Combining IMM Method with Particle filters for 3D maneuvering target tracking

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.

Video synthetic aperture radar (VideoSAR) combines SAR imaging and video techniques together, enabling continuous surveillance of a specific area, which has the advantages of high frame rate, high resolution, the ability of real-time tracking, etc. For VideoSAR systems, detecting and tracking the shadows of moving targets can effectively avoid the complex algorithms needed for moving target location and refocusing. In this paper, an interactive multiple model (IMM) filter is designed for VideoSAR moving target tracking task. Considering of the maneuverability of ground moving target is more complex than aerial target, we define three different target motion models according to the motion characteristics of ground moving targets, including a stop model and a rotated model. The experimental results show that the proposed IMM filter outperforms conventional filter for ground moving target tracking application.

Online displacement extraction and vibration detection based on interactive multiple model algorithm

Respiration induces significant movement of tumours in the vicinity of thoracic and abdominal structures. Real-time image-guided radiotherapy (IGRT) aims to adapt radiation delivery to tumour motion during irradiation. One of the main problems for achieving this objective is the presence of time lag between the acquisition of tumour position and the radiation delivery. Such time lag causes significant beam positioning errors and affects the dose coverage. A method to solve this problem is to employ an algorithm that is able to predict future tumour positions from available tumour position measurements. This paper presents a multiple model approach to respiratory-induced tumour motion prediction using the interacting multiple model (IMM) filter. A combination of two models, constant velocity (CV) and constant acceleration (CA), is used to capture respiratory-induced tumour motion. A Kalman filter is designed for each of the local models and the IMM filter is applied to combine the predictions of these Kalman filters for obtaining the predicted tumour position. The IMM filter, likewise the Kalman filter, is a recursive algorithm that is suitable for real-time applications. In addition, this paper proposes a confidence interval (CI) criterion to evaluate the performance of tumour motion prediction algorithms for IGRT. The proposed CI criterion provides a relevant measure for the prediction performance in terms of clinical applications and can be used to specify the margin to accommodate prediction errors. The prediction performance of the IMM filter has been evaluated using 110 traces of 4-minute free-breathing motion collected from 24 lung-cancer patients. The simulation study was carried out for prediction time 0.1–0.6 s with sampling rates 3, 5 and 10 Hz. It was found that the prediction of the IMM filter was consistently better than the prediction of the Kalman filter with the CV or CA model. There was no significant difference of prediction errors for the sampling rates 5 and 10 Hz. For these sampling rates, the errors of the IMM filter for 0.4 s prediction time were less than 2.1 mm in terms of the 95% CI criterion or 1.1 mm in terms of the standard deviation (SD) or root mean squared errors (RMSE) criterion. For the prediction time of 0.6 s the errors were less than 3.6 mm in terms of the 95% CI criterion or 1.8 mm in terms of the SD/RMSE criterion. The prediction error analysis showed that the average percentage of the target lies outside the 95% CI margin was 5.2% and outside the SD/RMSE margin was 24.3%. This indicates the effectiveness of the 95% CI criterion as a margining strategy to accommodate prediction errors.

Adaptive Cruise Control (ACC) is an important part of automotive autonomy. To have a robust Adaptive Cruise Control system, a well-defined sensor fusion system is required. This paper focuses on feature-level sensor fusion system where three fusion techniques are explored: independent Kalman filtering, interacting multiple model (IMM) filtering, and a novel hybrid technique using a combination of both an IMM Filter and deep neural network (DNN). Kalman Filtering is a popular approach for automotive sensor fusion, but heavily relies on the given kinematic models to make state estimations. We explore the IMM filter to capture multi-model motion as well as a DNN approach to build a data-driven model of the system. Our IMM filter is built with several Kalman Filters featuring different kinematic models. The proposed DNN used is a Long Short-Term Memory (LSTM) network trained on radar and camera data to forecast a vehicle's state. To overcome the weaknesses in both IMM filtering and LSTM networks, we propose a hybrid technique of consisting of both the IMM filter and the LSTM network. The proposed hybrid system uses a single filter for each sensor. The filtered sensor data is synchronized and used as the input for a trained LSTM network. Our LSTM network was trained on over 100 simulated highway driving scenarios that might occur in an ACC application. Simulations and code were developed using MATLAB and the Autonomous Driving Toolbox. Our hybrid IMM-LSTM system outperformed the independent Kalman Filtering approach in longitudinal and lateral tracking accuracy (RMSE) by 23 percent and had promising results compared to the IMM filter where the tracking error was decreased by nearly 50 percent in certain driving scenarios.

Hybrid systems consist of both continuous state evolutions and discrete state (or mode) transitions. In many hybrid systems, mode transitions are governed by guard conditions that are dependent on the continuous state. These kind of mode transitions can be described by continuous-state-dependent mode transition probabilities. However, most multiple model Kalman filter based algorithms, such as the well-known interacting multiple model (IMM) algorithm, assume constant mode transition probabilities. We propose a hybrid estimation algorithm based on the IMM approach for the stochastic hybrid systems with continuous-state-dependent transitions. We first develop two models to describe the guard conditions for various stochastic hybrid systems. From the models of the guard conditions, we derive the corresponding continuous-state-dependent mode transition probabilities, which are expressed in terms of Gaussian probability density functions (pdfs) or Gaussian cumulative density functions (cdfs). We then propose a hybrid estimation algorithm for the stochastic hybrid systems based on the IMM algorithm. Like the IMM algorithm, our algorithm utilizes Gaussian distributions to represent the continuous state pdfs which are updated analytically at each time step. We also use analytical integration methods to reduce the computational cost of updating the mode probabilities. As a result, the proposed algorithm is computationally efficient and is applicable to high-dimensional problems. The performance of the proposed algorithm is illustrated with two examples in air traffic control tracking applications.

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.

In this paper, we present an efficient filtering algorithm to perform accurate estimation in jump Markov nonlinear systems, in case of multi-target tracking. With this paper, we aim to contribute in solving the problem of model-based body motion estimation by using data coming from visual sensors. The interacting multiple model (IMM) algorithm is specially designed to track accurately targets whose state and/or measurement (assumed to be linear) models changes during motion transition. However, when these models are nonlinear, the IMM algorithm must be modified in order to guarantee an accurate track. In this paper we propose to avoid the extended Kalman filter because of its limitations and substitute it with the unscented Kalman filter which seems to be more efficient especially according to the simulation results obtained with the nonlinear IMM algorithm (IMM-UKF). To resolve the problem of data association, we propose to use a Fuzzy approach. The later is then combined with the IMM-UKF algorithm; the derived algorithm is called fuzzy-IMM-UKF.

Space systems are characterized by a low-intensity process noise resulting from uncertain forces and moments. In many cases, their scalar measurement channels can be assumed to be independent, with one-dimensional internal dynamics. The nominal operation of these systems can be severely damaged by faults in the sensors. A natural method that can be used to yield fault tolerant estimates of such systems is the interacting multiple model (IMM) filtering algorithm, which is known to provide very accurate results. However, having been derived for a general class of systems with switching parameters, the IMM filter does not utilize the independence of the measurement errors in different channels, nor does it exploit the fact that the process noise is of low intensity. Thus, the implementation of the IMM in this case is computationally expensive. A new estimation technique is proposed herein, that explicitly utilizes the aforementioned properties. In the resulting estimation scheme separate measurement channels are handled separately, thus reducing the computational complexity. It is shown that, whereas the IMM complexity is exponential in the number of fault-prone measurements, the complexity of the proposed technique is polynomial. A simulation study involving spacecraft attitude estimation is carried out. This study shows that the proposed technique closely approximates the full-blown IMM algorithm, while requiring only a modest fraction of the computational cost.

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

For multi-target tracking, the IMM (interactive multiple model) algorithm has been proposed. The IMM is expected to reduce tracking errors for both nonmaneuvering and maneuvering targets. However, the IMM requires a heavy computational burden, because it utilizes multiple Kalman filters in parallel. On the other hand, the Kalman filter with a turning acceleration estimator, which can adapt a maneuvering target, has been proposed. The Kalman filter with a turning acceleration estimator is a single two-stage type filter and has a problem of setting threshold for the maneuver detector. In this paper, we propose the hybrid filter with a constant-velocity (CV) filter and a turning acceleration estimation filter. The proposed filter does not require a maneuver detector, because it integrates the outputs of two filters using the likelihood of each filter. And its computational requirement is smaller than the IMM, since it consists of only two Kalman based filters. The proposed method can prevent deteriorating tracking accuracy by reducing the risk of maneuver misdetection when a target maneuvers. We evaluate the performance of the proposed filter by computer simulation, and show the effectiveness of the proposed filter, comparing with the conventional Kalman filter and the two-stage Kalman filter.

Recently, targets tracking plays an important role in the rapidly expanding field of autonomous driving. With the presentation of vehicle-to-vehicle (V2V) communication standards and the improvement of Global Navigation Satellite System (GNSS) technology, the accuracy of cooperative vehicle tracking should be greatly improved. However, high-precision positioning suffers from a number of vulnerabilities and is unstable in clutter environment. In this paper, a modified approach using particle filter (PF) integrated with Interacting Multiple Models (IMM) algorithm is proposed to improve the accuracy of cooperative vehicle tracking in changing V2V environment. This paper focuses on a novel framework for cooperative vehicle tracking and implementation of data fusion originating from positioning information receiving from radars and connected vehicles. The simulations on scenarios of single vehicle and multi-vehicle tracking were implemented by utilizing Matlab. The performance of the proposed modified IMM-PF algorithm was evaluated. The results demonstrated that the proposed approach can adapt to a changing accuracy of positioning information and significantly reduce the tracking errors by approximately 50% compared with traditional methods. Consequently, the proposed method can effectively enhance the security and reliability of autonomous driver assistance systems, and its application has potential to support urban planning for smart cities.

The interacting multiple model (IMM) algorithm is specially designed to track accurately targets whose state and measurement models changes during motion transition. However, when these models are nonlinear, the IMM algorithm must be modified in order to guarantee an accurate track. Recently, the cubature Kalman filter (CKF) has been proposed to estimate the nonlinear system, and could perform better than unscented Kalman filter (UKF). In this paper, the IMM algorithm CKF based (IMM-CKF) is presented to track the maneuvering target using angular measurements. The simulation results demonstrate the improved performance of IMM-CKF over IMM-UKF, and the execution time of the former algorithm is shorter than the latter.

Combining the interacting multiple model (IMM) and the unscented particle filter (UPF), a new multiple model filtering algorithm is presented. Multiple models can adapt to targets’ high maneuvering. Particle filter can deal with the nonlinear or non-Gaussian problems and the unscented Kalman filter (UKF) may improve the approximate accuracy. Compared with other interacting multiple model algorithms in the target tracking simulations, the results demonstrate the validity of the new filtering method, that is, particle filter with the UKF proposal.

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.