A Robust Interacting Multiple Model Smoother with Heavy-Tailed Measurement Noises

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.

In many applications, the interacting multiple model (IMM) estimator provides better performance over the single model Kalman filter (KF). However, there are two high frequency surface wave radar (HFSWR) factors which seem to make the IMM estimator less attractive: Firstly, the radar has a very long integration time, up to a few hundred seconds for ship detection; Secondly, the radar has very limited detection capability of maneuvering targets. It is unknown whether the IMM estimator will perform better over an EKF for real time HFSWR. The purpose of this paper is to compare the EKF with the IMM estimator. An optimal noise level and critical value have been found for HFSWR EKF design. The results demonstrated that the IMM estimator does not yield improved performance.

In multi-target tracking, Multiple Hypothesis Tracking (MHT) can effectively solve the data association problem. However, traditional MHT can not make full use of motion information. In this work, we combine MHT with Interactive Multiple Model (IMM) estimator and feature fusion. New algorithm greatly improves the tracking performance due to the fact that IMM estimator provides better estimation and feature information enhances the accuracy of data association. The new algorithm is tested by tracking tropical fish in fish container. Experimental result shows that this algorithm can significantly reduce tracking lost rate and restrain the noises with higher computational effectiveness when compares with traditional MHT.

The tracking of highly maneuvering targets using an interacting multiple model (IMM) estimator is considered. Two IMM estimators are evaluated: one which incorporates a horizontal coordinated turn model and one which incorporates a 3D coordinated turn model. An objective comparison of the track performances achievable with the two IMM estimators is given in the paper. Since the models in each IMM have different state dimensions, special care must be taken during the mixing stage to prevent biases. Previously, an unbiased mixing procedure was developed for an IMM estimator with two modes, and this work extends the previous result to an IMM estimator with three modes. Performance assessment of the IMM estimators was performed using a high fidelity radar simulation and benchmark scenarios. Results show that both IMM estimators provide performance enhancements over the default solution during horizontal turns. However, the IMM estimator that incorporates a 3D coordinated turn model performed better during vertical maneuvers.

An approach to observer trajectory optimization for maneuvering target is proposed in this paper through minimizing the cost function based on Extended Kalman Filter (EKF) related with uncertainties of state estimate. Computer simulation results demonstrate that the significant improvement in accuracy can be further achieved through combining observer trajectory optimization with Interacting Multiple Model (IMM) estimator.

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.

The significant challenge in shallow water environments is performing reliable target detection and classification while maintaining a reasonable false alert rate. Recent Navy operational experiences in shallow water environments have shown that existing active sonar systems experience excessive amounts of clutter and false alerts which result in a significant reduction in platform tactical advantage and survivability. A target motion discriminator (TMD) technique based on the Interacting Multiple Model (IMM) estimation algorithm is presented to exploit the consistency of position and motion information observed over multiple pings to form a robust classification decision. Several motion class models reside within the TMD, to provide accurate target state estimates and target likelihood functions for both maneuvering and non-maneuvering contacts. Classification performance is dramatically enhanced by using a "no target model" to reject contacts which exhibit erratic motion, i.e., inconsistent with a target motion model while promoting contacts with consistent motion. The accurate estimation of target dynamics obtained by the IMM approach provides the capability to reject stationary clutter resulting from surface and bottom reverberation and reliably detect the slow moving threat. A robust sequential likelihood ratio test which minimizes the classification decision time and improves classification performance is developed and demonstrated using sea test data collected in various environments.

Fault detection and diagnosis based on particle filters combined with interactive multiple-model estimation in dynamic process systems

Common ground target dynamic models include the nearly constant velocity (NCV), nearly constant acceleration (NCA), and nearly constant turn (NCT) models. Most of the papers on the interacting multiple model (IMM) estimator use a constant Markov chain transition probability matrix (TPM) corresponding to a constant measurement sampling interval. However, a multi-sensor ground target tracking system usually employs ground moving target indicator radar, electro-optical, infrared, video, acoustic, and seismic sensors, for which the sampling intervals are different. Modeling such systems requires using a variable sampling interval in the IMM estimator, which in turn requires the use of a non-constant TPM. An analytic expression for the TPM with variable sampling interval exists for two dynamic models. When the number of dynamic models is greater than two, the TPM can be numerically calculated efficiently. We present the technical approach for the IMM estimator with variable sampling intervals. Preliminary numerical results are presented for a maneuvering target with the NCV, NCA, and NCT models using 200 Monte Carlo simulations

Variable Structure Multiple Model (VSMM) estimation generalizes Multiple Model (MM) estimation by assuming that the set of models used for MM estimation is time varying. By using VSMM estimation, a large model set which may cover all possible target maneuvers can be used without significant increase of computational load, while maintaining a reasonable estimation accuracy. Various implementable VSMM algorithms, like Model Group Switching (MGS), Likely Model Set (LMS) and Minimal Sub-Model-Set Switching (MSMSS) using the Interacting Multiple Model (IMM) algorithm with a sub-model-set adaptation logic have appeared in the recent literature. However, the use of these algorithms for tracking maneuvering target in clutter has not been explored. In presence of clutter, one need to use data association technique to differentiate target originated measurement from clutter. The probabilistic data association (PDA) has been popularly adopted to many algorithms for tracking in clutter. In this paper, we integrate PDA technique with MSMSS and propose a VSIMM-PDA algorithm for maneuvering target tracking in clutter. A new grating technique to account for potential model errors is used. A numeric example via multiple Monte Carlo runs, which compares the performance of the new algorithm to a standard IMM-PDA in terms of Root Mean Squared error (RMS) and percentage of track loss, is presented.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

For maneuvering target tracking, general interacting multiple model (IMM) algorithms have a fixed structure. It has been overlooked that how the performance of these algorithms depends on the set of models used. The use of too many models is as bad as that of too few models. Therefore, a variable structure IMM (VSIMM) was presented and applied to ground target tracking. This algorithm eliminates the need for carrying all the possible models throughout the entire tracking period as in the standard IMM estimator, significantly improving performance and reducing computational load. But it is difficult to apply the VSIMM to other scenario (for example, aerial target) without auxiliary information such as map for ground target. This paper then presents a model set multiple hypotheses IMM algorithm (MS-MHIMM) which leads to a systematic treatment of model-set adaptation without using any additional auxiliary information. The new approach is illustrated in detail with an aerial complex maneuvering target tracking example.

We present the development and implementation of a multisensor-multitarget tracking algorithm for large scale air traffic surveillance based on interacting multiple model (IMM) state estimation combined with a 2-dimensional assignment for data association. The algorithm can be used to track a large number of targets from measurements obtained with a large number of radars. The use of the algorithm is illustrated on measurements obtained from 5 FAA radars, which are asynchronous, heterogeneous, and geographically distributed over a large area. Both secondary radar data (beacon returns from cooperative targets) as well as primary radar data (skin returns from noncooperative targets) are used. The target IDs from the beacon returns are not used in the data association. The surveillance region includes about 800 targets that exhibit different types of motion. The performance of an IMM estimator with linear motion models is compared with that of the Kalman filter (KF). A number of performance measures that can be used on real data without knowledge of the ground truth are presented for this purpose. It is shown that the IMM estimator performs better than the KF. The advantage of fusing multisensor data is quantified. It is also shown that the computational requirements in the multisensor case are lower than in single sensor case, Finally, an IMM estimator with a nonlinear motion model (coordinated turn) is shown to further improve the performance during the maneuvering periods over the IMM with linear models.

In this paper we present and compare different fault diagnosis algorithms using space space models for nonlinear dynamic systems. Most fault diagnosis and isolation algorithms for dynamic systems, which can be modeled using a set of state space equations, have relied on the system being linear and the noise and disturbances being Gaussian. In such cases, optimal filtering ideas based on Kalman filtering are utilized in estimation followed by a residual analysis, for which whiteness tests are typically carried out. Linearized approximations (e.g., Extended Kalman filters) have been used in the nonlinear dynamic systems case. However, linearization techniques, being approximate, tend to suffer from poor detection or high false alarm rates. In this paper, we use the sequential Monte Carlo filtering approach where the complete posterior distribution of the estimates are represented through samples or particles as opposed to the mean and covariance of an approximated Gaussian distribution. The particle filter is combined with the innovation-based fault detection techniques to develop a fault detection and isolation scheme. The advantage of particle filters is that they are capable of handling any functional nonlinearity and system or measurement noise of any distribution. An improvement on using a single Extended Kalman filter matched to a particular model is to use the the Interacting Multiple Model estimator, which consists of a number of EKFs running in parallel. Such a multiple model estimator can handle the abrupt changes in the system dynamics, which is essential for fault diagnosis. Here, we compare the fault detection performances of these algorithms on different nonlinear systems.

The conventional interacting multiple models (IMM) approach for a hybrid system under the Gaussian assumption is limited for most real applications due to the noisy measurements often being in the presence of outliers. This paper aims at accommodating the IMM approach to the non‐Gaussian cases where outliers exist. In the proposed IMM algorithm, the Student‐t distribution is used to model the non‐Gaussian measurement noise. At the interaction step, the mixed statistics of the noise parameter under a Bayesian framework are obtained via a Gamma approximation and a recently reported moments matching method. To address the state noise‐coupled intractability in Bayesian filtering, a variational Bayesian method is utilized to approximate the posterior distributions of the noise and state recursively. The proposed algorithm is tested with a maneuvering target tracking example and is shown to be robust to the outliers.

In many practical fields, the unknown time-varying measurement biases (additive and multiplicative bias) and heavy-tailed measurement noise caused by some unpredictable anomalous behaviors may degrade the performance of conventional Kalman filter seriously. To solve the state estimation problem of systems with time-varying measurement biases and heavy-tailed measurement noise, this paper proposes a new variational Bayesian (VB) based robust filter. Firstly, the non-Gaussian measurement likelihood probability density function (ML-PDF) with multiplicative and additive measurement bias is built. Then, the conjugate prior distributions for unknown bias and noise scale parameters are selected, and the VB method is utilized to jointly infer the system state, unknown measurement biases and inaccurate measurement noise covariance matrix. Finally, a VB based robust filter is derived and its effectiveness is verified by the numerical simulations.