An IMM-PKF Method for Helicopter Tracking using Acoustic Arrays

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.

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.

In this paper, a road intersection estimation and prediction scheme of obstacle vehicles is proposed. And path planning method for unmanned ground vehicle (UGV) is adopted. Firstly, the interacting multiple model (IMM) algorithm based on constant velocity (CV) model, constant acceleration (CA) model and coordinated turn (CT) model is for state estimation of obstacle vehicles. Secondly, the future states of the obstacle vehicles are predicted according to the models and their probabilities. Then, the evaluation-execution framework of model predictive adaptive dynamic programming is designed to solve the problem of UGV path planning. Finally, the simulation results show the feasibility and effectiveness of the algorithm.

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.

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

The interacting multiple model (IMM) algorithm is a widely accepted state estimation scheme for solving maneuvering target tracking problems, which are generally nonlinear. During the IMM filtering process, serious errors can arise when a Gaussian mixture of posterior probability density functions is approximated by a single Gaussian. Particle filters (PFs) are effective in dealing with nonlinearity and non-Gaussianity. This work considers an IMM algorithm that includes a constant velocity model, a constant acceleration model and a 3D turning rate (3DTR) model for tracking three-dimensional (3D) target motion, using various combinations of nonlinear filters. In existing literature on combining IMM and particle filtering techniques to tackle difficult target maneuvers, a PF is usually used in every model In comparison, simulation results show that by using a computationally economical PF in the 3DTR model and Kalman filters in the remaining models, superior performance can be achieved with significant reduction in computational costs.

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.

Particle filters can provide better results than Kalman filter based algorithms in the problems where the nonlinear elements are dominant. In this study the problem of tracking an airborne platform using radar measurements, which has nonlinearities both in measurement and system models is considered. Different models are used for different target maneuvers; extended Kalman filter (EKF), interacting multiple model (IMM) structure and multiple model particle filter are compared on a sample scenario.

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

Under the condition of low data-rate measurement, it tends to mistrack or lose the target of high maneuvering targets by using the traditional single model tracking algorithm. This paper proposes a tracking method using Interacting Multiple Model (IMM) algorithm combined with Probabilistic Data Association (PDA) algorithm to solve the problem. Several measurement filtering thresholds are tuned to improve the accuracy of track association. Experiments show that this method achieves good tracking results.

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.

Tracking targets in clutter, with the inherent data association problem, naturally leads to a Gaussian mixture representation of the probability density function (pdf) of the target state vector, conditioned on the measurements observed. Online trackers require reduction of the number of components in the mixture on each processing cycle, and the integral square error (ISE) based mixture reduction algorithm (MRA) significantly outperforms known alternative algorithms. Moreover, to handle target maneuver onset and changing trajectory characteristics, one can use multiple model adaptive estimation in the form of either multiple model adaptive estimation (MMAE) or interacting multiple model (IMM) algorithms. For maneuvering targets in clutter, one can replace each Kalman filter within a conventional MMAE or IMM with an ISE-based MRA, or better yet, replace each Kalman filter within an ISE-based algorithm with an MMAE or IMM, to yield superior tracking of aggressive maneuvers in deep clutter. Such an ISE-based algorithm of MMAEs is seen to have performance attributes significantly superior to that of a current state-of-the-art tracker.

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.

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.