METRIC-Bayes: Measurements Estimation for Tracking in High Clutter using Bayesian Nonparametrics

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.

Ground moving target indicator (GMTI) RADAR system frequently incorporates space-time adaptive processing for successful moving targets discrimination in a highly cluttered environment. The minimum detectable velocity (MDV) of the target gets affected due to the added clutter impairments such as foliage penetration and angle independent channel mismatch. A novel clutter model is postulated in this work that includes assessment enacted in view of both angle and Doppler clutter impairments at a time instead of their individual analysis as in the reported literature. The performance of the GMTI RADAR in terms of the signal-to-interference-plus-noise ratio loss is evaluated using the extrusive beamforming methods namely sample matrix inversion and principal component canceller. In high decorrelated clutter environment, the later outperforms in terms of the MDV, making use of a lesser number of training snapshots. The approach is validated with mathematical modelling and numerical simulations.

It's important to design an appropriate tracking gate when tracking maneuvering target in clutter environment. Usually, the size of traditional tracking gate is some certain fixed value, which can't meet the requirements under unknown tracking status. For this problem, we present an adaptive tracking gate design mentod based on Markov chain in this paper. It is clear that the tracking gate is directly related to the residual error. Therefore, we propose a novel method to forecast the residual error and design tracking gates adaptively based on the residual prediction accordingly. Due to the improved prediction accuracy of resuidual error, the degined tracking gate shows better performance when tracking maneuvering targets. Simulation results demonstrate the proposed method.

In this paper, an optimal filter for maneuvering target tracking in clutter environment is derived by combining measurement association hypotheses and target model transition hypotheses. The optimal filter is not realizable since it should consider exponentially increasing hypotheses. To reduce the hypotheses, a new hypotheses pruning technique is proposed. And then a realizable suboptimal filter is suggested. Simulation results show that the proposed filter produces smaller estimation errors and takes better track maintenance than the interacting multiple model probabilistic data association filter.

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.

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

Based on the transformer model, a deep data association and track filtering network (DeepAF) was constructed in this paper to achieve the function of data association and end-to-end track filtering. Combined with the existing track initiation methods, DeepAF can be used to track multiple targets in clutter environments. Experimental results show that DeepAF can stably and effectively track targets moving in different models such as constant velocity, constant acceleration, and constant turn rate. Compared with the probability hypothesis density filter and the probabilistic data association method, which were set with different state transition matrices manually to match with the actual target motion models, DeepAF has similar estimation accuracy in respect of target velocity and better estimation accuracy in respect of target position with less time consumption. For position estimation, compared with PHD, DeepAF can reduce the estimation error by 49.978, 49.263, and 2.706 m in the CV, CA, and CT motion models. Compared with PDA, DeepAF can reduce the estimation error by 13.465, 23.98, and 4.716 m in CV, CA, and CT motion models. For time consumption, compared with PHD, DeepAF can reduce the time by 991.2, 982.3, and 979.5 s in CV, CA, and CT motion models. Compared with PDA, DeepAF can reduce the time by 61.6, 60.5, and 61.4 s in CV, CA, and CT motion models.

Synthetic Aperture Radar (SAR) systems have become indispensable tools for observing the physical properties of the Earth and other planetary bodies, as well as for detecting and identifying both natural and man-made structures. In this paper, a realistic and efficient three-dimensional (3D) terrain targets model was developed to explore the relationship between the backscattering characteristics of the electromagnetics and the physical features of ground objects. In order to simulate the real land surface, we proposed an improved Diamond-square algorithm and CLAMP model is employed for vegetation modeling. Specifically, geometric electromagnetic(EM)-CAD modeling and a land surface model are established. Furthermore, the effective image simulating method of SAR for complex 3D targets in clutter environment based on electromagnetic scattering was utilized. Finally, numerical experiments indicate that 2D and 3D visualization graphics of SAR images for the terrain targets are generated by the EM simulation in reasonable runtime. It is further demonstrated that the real-time 3D SAR imaging visualization system could be successfully realized.

Classic maneuvering targets tracking (MTT) algorithms require accurate kinematic models, the performance of which would be degraded significantly for the intricate and abrupt maneuvers. In addition, their sensitivity to maneuverability would be reduced in the presence of clutters. In this article, we consider the MTT problem without using preset kinematic models in the clutter environments, and propose a data-driven intelligent multiframe joint tracking method (DIMJTM) for maneuvering targets with clutters. Initially, we introduce a maneuverability characterization method using modified Mahalanobis distance. Based on this, a backtracking vertex sampling strategy is proposed for selecting multiframe historical track points matching the current maneuver pattern. Subsequently, we propose a pyramid shaped graph construction scheme to establish multiple spatio–temporal relationships among the selected track points and measurements of the current frame. Finally, the composed graph is fed into our designed interactive Transformer-graph attention network autoencoder. The simulated and real experimental results indicate that the DIMJTM not only accurately captures maneuverability changes, but also outperforms the mainstream interacting multiple model probabilistic data association (IMM-PDA)/integrated PDA algorithms and their improved variants in the single-target tracking scenarios and the multiple hypothesis tracking (MHT)/IMM-MHT algorithms in the multiple targets tracking scenario, achieving stable and high-precision tracking.

The great advances in deep learning enable human beings to extract the semantic information in ubiquitous unstructured data into high-dimensional vectors, leading to an urgent priority of managing vector data. Nearest neighbor (NN) query is a pivotal question in vector data management. Unfortunately, the NN query has been proved to be intrinsically hard. Researchers, thus, turn to approximate nearest neighbor (ANN) query which targets better efficiency by slightly compromising accuracy. Despite this, existing ANN methods still incur high time and space costs, which are mainly due to the high dimensionality. Specifically, in most in-memory ANN algorithms, the time cost is dominated by the time for comparing the distances among vectors. Each distance comparison operation (DCO) involves hundreds of arithmetic operations as each vector has hundreds of dimensions. Similarly, the space cost is dominated by the space for storing the vectors. Towards the goal of reducing the time and space costs, we present three methods in this thesis. First, we observe that, for a DCO, if an approximate distance can confirm that a vector is not a NN, then it can be discarded without computing exact distances. Based on this observation, we propose a method named ADSampling. For a DCO, it iteratively and incrementally samples a few dimensions and computes an approximate distance. When this distance is accurate enough to decide the result of the DCO, it terminates sampling. Second, to further improve the efficiency of DCOs, we design an efficient distance estimator. We propose a new quantization method named RaBitQ, which maps $D$-dimensional vectors into $D$-bit strings. RaBitQ provides an unbiased and asymptotically optimal estimator with good empirical accuracy. In addition, we introduce efficient implementations of RaBitQ based on bitwise operations or SIMD-based operations. Third, by extending the RaBitQ method, we develop an algorithm which compresses a floating-point vector into a $B$-bit unsigned integer vector. We prove that our algorithm is asymptotically optimal in terms of the space-accuracy trade-off.

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. >

Case Based Reasoning (CBR) is a method that aims to resolve a new case by adapting the solutions contained in previous cases that are similar to the new case. The system built in this study is the CBR system to make recommendations on the topic of student thesis concentration. This study used data from undergraduate students of Informatics Engineering IST AKPRIND Yogyakarta with a total of 115 data consisting of 80 training data and 35 test data. This study aims to design and build a Case Based Reasoning system using the Nearest Neighbor and Manhattan Distance Similarity Methods, and to compare the results of the accuracy value using the Nearest Neighbor Similarity and Manhattan Distance Similarity methods. The recommendation process is carried out by calculating the value of closeness or similarity between new cases and old cases stored on a case basis using the Nearest Neighbor Method and Manhattan Distance. The features used in this study consisted of GPA and course grades. The case taken is the case with the highest similarity value. If a case doesnt get a topic recommendation or is less than the trashold value of 0.8, a case revision will be carried out by an expert. Successfully revised cases are stored in the system to be made new knowledge. The test results using the Nearest Neighbor Method get an accuracy value of 97.14% and Manhattan Distance Method 94.29%.

A range nearest-neighbor (RNN) query retrieves the nearest neighbor (NN) for every point in a range. It is a natural generalization of point and continuous nearest-neighbor queries and has many applications. In this paper, we consider the ranges as (hyper)rectangles and propose efficient in-memory processing and secondary memory pruning techniques for RNN queries in both 2D and high-dimensional spaces. These techniques are generalized for kRNN queries, which return the k nearest neighbors for every point in the range. In addition, we devise an auxiliary solution-based index EXO-tree to speed up any type of NN query. EXO-tree is orthogonal to any existing NN processing algorithm and, thus, can be transparently integrated. An extensive empirical study was conducted to evaluate the CPU and I/O performance of these techniques, and the study showed that they are efficient and robust under various data sets, query ranges, numbers of nearest neighbors, dimensions, and cache sizes.

An independent visual objects tracking is less reliable than the data association of visual objects tracking. This paper describes a tracking method based on the nearest neighbor (NN) data association, which serves lower computational than do the multiple hypothesis tracking (MHT) or the joint probabilistic data association filter (JPDAF) but gives low reliability, if the number of targets is increased. This reliability can be increased by selecting appropriate visual object model. To obtain low computation while capable of handling non-rigid object, we propose an object model which combines the threshold of accumulated object region and the object bounding box. The elements of the association matrix are the distance function that is proposed as a mixture of object models of distance function. The combinations of object models of distance function are important mechanism for determining appropriate state of object correspondence which can be divided into six groups: updated track, missing track, newly track, grouped track, merged track and complex track. The missing track is solved by the track life time criterion while the grouping, the merged and the complex track are resolved by using the proposed NN algorithm again. The experimental results are correctly shown on various situations of correspondence problem from surveillance image sequences