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JPDAS multi-target tracking algorithm for cluster bombs tracking
Abstract
PDAF is a method of updating targets state estimation by using posteriori probability that measurements are originated from existing target in multi-target tracking. In this paper, we propose a multi-target tracking algorithm for falling cluster bombs separated from a mother bomb based on JPDAS method which is obtained by applying fixed-interval smoothing technique to JPDAF. The performance of JPDAF and JPDAS multi-target tracking algorithm is compared by observing the average of the difference between targets' state estimations obtained from 100 independent executions of two algorithms and targets' true states. Based on this, results of simulations for a radar tracking problem that show proposed JPDAS has better tracking performance than JPDAF is presented.
... With the same procedures but different choices of the optimal measurement criteria, many data-target association techniques have already been developed. Among them, the wellknown techniques include the global nearest neighbor standard filter (Global NNSF) [9], joint probabilistic data association filter (JPDAF) [10][11][12][13], and multiple hypothesis tracking (MHT) [14]. ...
In this paper, we focus on developing a novel unsupervised machine learning algorithm, named graph based multi-layer k-means++ (G-MLKM), to solve the data-target association problem when targets move on a constrained space and minimal information of the targets can be obtained by sensors. Instead of employing the traditional data-target association methods that are based on statistical probabilities, the G-MLKM solves the problem via data clustering. We first develop the multi-layer k-means++ (MLKM) method for data-target association at a local space given a simplified constrained space situation. Then a p-dual graph is proposed to represent the general constrained space when local spaces are interconnected. Based on the p-dual graph and graph theory, we then generalize MLKM to G-MLKM by first understanding local data-target association, extracting cross-local data-target association mathematically, and then analyzing the data association at intersections of that space. To exclude potential data-target association errors that disobey physical rules, we also develop error correction mechanisms to further improve the accuracy. Numerous simulation examples are conducted to demonstrate the performance of G-MLKM, which yields an average data-target association accuracy of 92.2%.
In this paper, we focus on developing a novel unsupervised machine learning algorithm, named graph based multi-layer k-means++ (G-MLKM), to solve data-target association problem when targets move on a constrained space and minimal information of the targets can be obtained by sensors. Instead of employing the traditional data-target association methods that are based on statistical probabilities, the G-MLKM solves the problem via data clustering. We first will develop the Multi-layer K-means++ (MLKM) method for data-target association at local space given a simplified constrained space situation. Then a p-dual graph is proposed to represent the general constrained space when local spaces are interconnected. Based on the dual graph and graph theory, we then generalize MLKM to G-MLKM by first understanding local data-target association and then extracting cross-local data-target association mathematically analyze the data association at intersections of that space. To exclude potential data-target association errors that disobey physical rules, we also develop error correction mechanisms to further improve the accuracy. Numerous simulation examples are conducted to demonstrate the performance of G-MLKM.
Data-target association is an important step in multi-target localization for the intelligent operation of un- manned systems in numerous applications such as search and rescue, traffic management and surveillance. The objective of this paper is to present an innovative data association learning approach named multi-layer K-means (MLKM) based on leveraging the advantages of some existing machine learning approaches, including K-means, K-means++, and deep neural networks. To enable the accurate data association from different sensors for efficient target localization, MLKM relies on the clustering capabilities of K-means++ structured in a multi-layer framework with the error correction feature that is motivated by the backpropogation that is well-known in deep learning research. To show the effectiveness of the MLKM method, numerous simulation examples are conducted to compare its performance with K-means, K-means++, and deep neural networks.
It is shown that the problem of recursive smoothing of the past states for discrete-time linear systems can be transformed to a filtering problem by introducing an enlarged state and modifying the system equations. The smoothing equations are then obtained from Kalman filter equations. Equations for the fixed-point time smoothing problem results directly from the filter equations.
The problem of associating data with targets in a cluttered multi-target environment is discussed and applied to passive sonar tracking. The probabilistic data association (PDA) method, which is based on computing the posterior probability of each candidate measurement found in a validation gate, assumes that only one real target is present and all other measurements are Poisson-distributed clutter. In this paper, a new theoretical result is presented: the joint probabilistic data association (JPDA) algorithm, in which joint posterior association probabilities are computed for multiple targets (or multiple discrete interfering sources) in Poisson clutter. The algorithm is applied to a passive sonar tracking problem with multiple sensors and targets, in which a target is not fully observable from a single sensor. Targets are modeled with four geographic states, two or more acoustic states, and realistic (i.e., low) probabilities of detection at each sample time. A simulation result is presented for two heavily interfering targets illustrating the dramatic tracking improvements obtained by estimating the targets' states using joint association probabilities.
An algorithm for tracking multiple targets in a cluttered environment is developed. The algorithm is capable of initiating tracks, accounting for false or missing reports, and processing sets of dependent reports. As each measurement is received, probabilities are calculated for the hypotheses that the measurement came from previously known targets in a target file, or from a new target, or that the measurement is false. Target states are estimated from each such data-association hypothesis, using a Kalman filter. As more measurements are received, the probabilities of joint hypotheses are calculated recursively using all available information such as density of unknown targets, density of false targets, probability of detection, and location uncertainty. The branching techique allows correlation of a measurement with its source based on subsequent, as well as previous, data.
Two-filter smoothing is a principled approach for performing optimal smoothing in non-linear non-Gaussian state–space models
where the smoothing distributions are computed through the combination of ‘forward’ and ‘backward’ time filters. The ‘forward’
filter is the standard Bayesian filter but the ‘backward’ filter, generally referred to as the backward information filter,
is not a probability measure on the space of the hidden Markov process. In cases where the backward information filter can
be computed in closed form, this technical point is not important. However, for general state–space models where there is
no closed form expression, this prohibits the use of flexible numerical techniques such as Sequential Monte Carlo (SMC) to
approximate the two-filter smoothing formula. We propose here a generalised two-filter smoothing formula which only requires approximating probability distributions and applies to any state–space model,
removing the need to make restrictive assumptions used in previous approaches to this problem. SMC algorithms are developed
to implement this generalised recursion and we illustrate their performance on various problems.
The problem of constructing low complexity suboptimal fixed-lag estimators is discussed. First, it is shown that any optimal fixed-lag estimator structure generally performs better if more delay is accepted than the designed lag. As this holds for any design lag including zero-lag, it is demonstrated that the zero-lag filter treated as a suboptimal fixed-lag smoother has an error considerably lower than the conventional zero-lag error. A near optimal fixed-lag smoother is then found by a straightforward extention of the zero-lag filter. Several examples are considered. Finally, the usefulness of the conventional fixed-lag mmse criterion is discussed.
An algorithm is presented for the recursive tracking of multiple
targets in cluttered environment by making use of the joint
probabilistic data association fixed-lag smoothing (JPDAS) techniques.
It is shown that a significant improvement in the accuracy of track
estimation of both nonmaneuvering and maneuvering targets may be
achieved by introducing a time lag of one or two sampling periods
between the instants of estimation and latest measurement. Results of
simulation experiments for a radar tracking problem that demonstrate the
effects of fixed-lag smoothing are also presented