IMMPDAF Approach for L-Band Radar Multiple Target Tracking

A single-sensor, single-target mixture reduction (MR) data association algorithm is extended for use in multisensor, multitarget tracking situations. MR is extended for tracking an arbitrary number of targets using an arbitrary number of sensors under the assumption that the sensor measurement errors are independent across sensors. Like the single-sensor, single-target MR algorithm, which gives better performance than the probabilistic data association (PDA) filter, the multisensor, multitarget MR extensions give similar improvements in performance compared to the joint PDA (JPDA) and multisensor JPDA (MSJPDA) algorithms. Further, in the formulations for the multisensor and multitarget MR algorithms, the equations for the calculation of the data association probabilities have been put in the same form as for the JPDA, thus allowing previously developed fast JPDA computational techniques to be applicable. N the problem of tracking targets in random clutter, the optimal Bayesian solution leads to Gaussian mixture distributions that consist of an exponentially increasing number of components.1 In practice, the number of components in each mixture is kept in check by approximating it with fewer components. The nearest neighbor (NN) approximation reduces each target's mixture to its largest component.13 The joint probabilistic data association (JPDA) approximation merges the components of each target's mixture into a single Gaussian component.1'4 However, when there are several significant, well-spaced components in the original mixture, important information may be lost by using the NN or JPDA methods. A more flexible approximation method for single-sensor, single-target tracking, known as mixture reduction (MR), has been proposed by Salmond.5 This MR algorithm preserves the mean and covariance of the original mixture of components, successively merging components until the number of components is reduced to some userspecified limit. In this paper, we first review Salmond's MR algorithm for single-sensor tracking of a single target in clutter. We then derive extensions to Salmond's MR algorithm for use in tracking multiple targets and when there are measurements available from multiple sensors. Just as the single-sensor, single-target MR algorithm gives better performance5 than the probabilistic data association (PDA) filter, the multisensor, multitarget MR extensions are shown to give similar improvements in performance as compared to the JPDA and multisensor JPDA (MSJPDA)6 algorithms. Extension of the MR algorithm for tracking of multiple targets is necessary for use in realistic tracking scenarios where there are usually many targets that need to be tracked. Moreover, many current tracking systems have been designed with multiple sensors, thus requiring the further extension to a multisensor algorithm. The paper is organized as follows. In Sec. II, the target dynamics and measurement equations are defined. We review the singlesensor, single-target MR algorithm5 in Sec. Ill, and we extend the algorithm to the multitarget and multisensor cases in Sec. IV and V, respectively. In Sec. VI, simulation results evaluating the performances of the MR extensions are presented. Finally, concluding remarks are given in Sec. VII.

The well-known probabilistic data association (PDA) filter handles the uncertainty in measurement origins inherent in tracking-in-clutter problems by using a probabilistically weighted sum of all measurements in the gate. In fact, the measurements in the gate may or may not include the one originated from the target. As such, two hypothetical models can be set up, corresponding to the events that the target measurements is and is not in the gate, respectively. This paper present an approach that integrates the PDA filter with the multiple-order method in a coherent manner based on the use of the above two hypothetical models. It is shown theoretically that the standard PDA filter is a special case of the first-order Generalized Pseudo Bayesian algorithm in the proposed formulation using a particular set of model transition probabilities. It is then proposed to adopt the superior interacting multiple-model architecture in this new formulation to improve the performance. The new algorithm is capable of achieving better performance by tuning the transition probabilities at a computational complexity comparable to that of the PDA filter. Simulation results are provided.

Object-Oriented Environment for Assessing Tracking Algorithms

ADS-B and radar will coexist for a long time in the future. For the ADS-B and multi-radar asynchronous track fusion problem in the air traffic control system, an ADS-B and radar fusion architecture and an asynchronous multi-sensor track fusion algorithm based on augmented state interacting multiple model(IMM) filter with probability data association(PDA) are proposed in this paper. The fusion algorithm is developed by applying the standard IMM approach, the PDA technique, and asynchronous measurement updating to a state-augmented system for the target motion. The state vector is augmented to include the past states which correspond to those asynchronous measurements. A PDA filter for parallel sensor processing is developed for target tracking under clutter. Real data from the ADS-B equipped aircraft and radar are used to test the performance of the algorithm. The simulation result shows that the track accuracy can be improved by this algorithm and the performance is comparable with the distributed multi-rate track fusion algorithm.

Square-root formulations have not been developed for state-of-the-art tracking algorithms. The only exception is the square-root implementation of the PDAF by R. Kenefic (1990). It is shown that there is a substantially better implementation of the square-root probabilistic data association filter (PDAF) than Kenefic's algorithm in terms of both numerical robustness and computational efficiency. On the average, the proposed algorithm requires half the number of computations required by Kenefic's algorithm for square-root PDAF. The same approach is extended to develop computationally efficient square-root algorithms for the interesting multiple model (IMM) and IMM probabilistic data association (IMMPDA) filters. >

Variable Structure Multiple Model (VSMM) estimation generalizes Multiple Model (MM) estimation by assuming that the set of models used for MM estimation is time varying. By using VSMM estimation, a large model set which may cover all possible target maneuvers can be used without significant increase of computational load, while maintaining a reasonable estimation accuracy. Various implementable VSMM algorithms, like Model Group Switching (MGS), Likely Model Set (LMS) and Minimal Sub-Model-Set Switching (MSMSS) using the Interacting Multiple Model (IMM) algorithm with a sub-model-set adaptation logic have appeared in the recent literature. However, the use of these algorithms for tracking maneuvering target in clutter has not been explored. In presence of clutter, one need to use data association technique to differentiate target originated measurement from clutter. The probabilistic data association (PDA) has been popularly adopted to many algorithms for tracking in clutter. In this paper, we integrate PDA technique with MSMSS and propose a VSIMM-PDA algorithm for maneuvering target tracking in clutter. A new grating technique to account for potential model errors is used. A numeric example via multiple Monte Carlo runs, which compares the performance of the new algorithm to a standard IMM-PDA in terms of Root Mean Squared error (RMS) and percentage of track loss, is presented.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper, an algorithm is proposed for tracking a highly maneuvering target in the presence of clutter by fusion of multiple detection radar and infrared sensor. It is presented by combining interactive multiple model (IMM) and multiple detection probabilistic data association filter (MDPDAF) in a multi-sensor (radar and infrared) scenario known as IMM/MS-MDPDAF algorithm. Multiple radar detection could be due to multipath or extended nature of the target such that in each scan there would be more than one valid target detection. In the presence of multiple radar detection there is uncertainty in data association in addition to the measurements origin (target or false alarm), in the number of measurements arising from the target. Accordingly MDPDAF algorithm that considers both uncertainties is developed instead of the standard PDAF algorithm which only considers the uncertainty in the measurements origin. The simulation has shown that in the presence of multiple radar detection, tracking with the proposed algorithm that considers both uncertainties has considerable improvement compared to the IMM/MSPDAF algorithm that only considers uncertainty in the measurements origin.

A methodology for the use of the multirate sampling technique in the measurement acquisition process of a probabilistic data association (PDA) filter is presented. The proposed filter, called the multirate sample probabilistic data association (MSPDA) filter, increases the computational efficiency of the tracking system without compromising the accuracy of the tracking algorithm. The use of multirate sampling enhances the utilization of the central processor, since the time spent in acquiring and processing certain measurements relevant to the components of a state vector is considerably saved. The performance of the MSPDA filter is compared with that of the traditional PDA tracker and other presently used filters. It is shown that the computational saving is about 25% while the degradation in accuracy is only to the extent of 5% of the MSE of the corresponding state vector component. >

Aim: Prediction of coronary illness utilizing novel Novel k nearest neighbor (KNN) and contrasting its accuracy with decision tree algorithm. Materials and Methods: Two gatherings are proposed for foreseeing the accuracy (%) of coronary illness. To be specific, novel Novel k nearest neighbor and decision tree algorithm. Here we take 20 examples each for assessment and look at. The sample size was calculated using G power with pretest power at 80% and the alpha of 0.05 value. Result: The decision tree gives better accuracy (84.95%) contrasted with the Novel k nearest neighbor accuracy (76.29 %). Along these lines the factual meaning of the decision tree is superior to the novel k nearest neighbor algorithm with significance value of 0.115. Conclusion: From the outcome, it may very well be inferred that the decision tree helps in anticipating the coronary illness with more precision contrasted with the novel k nearest neighbor algorithm.

In tracking a single target in clutter, many algorithms have been developed ranging in complexity from nearest neighbor (NN) and probabilistic data association (PDA) to the optimal Bayesian filter. In multiple-target tracking, a number of the techniques have been exercised such as the JPDA and the multiple hypothesis (MHT) schemes. Sub-optimal algorithms, such as the PDA filter, have been used widely since the optimal algorithms have an exponentially increasing computational complexity since all the possible sequences of target-to-measurement associations must be considered. In this paper, the Viterbi algorithm (VA) is used to develop a parallel search data association algorithm, called the Viterbi Data Association (VDA) technique. This algorithm includes the gating, automatic track initiation and termination modules. Simulations have been carried out to verify the performance and the robustness of the proposed algorithms Moreover, the VDA algorithm is compared with the fuzzy data association (FDA) algorithm when tracking a target in a cluttered, low signal-to-noise ratio (SNR) environment.

This paper presents a simultaneous localization,mapping (SLAM) and object tracking(OT) method based on interacting multiple model (IMM) filter to achieve simultaneous estimation of robot and object's trajectories in unknown environments. The proposed approach integrates IMM based object tracking and EKF-based SLAM. Since the implementation of IMM, the method can help the robot to track object and estimate its motion model, which improves the accuracy of object localization. Moreover, this approach can help robot to track the object that have more ability to escape, and improve it practicality. Simulation and real robot experiment results validate the effectiveness of the proposed method in robot and target localization and mapping. The results also show the accuracy of target motion model estimation and the system ability to track maneuvering target.

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.

Introduction: Propensity score matching (PSM) is a method to reduce the impact of essential and confounders. When the number of confounders is high, there may be a problem of matching, in which, finding matched pairs for the case group is difficult, or impossible. The propensity score (PS) minimizes the effect of the confounders, and it is reduced to one dimension. There are various algorithms in the field of PSM. This study aimed to compared the nearest neighbor and caliper algorithms. Methods: Data obtained in this study were from patients undergoing angiography at Ghaem Hospital in Mashhad, between 2011-12. The study was a retrospective case-control using PSM. In total, 604 patients were included in the case and control groups. A logistic regression model was used to calculate the propensity score and adjust the variables, such as age, gender, Body Mass Index (BMI), systolic blood pressure, smoking status, and triglyceride. Then, the Odds Ratios (ORs) with 95% Confidence Intervals (CIs) for the raw data and two matching algorithms were determined to examine the relationship between type 2 diabetes and coronary artery disease (CAD). Results: Propensity score in the nearest neighbor and caliper algorithms matched the total number of 604 samples, 200 and 178 pairs, respectively. All variables were significantly different between the two groups before matching (P<0.05). The gender was significantly different between the two groups after matching using the nearest neighbor algorithm (P=0.002). No variables created a significant difference between the two groups after matching with the caliper algorithm. Conclusion: Bias reduction in the caliper algorithm was greater than for the nearest neighbor algorithm for all variables except the triglyceride variable.

Robust tracking of a target in a clutter environment is an important and challenging task. In recent years, the nearest neighbor methods and probabilistic data association filters were proposed. However, the performance of these methods diminishes as number of measurements increases. In this paper, we propose a robust generative approach to effectively model multiple sensor measurements for tracking a moving target in an environment with high clutter. We assume a time-dependent number of measurements that include sensor observations with unknown origin, some of which may only contain clutter with no additional information. We robustly and accurately estimate the trajectory of the moving target in high clutter environment with unknown number of clutters by employing Bayesian nonparametric modeling. In particular, we employ a class of joint Bayesian nonparametric models to construct the joint prior distribution of target and clutter measurements such that the conditional distributions follow a Dirichlet process. The marginalized Dirichlet process prior of the target measurements is then used in a Bayesian tracker to estimate the dynamically-varying target state. We show through experiments that the tracking performance and effectiveness of our proposed framework are increased by suppressing high clutter measurements. In addition, we show that our proposed method outperforms existing methods such as nearest neighbor and probability data association filters.

The paper addresses the problem of adaptive manoeuvring targets tracking in clutter with a phased array radar. The tracking algorithm is based on the combination of the interacting multiple models (IMM) algorithm and the joint probabilistic data association filter (JPDAF), the resulting algorithm is named IMMJPDAF algorithm. Moreover, the phased array radar is a multifunction radar with the capability to select adaptively the sampling time interval; consequently, the tracking performance is improved. First, a complete comparative study between the IMMJPDAF algorithm and the multirate IMMJPDAF (MRIMMJPDAF) algorithm for tracking close manoeuvring targets with varying amounts of clutter density is presented. Then a description is made of the integration of a new fast method into the IMMJPDAF algorithm to adaptively select the next update time according to the targets motions. We call the resulting algorithm, the fast adaptive IMMJPDAF (FAIMMJPDAF) algorithm. Furthermore, an enhancement of the tracking accuracy in the FAIMMJPDAF algorithm is made by also taking into account the separation distance between targets in the selection of the next update time. The performance of the proposed algorithm, named improved fast adaptive IMMJPDAF (IFAIMMJPDAF) algorithm is assessed via Monte Carlo Simulations and compared with that of four algorithms that use an adaptive selection of the update time: FAIMMJPDAF algorithm, the adaptive IMMJPDAF that uses a modified version of the van Keuk criterion (MAIMMJPDAF), the adaptive IMMJPDAF that uses the original van Keuk method (AIMMJPDAF), and the IMMJPDAF (CIMMJPDAF) that uses a constant update time.