Interactive multi-model maneuvering extended target tracking algorithm with variational Bayes inference

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.

This paper addresses the problem of joint tracking and classification (JTC) of a single extended target with a complex shape. To describe this complex shape, the spatial extent state is first modeled by star-convex shape via a random hypersurface model (RHM), and then used as feature information for target classification. The target state is modeled by two vectors to alleviate the influence of the high-dimensional state space and the severely nonlinear observation model on target state estimation, while the Euclidean distance metric of the normalized Fourier descriptors is applied to obtain the analytical solution of the updated class probability. Consequently, the resulting method is called the “JTC-RHM method.” Besides, the proposed JTC-RHM is integrated into a Bernoulli filter framework to solve the JTC of a single extended target in the presence of detection uncertainty and clutter, resulting in a JTC-RHM-Ber filter. Specifically, the recursive expressions of this filter are derived. Simulations indicate that: (1) the proposed JTC-RHM method can classify the targets with complex shapes and similar sizes more correctly, compared with the JTC method based on the random matrix model; (2) the proposed method performs better in target state estimation than the star-convex RHM based extended target tracking method; (3) the proposed JTC-RHM-Ber filter has a promising performance in state detection and estimation, and can achieve target classification correctly.

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 the extended target tracking using Gaussian process (GP) or other methods to estimate the extension state, all of them is necessary to obtain the measurement model, and the deviation from the true kinematic state affects the extension result easily. Meanwhile, with the growth of the shape complexity, the corresponding covariance matrix dimension increases, leading to a very high computational burden. To this end, we present an extended target tracking algorithm based on deep learning, which adopts Gaussian mixture (GM) probability hypothesis density (PHD) filter for extended target (ET) tracking, called the ET-GM-PHD filter, to estimate the kinematic state, and uses convolutional conditional neural process (ConvCNP) to estimate the extension state (i.e., the shape of the target) avoiding the complex computation and dependence on priors. Therefore, the proposed algorithm is named as the ConvCNP-GM-PHD filter. In our algorithm, ConvCNP lies on the neural network (NN) and GP, where the former can learn the rules from a large amount of data without any priors, while the latter uses the covariance function to express the distribution over possible functions according to a small number of context observations. Due the proposed algorithm can effectively combine the advantages of both, it is reliable to get a model via training which is able to realize function regression flexibly. Thus, ConvCNP is able to estimate the shape function by putting the angles and radial value between the kinematic state and associated measurements into the pre-trained model. The results show that the accuracy of the extension state estimation of the proposed ConvCNP-GM-PHD filter is improved and its computational complexity is also reduced. It implies that the proposed algorithm is more real-time and effective, and has a good application prospect.

Extended target tracking (ETT) based on random matrices typically assumes that the measurement model is linear. However, nonlinear measurements (such as range and azimuth) depending on locations of a series of unknown scattering centers always exist in many practical tracking applications. To address this issue, this paper proposes an iteratively extended target tracking based on random matrices by using decorrelated unbiased conversion of nonlinear measurements (ETT-IDUCM). First, we utilize a decorrelated unbiased converted measurement (DUCM) method to convert nonlinear measurements depending on unknown scatters of target extent in polar coordinates into the ones in Cartesian coordinates with equivalent measurement noise covariances. Subsequently, a novel method, combining iteratively extended Kalman filter (IEKF) updates with variational Bayesian (VB) cycles is developed for precise estimation of the target's kinematic state and extension. This method leverages the synergy between external IEKF iterations, which use the estimated state as a new prediction and input for DUCM, and internal VB iterations, which realize a closed-form approximation of the joint posterior probability. This approach progressively enhances estimation accuracy. Simulation results demonstrate the ETT-IDUCM algorithm's superior precision in estimating the target's kinematic state and extension compared to existing methods.

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.

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.

To improve the accuracy of multiple target tracking in the clutter environment, a new joint probabilistic data association (JPDA) algorithm based on variational Bayesian adaptive moment estimation is proposed. First, considering the existence of measurements, the posterior distribution of the target state in JPDA is composed of two parts of probability weighting, that is, the posterior distribution of the target state that the real measurement exists in the association gate and the posterior distribution of the target state that the real measurement does not exist in the association gate. By combining the conjugate properties of the prior and posterior distributions, the prior distributions of the target state in the two cases are classified to provide more accurate a priori information to filter, so as to improve the accuracy of data association. Second, considering the coupling effect between state estimation and data association process, combined with variational Bayesian inference, the problem of minimizing Kullback–Leibler divergence is transformed into the problem of maximizing the evidence lower bound, thereby effectively measuring the distance between the posterior distribution of target state estimation and the real posterior distribution, so as to improve the accuracy of data association again from the perspective of optimizing nonlinear filter. Finally, the adaptive momentum estimation strategy is introduced to iteratively solve the variable distribution that meets the maximization of the evidence lower bound, and the optimization of the posterior distribution of the target state is completed. Theoretical derivation and simulation experiments are conducted to verify the feasibility and effectiveness of the algorithm.

An extended target tracking problem for high resolution sensors is considered. An ellipsoidal model is proposed to exploit sensor measurement of target extent, which can provide extra information to enhance tracking accuracy, data association performance, and target identification. Due to the presence of high nonlinearity of the model, a Rao-Blackwellised unscented Kalman filter (RBUKF) is adopted in this paper. In contrast to the most commonly used extended Kalman filter (EKF), the RBUKF provides more accurate and reliable estimation performance, without increasing any computational complexity. An interacting multiple model (IMM) technique is combined with the RBUKF method to adapt the target maneuver and motion mode switching problem which is vital for nonlinear filtering. The developed IMM-RBUKF algorithm on extended target tracking problem is validated and evaluated by computer simulations.

This paper presents Track-LITE, a novel target-tracking framework that synergistically integrates an Interacting Multiple Model (IMM) filter with a Long Short-Term Memory (LSTM) network, governed by a dynamic on–off trigger mechanism. The IMM filter provides a reliable baseline for gradual motion, while the LSTM is selectively activated to refine estimates following abrupt maneuvers, a key contribution enabling adaptive accuracy. Quickest Change Detection (QCD) serves as the mechanism to detect these motion changes, collecting evidence of significant shifts and triggering the powerful LSTM to enhance prediction results. A bespoke feedback loop, another significant innovation, leverages LSTM residual errors to iteratively adjust IMM model weights, ensuring continuous adaptability across diverse motion profiles. The activation threshold, a critical derived design contribution, is optimized by jointly balancing false-alarm rate and latency, enabling precise coordination between the IMM and LSTM modules. With LSTM active only 30% of the time, Track-LITE achieves an RMSE comparable to continuous LSTM, while reducing computational load by 70%, a testament to its efficiency. This performance trade-off makes Track-LITE exceptionally well-suited for real-time, resource-constrained applications such as autonomous navigation and drone tracking.

The problem is target motion analysis (TMA) in situations where the variance (standard deviation) of additive white Gaussian measurement noise is unknown and time-varying. In particular, the paper examines a somewhat surprising result from the theoretical analysis based on the Cramer-Rao bound, which suggests that the best-achievable (second-order) error in target state estimation is unaffected by the lack of knowledge of the measurement noise variance. In order to examine this result, the paper develops three recursive Bayesian filters for TMA, which jointly estimate the target state and the measurement variance. The basis of all filters is the Cubature Kalman filter for bearings-only tracking, combined with (i) the variational Bayesian approach, (ii) the Rao-Blackwellised particle filter, and (iii) the interactive multiple-model (IMM), to deal with the unknown time-varying measurement variance. The paper presents extensive numerical simulation results and comparisons, which confirm that the lack of knowledge of the measurement noise variance is by no means a handicap for TMA.

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

We investigate cooperative target tracking of multiple unmanned aerial vehicles (UAVs) with a limited communication range. This is an integration of UAV motion control, target state estimation, and network topology control. We first present the communication topology and basic notations for network connectivity, and introduce the distributed Kalman consensus filter. Then, convergence and boundedness of the estimation errors using the filter are analyzed, and potential functions are proposed for communication link maintenance and collision avoidance. By taking stable target tracking into account, a distributed potential function based UAV motion controller is discussed. Since only the estimation of the target state rather than the state itself is available for UAV motion control and UAV motion can also affect the accuracy of state estimation, it is clear that the UAV motion control and target state estimation are coupled. Finally, the stability and convergence properties of the coupled system under bounded noise are analyzed in detail and demonstrated by simulations.

Existing studies on sparse Bayesian learning for structural damage detection usually assume that the posterior probability density functions follow standard distributions which facilitate to circumvent the intractable integration problem of the evidence by means of numerical sampling or analytical derivation. Moreover, the uncertainties of each mode are usually quantified as a common parameter to simplify the calculation. These assumptions may not be realistic in practice. This study proposes a sparse Bayesian method for structural damage detection suitable for standard and nonstandard probability distributions. The uncertainty corresponding to each mode is assumed as different. Variational Bayesian inference is developed and the posterior probability density functions of each unknown are individually derived. The parameters are found to follow the gamma distribution, whereas the distribution of the damage index cannot be directly obtained because of the nonlinear relationship in its posterior probability density function. The delayed rejection adaptive Metropolis algorithm is then adopted to generate numerical samples of the damage index. The coupled damage index and parameters in the variational Bayesian inference are successively calculated via an iterative process. A laboratory-tested frame is utilised to verify the effectiveness of the proposed method. The results indicate that the sparse damage can be accurately detected. The proposed method has the advantage of high accuracy and broad applicability.

Underwater acoustic sensor networks (UASNs) play an important role in the ocean's protection. They can realize real-time data collection, monitoring, exploration, and many other underwater applications by connecting and coordinating seafloor sensors and underwater vehicles. To achieve these application objectives, such as fishes tracking in biological monitoring field and submarines tracking in military field, target tracking is one of the key techniques. This paper presents a centralized fusion algorithm based on the interacting multiple models and the adaptive Kalman filter (IMMCFAKF) for target tracking in UASNs. Specifically, by introducing an adaptive forgetting factor into the optimal centralized fusion Kalman filter algorithm, the optimal centralized fusion adaptive Kalman filter (CFAKF) algorithm is obtained first. Then, combining the superiorities of both the optimal CFAKF algorithm and the conventional IMM algorithm, the optimal IMMCFAKF is achieved. The numerical simulations are provided to demonstrate the effectiveness of the proposed optimal IMMCFAKF algorithm.