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

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.

The trajectory estimation of a highly maneuvering target is a challenging problem and has practical applications. The interacting multiple model (IMM) filter is a well-established filtering algorithm for the trajectory estimation of maneuvering targets. In this study, we present an overview of IMM filtering algorithms for tracking a highly-maneuverable fighter aircraft using an air moving target indicator (AMTI) radar on another aircraft. This problem is a nonlinear filtering problem due to nonlinearities in the dynamic and measurement models. We first describe single-model nonlinear filtering algorithms: the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). Then, we summarize the IMM-based EKF (IMM-EKF), IMM-based UKF (IMM-UKF), and IMM-based CKF (CKF). In order to compare the state estimation accuracies of the IMM-based filters, we present a derivation of the posterior Cramér-Rao lower bound (PCRLB). We consider fighter aircraft traveling with accelerations 3g, 4g, 5g, and 6g and present numerical results for state estimation accuracy and computational cost under various operating conditions. Our results show that under normal operating conditions, the three IMM-based filters have nearly the same accuracy. This is due to the accuracy of the measurements of the AMTI radar and the high data rate.

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.

In this paper, according to the characteristics of underwater target tracking, extended Kalman filter (EKF) algorithm was applied to address underwater bearing-only non-maneuverable target tracking problem. To ensure the observability in bearing-only passive target tracking, we use two sensor arrays in uniform rectilinear motion to track the single target. EKF is recursive Bayesian filter algorithm based on the linearization of the nonlinearities in the state and the measurement system. And the simulation experiment shows that, to the constant velocity single target, the bearings-only EKF algorithm with dual-array has good results, also the EKF has lower computation complexity than unscented Kalman filter and particle filter. It confirms the effectiveness of the EKF algorithm in solving the underwater bearing-only target tracking problem.

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.

Underwater target tracking system can be kept covert using the bearing-only or the bearing-Doppler measurements (passive measurements), which will reduce the risk of been detected. According to the characteristics of underwater target tracking, the square root unscented Kalman filter (SRUKF) algorithm, which is based on the Bayesian theory, was applied to the underwater bearing-only and bearing-Doppler non-maneuverable target tracking problem. Aiming at the shortcomings of the unscented Kalman filter (UKF), the SRUKF uses the QR decomposition and the Cholesky factor updating, in order to avoid that the process noise covariance matrix loses its positive definiteness during the target tracking period. The SRUKF uses sigma sampling to avoid the linearization of the nonlinear bearing-only and the bearing-Doppler measurements. To ensure the target state observability in underwater target tracking, the paper uses single maneuvering observer to track the single non-maneuverable target. The simulation results show that the SRUKF has better tracking performance than the extended Kalman filter (EKF) and the UKF in tracking accuracy and stability, and the computational complexity of the SRUKF algorithm is low.

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.

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

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.

Inserting synthetic objects into video sequences has gained much interest in recent years. Fast and robust vision-based algorithms are necessary to make such an application possible. Traditional pose tracking schemes using recursive structure from motion techniques adopt one Kalman filter and thus only favor a certain type of camera motion. We propose a robust simultaneous pose tracking and structure recovery algorithm using the interacting multiple model (IMM) to improve performance. In particular, a set of three extended Kalman filters (EKFs), each describing a frequently occurring camera motion in real situations (general, pure translation, pure rotation), is applied within the IMM framework to track the pose of a scene. Another set of EKFs,one filter for each model point, is used to refine the positions of the model features in the 3-D space. The filters for pose tracking and structure refinement are executed in an interleaved manner. The results are used for inserting virtual objects into the original video footage. The performance of the algorithm is demonstrated with both synthetic and real data. Comparisons with different approaches have been performed and show that our method is more efficient and accurate.

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.

in estimating the vertical velocity of the aircraft which influences altitude prediction. Altitude prediction is important in conflict alarm systems. This problem is investigated and several Bayesian estimators, including the Interacting Multiple Model (IMM) algorithm, are tuned and tested on real measurement data for a performance comparison. It is shown that a single model filter with maneuver handling using the Unscented Kalman Filter is superior to IMM estimators and Kalman filters for long term predictions.

In this paper, the interacting multiple model was used to design two adaptive controllers for a dynamic spacecraft system. Using knowledge of the system mode, the gains of a proportional-derivative and sliding mode controller corresponding to a nominal and a fault mode of the system were mixed to create a control input that more accurately represented the current system state. By implementing the interacting multiple model with an unscented Kalman filter, this technique was extended to a nonlinear dynamic system. The developed strategies are validated on a simulated spacecraft system and evaluated using Monte Carlo simulations by means of root mean squared errors. Results emphasize the preservation and increase in tracking performance permitted by the adaptive strategies in the presence of faults.

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.

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.