An Interacting Multiple Model Approach for State Estimation with Non‐Gaussian Noise Using a Variational Bayesian Method

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.

Adaptive interacting multiple model for underwater maneuvering target tracking with one-step randomly delayed measurements

An improved Interacting Multiple Model tracking algorithm is presented to solve the maneuvering target tracking problem. The model set including Constant Velocity Model, Constant Acceleration Model and Current Statistical Model is designed, and the Interacting Multiple Model method is used to select model. The improved unscented Kalman filter algorithm is proposed to enhance filtering effect. The simulation and actual tracking experiment results indicate that the algorithm in maneuvering target tracking is valid.

Robust state estimation for jump Markov linear systems with missing measurements

Estimation of 3D piecewise coordinated turn target maneuvers with unknown turning rates is considered. The State Dependent Differential-Difference Riccati Equation (SDDRE) and the Interacting Multiple Model (IMM) approaches are compared. The comparison is kept as simple as possible and effort is made to perform it on a common basis. The SDDRE uses a non-linear modeling of the target's equations of motion that takes into account the rotation of the velocity and acceleration vectors as the target maneuvers. The IMM implements two models: a constant acceleration target model and a simple uncoupled coordinated turn maneuver model using the average-expected turn rate. The simulated trajectory is a combination of constant velocity trajectory segments and coordinated turn segments. The simulations show advantages and disadvantages of each of the approaches. It is demonstrated that the SDDRE approach filter is not sensitive to the trajectory orientation and that it has faster transient thus demonstrates a kind of adaptivity to the turning rate level. The IMM approach filter has the advantages that when the target trajectory is close to one of the hypotheses it has better performance than the SDDRE based filter.

This paper presents a simple yet efficient adaptive Kalman filter for tracking targets expected to perform varying turn maneuvers. The process noise covariance level of a second order Kalman filter is adjusted at each time step according to the calculated turn rate. The turning rate is estimated from the magnitude of the calculated acceleration divided by the estimated speed of the target. At each scan the previous and current velocity estimates are used to calculate the acceleration. The comparison of the performance of the proposed algorithm is made with that of an interacting multiple model (IMM) algorithm, employing three models with different levels of process noise covariance and also to that of a second order Kalman filter. Two different assumptions have been made for selecting the process noise values for the the IMM and Kalman filter algorithms, in the first case it was assumed that there was no prior information about the target motion whereas in the second case it was assumed that the largest turn rate that the target of interest could perform was known. The IMM algorithm utilizing three models gives slightly better estimates during the nonmaneuvering periods, but the proposed algorithm is superior to the IMM algorithm during maneuvering periods in terms of estimation errors. Also the proposed algorithm requires 78% less computation, almost the same number of calculations required by a single fixed process noise Kalman filter, than the IMM algorithm.

Correct knowledge of noise statistics is essential for an effective estimator in maneuvering target tracking. In practice, however, the noise statistics are usually unknown or not perfectly known. To deal with the estimation problem in linear discrete-time systems with Markov jump parameters, where the measurement noise covariance is unknown, a novel approach is presented in this paper. This approach is based on the interacting multiple model (IMM) framework. An H ∞ filter is employed to construct a noise statistics estimator to obtain the information which is necessary for the IMM algorithm. In our approach, even the priori knowledge of noise statistics is not needed. The noise statistics loss problem is solved while the merits of IMM algorithm is reserved. The effectiveness of the proposed approach is demonstrated in comparison with single-model H ∞ filter through Monte Carlo simulation for maneuvering target tracking.

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.

Previous papers (1997, 1999, 2000) have described a tracking approach which utilized a Combined Kalman Filter (CKF), adaptive tracking for maneuver tracking, and the JVC association algorithm for reports to tracks, for use in Airborne Early Warning (AEW) applications. In this paper we present our incorporation of Interacting Multiple Model (IMM) tracking. First our previous AEW tracking approach is briefly reviewed as most of this approach is still utilized and forms our baseline. The new IMM approach and equations are then described. Then the two IMM tracking approaches used are discussed. One involves a two model IMM containing two constant velocity models, one a low process noise and the other a high process noise model. The other approach involves three IMM filter models, a coordinated turn filter model, and the same two constant velocity filter models as in the two model IMM approach. Results for both IMM approaches and the baseline tracker are shown. The results presented involve a 120 target scenario with two second update time with simulated radar data. In addition computer timing results are presented. These results indicate that while the three model IMM approach provides the best tracking results, it does so at a substantial computational cost. The two model IMM provides comparable tracking improvement but at a far less computational cost.

To enhance the tracking accuracy of multi-ellipse extended target tracking for maneuvering targets, we propose a Variational Bayesian-based Interacting Multiple Model Maneuvering Extended Target Tracking Algorithm. The algorithm leverages multiple kinematic models within an Interacting Multiple Model framework to predict the target state, enabling better adaptation to various target kinematic modes during the time update. Following the prediction step, variational Bayesian inference, which includes inference of unknown measurement noise, is applied independently within each model to estimate the target’s position and shape. Then, model probabilities are updated based on the likelihood functions, and the model transition probabilities are adaptively learned. Concurrently, an ellipsoid fusion method is employed to combine the shape estimates from different models, while kinematic states are fused using model weights, yielding a robust overall target state estimate. The feasibility and performance of the proposed algorithm are validated by comparing its target tracking simulation results with those of other algorithms under different scenarios.

Distributed asynchronous multiple sensor fusion with nonlinear multiple models

This paper presents a tracking algorithm based on the interacting multiple model (IMM) algorithm and pseudo linear Kalman filter (PKF) in order to improve the performance of traditional methods in maneuvering target tracking. The IMM-PKF algorithm uses the constant velocity (CV) model and coordinated turn (CT) model to form a model set, and the filtering algorithm uses PKF. In target tracking, IMM is used to improve the matching between state prediction and actual motion, therefore improving the accuracy of maneuvering tracking. The performance of extended Kalman filter (EKF), PKF, and IMM-PKF is compared through simulation and experiment. The results show that the IMM-PKF method has the best tracking accuracy among the three methods in helicopter tracking.

An interacting Fuzzy-Fading-Memory-based Augmented Kalman Filtering method for maneuvering target tracking

Aiming at improving the performance of tracking unmanned aerial vehicle in the battlefield, this paper focuses on the algorithm involving tracking the maneuvering target with a distributed sensor network under non-Gaussian measurement noise. A novel distributed maximum correntropy cubature information filtering based on interactive multiple model is proposed. Taking advantage of the correntropy, we design a maximum correntropy cubature information filtering for each node to estimate the target state under non-Gaussian measurement noise. Then, distributed information fusion based on weighted average consensus is conducted to improve the stability of the sensor network. After that, the information pair is changed, so that a distributed state estimation algorithm based on interactive multiple model is developed to increase the accuracy of maneuvering target tracking. Simulation results and comparison with other algorithms in three typical non-Gaussian measurement noise scenarios are given to evaluate the effectiveness of the proposed algorithm.

Accurate subcategorization of tumour types through gene-expression profiling requires analytical techniques that estimate the number of categories or clusters rigorously and reliably. Parametric mixture modelling provides a natural setting to address this problem. We compare a criterion for model selection that is derived from a variational Bayesian framework with a popular alternative based on the Bayesian information criterion. Using simulated data, we show that the variational Bayesian method is more accurate in finding the true number of clusters in situations that are relevant to current and future microarray studies. We also compare the two criteria using freely available tumour microarray datasets and show that the variational Bayesian method is more sensitive to capturing biologically relevant structure.