the system model involves uncertainty. This paper presents an interacting multiple model (IMM) estimation-based adaptive robust UKF to address this problem. This method combines the merits of the adaptive fading UKF and robust UKF and discards their demerits to inhibit the disturbance of system model uncertainty on the filtering solution. An adaptive fading UKF for the case of process model uncertainty and a robust UKF for the case of measurement model uncertainty are established based on the principle of innovation orthogonality. Subsequently, an IMM estimation is developed to fuse the adaptive fading UKF and robust UKF as sub-filters according to the mode probability. The system state estimation is achieved as a probabilistic weighted sum of the estimation results from the two sub-filters. Simulations, experiments and comparison analysis validate the efficacy of the proposed method.

Distributed estimation for stochastic hybrid systems with event‐triggered sensor schedule

This study deals with the state estimation problem for stochastic hybrid systems with event-triggered sensor schedule. By employing the basic interacting multiple model (IMM) approach, a novel event-triggered state estimator has been proposed for stochastic hybrid systems based on a closed-loop schedule rule. To compute the mode probabilities in the IMM estimator, a set of sigma points are generated to produce the pseudo-measurements when the sensor measurements are unavailable. Then, the event-triggered state estimator is extended to develop a distributed estimator in the sense of linear minimum mean square error, where the fused estimates are used to implement the re-initialisation in the interacting stage of the IMM estimator. The performance of proposed estimators is illustrated through the Monte Carlo simulations involving tracking a manoeuvring target in the two-dimensional experiment. Simulation results show that the performance of the proposed estimator is compared with that of the existing filter with a reduced computational burden.

Beating Heart Motion Accurate Prediction Method Based on Interactive Multiple Model: An Information Fusion Approach.

Robot-assisted motion compensated beating heart surgery has the advantage over the conventional Coronary Artery Bypass Graft (CABG) in terms of reduced trauma to the surrounding structures that leads to shortened recovery time. The severe nonlinear and diverse nature of irregular heart rhythm causes enormous difficulty for the robot to realize the clinic requirements, especially under arrhythmias. In this paper, we propose a fusion prediction framework based on Interactive Multiple Model (IMM) estimator, allowing each model to cover a distinguishing feature of the heart motion in underlying dynamics. We find that, at normal state, the nonlinearity of the heart motion with slow time-variant changing dominates the beating process. When an arrhythmia occurs, the irregularity mode, the fast uncertainties with random patterns become the leading factor of the heart motion. We deal with prediction problem in the case of arrhythmias by estimating the state with two behavior modes which can adaptively “switch” from one to the other. Also, we employed the signal quality index to adaptively determine the switch transition probability in the framework of IMM. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The test results indicate that the new proposed approach reduces prediction errors significantly.

A model-based, multichannel, real-time capable sawtooth crash detector

Control of the time between sawtooth crashes, necessary for ITER and DEMO, requires real-time detection of the moment of the sawtooth crash. In this paper, estimation of sawtooth crash times is demonstrated using the model-based interacting multiple model (IMM) estimator, based on simplified models for the sawtooth crash. In contrast to previous detectors, this detector uses the spatial extent of the sawtooth crash as detection characteristic. The IMM estimator is tuned and applied to multiple ECE channels at once. A model for the sawtooth crash is introduced, which is used in the IMM algorithm. The IMM algorithm is applied to seven datasets from the ASDEX Upgrade tokamak. Five crash models with different mixing radii are used. All sawtooth crashes that have been identified beforehand by visual inspection of the data, are detected by the algorithm. A few additional detections are made, which upon closer inspection are seen to be sawtooth crashes, which show a partial reconnection. A closer inspection of the detected normal crashes shows that about 42% are not well fitted by any of the full reconnection models and show some characteristics of a partial reconnection. In some case, the measurement time is during the sawtooth crashes, which also results in an incorrect estimate of the mixing radius. For data provided at a sampling rate of 1 kHz, the run time of the IMM estimator is below 1 ms, thereby fulfilling real-time requirements.

Fusion of Gaussian Mixture Models for Maneuvering Target Tracking in the Presence of Unknown Cross‐correlation

The paper addresses the problem of estimation fusion for maneuvering target tracking in the presence of unknown cross-correlation. To improve the fusion accuracy, two major points are concerned. Firstly, the Interacting multiple model (IMM) estimator is performed for each sensor, and the local estimate is represented by a Gaussian mixture model instead of a Gaussian density to keep more details of the local tracker. Next, a close-formed solution of fusing two Gaussian mixtures in the Covariance intersection (CI) framework is derived to cope with the unknown cross-correlation of local estimation errors. Experimental results demonstrate that the proposed approach provides some improvements in the fusion accuracy over the competitive methods.

Real-time motion detection for high-assurance aircraft tracking system using Downlink Aircraft Parameters

With the rapid increase in air traffic demands, the more accurate and reliable tracking system for aircraft surveillance is required to improve the capacity, safety and efficiency of Air Traffic Control services. As a considered part of the surveillance infrastructure, the Secondary Surveillance Radar Mode S has been widely used in the aircraft tracking systems. Moreover, in the Mode S Enhanced Surveillance, the Downlink Aircraft Parameters are available for obtaining updated and detailed information from aircrafts. However, this information of aircraft parameters has not been used systematically to improve the performance of current tracking systems. In this paper, a high-assurance aircraft tracking system is proposed by applying these aircraft parameters. The system with a high-accuracy estimator and a high-reliability checker enables not only tracking aircraft with changing flight modes in real time but also identifying potential faults of these parameters by pre-to-post data verification. The results of computer simulation and practical experiment show the effectiveness of proposed system by comparing with the Interacting Multiple Model estimator.

Kullback–Leibler divergence for interacting multiple model estimation with random matrices

The problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance is studied. The system state and the unknown covariance are jointly estimated, where the unknown covariance is modelled as a random matrix according to an inverse-Wishart distribution. For the IMM estimation with random matrices, one difficulty encountered is the combination of a set of weighted inverse-Wishart distributions. Instead of using the moment matching approach, this difficulty is overcome by minimising the weighted Kullback–Leibler divergence for inverse-Wishart distributions. It is shown that a closed-form solution can be derived for the optimisation problem and the resulting solution coincides with an inverse-Wishart distribution. Simulation results show that the proposed filter outperforms the previous work using the moment matching approach.

An Improved IMM Estimator Combined with Intelligent Input Estimation Technique for Tracking Maneuvering Target

The estimation performance of interactive multiple model (IMM) estimator for tracking a maneuvering target is influenced by the target motion models and application of filters. An improved IMM estimation algorithm combined with the intelligent input estimation technique is proposed in this study. The target motion models include the constant velocity (CV) model and the modified Singer acceleration model. The intelligent fuzzy weighted input estimation (IFWIE) is used to compute the acceleration input for the modified Singer acceleration model besides the application of standard Kalman filter (KF). The combination of KF and IFWIE can estimate the target motion state precisely and the proposed method is compared with the common IMM estimator. The simulation results prove the improved IMM estimator has superior estimation performance than the common IMM estimator, especially when the target changes the acceleration violently. The utilization of IFWIE for the improved IMM estimator can estimate the acceleration input effectively.

IMM estimator based on fuzzy weighted input estimation for tracking a maneuvering target

The application of target motion models and filters for interactive multiple model (IMM) estimator determines the effectiveness of maneuvering target tracking. In this paper, the fuzzy logic theory is utilized to construct the fuzzy weighting factor to improve the input estimation method and that is used to compute the unknown acceleration input for the modified Singer acceleration model. The proposed IMM estimator is operated mainly by two different target motion models combined with filters and the switch of target models is through the Markov transition probability matrix. The constant velocity model is combined with Kalman filter for the uniform target state estimation and the other one uses the modified Singer acceleration model to track the maneuvering target by the fuzzy weighted input estimation method. The performance of the proposed algorithm is verified by two different scenarios and compared with two IMM estimators. The target motion state of simulation condition contains the constant velocity, weak acceleration and strong acceleration. The simulation results show that the proposed IMM estimator has the better estimation precision in terms of tracking error. The modified Singer acceleration model combined with the fuzzy weighted input estimation method can track the maneuvering target effectively.

Stochastic Hybrid System Actuator Fault Diagnosis by Adaptive Estimation

Based on the interacting multiple model (IMM) estimator for hybrid system state estimation and on the adaptive Kalman filter for time varying system joint state-parameter estimation, a new algorithm, the adaptive IMM estimator, is proposed in this paper for actuator fault diagnosis in stochastic hybrid systems. The working modes of the considered hybrid systems are described by stochastic state-space models, and the mode transitions are characterized by a Markov model. Actuator faults are modeled as parameter changes, and the related fault diagnosis problem is solved by the proposed adaptive IMM estimator through joint state-parameter estimation. Numerical examples are presented to illustrate the performance of the proposed method.

An integrated estimation/guidance approach for seeker-less interceptors

This paper addresses the problem of intercepting highly maneuverable threats using seeker-less interceptors that operate in the command guidance mode. These systems are more prone to estimation errors than standard seeker-based systems. In this paper, an integrated estimation/guidance (IEG) algorithm, which combines interactive multiple model (IMM) estimator with differential game guidance law (DGL), is proposed for seeker-less interception. In this interception scenario, the target performs an evasive bang–bang maneuver, while the sensor has noisy measurements and the interceptor is subject to acceleration bound. The IMM serves as a basis for the synthesis of efficient filters for tracking maneuvering targets and reducing estimation errors. The proposed game-based guidance law for two-dimensional interception, later extended to three-dimensional interception scenarios, is used to improve the endgame performance of the command-guided seeker-less interceptor. The IMM scheme and an optimal selection of filters, to cater to various maneuvers that are expected during the endgame, are also described. Furthermore, a chatter removal algorithm is introduced, thus modifying the differential game guidance law (modified DGL). A comparison between modified DGL guidance law and conventional proportional navigation guidance law demonstrates significant improvement in miss distance in a pursuer-evader scenario. Simulation results are also presented for varying flight path angle errors. A numerical study is provided which demonstrates the performance of the combined interactive multiple model with game-based guidance law (IMM/DGL). Simulation study is also carried out for combined IMM and modified DGL (IMM/modified DGL) which exhibits the superior performance and viability of the algorithm reducing the chattering phenomenon. The results are illustrated by an extensive Monte Carlo simulation study in the presence of estimation errors.