| 1. |
- Garcia, Angel, 1984, et al.
(författare)
-
A Metric on the Space of Finite Sets of Trajectories for Evaluation of Multi-Target Tracking Algorithms
- 2020
-
Ingår i: IEEE Transactions on Signal Processing. - 1941-0476 .- 1053-587X. ; 68, s. 3917-3928
-
Tidskriftsartikel (refereegranskat)abstract
- In this article, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different algorithms with the ground truth of trajectories. The proposed metric includes intuitive costs associated to localization error for properly detected targets, missed and false targets and track switches at each time step. The metric computation is based on solving a multi-dimensional assignment problem. We also propose a lower bound for the metric, which is also a metric for sets of trajectories and is computable in polynomial time using linear programming. We also extend the proposed metrics on sets of trajectories to random finite sets of trajectories.
|
|
| 2. |
- Garcia, Angel, 1984, et al.
(författare)
-
A time-weighted metric for sets of trajectories to assess multi-object tracking algorithms
- 2021
-
Ingår i: Proceedings of 2021 IEEE 24th International Conference on Information Fusion, FUSION 2021. ; , s. 363-370
-
Konferensbidrag (refereegranskat)abstract
- This paper proposes a metric for sets of trajectories to evaluate multi-object tracking algorithms that includes time-weighted costs for localisation errors of properly detected targets, for false targets, missed targets and track switches. The proposed metric extends the metric in [1] by including weights to the costs associated to different time steps. The time-weighted costs increase the flexibility of the metric [1] to fit more applications and user preferences. We first introduce a metric based on multi-dimensional assignments, and then its linear programming relaxation, which is computable in polynomial time and is also a metric. The metrics can also be extended to metrics on random finite sets of trajectories to evaluate and rank algorithms across different scenarios, each with a ground truth set of trajectories.
|
|
| 3. |
- Rahmathullah, Abu Sajana, 1986, et al.
(författare)
-
A batch algorithm for estimating trajectories of point targets using expectation maximization
- 2016
-
Ingår i: IEEE Transactions on Signal Processing. - 1941-0476 .- 1053-587X. ; 64:18, s. 4792 - 4804
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a strategy that is based on expectation maximization for tracking multiple point targets. The algorithm is similar to probabilistic multi-hypothesis tracking (PMHT) but does not relax the point target model assumptions. According to the point target models, a target can generate at most one measurement, and a measurement is generated by at most one target. With this model assumption, we show that the proposed algorithm can be implemented as iterations of Rauch-Tung-Striebel (RTS) smoothing for state estimation, and the loopy belief propagation method for marginal data association probabilities calculation. Using example illustrations with tracks, we compare the proposed algorithm with PMHT and joint probabilistic data association (JPDA) and show that PMHT and JPDA exhibit coalescence when there are closely moving targets whereas the proposed algorithm does not. Furthermore, extensive simulations c comparing the mean optimal subpattern assignment (MOSPA) performance of the algorithm for different scenarios averaged over several Monte Carlo iterations show that the proposed algorithm performs better than JPDA and PMHT. We also compare it to benchmarking algorithm: N-scan pruning based track-oriented multiple hypothesis tracking (TOMHT). The proposed algorithm shows a good tradeoff between computational complexity and the MOSPA performance.
|
|
| 4. |
- Rahmathullah, Abu Sajana, 1986, et al.
(författare)
-
A low-complexity algorithm for intrusion detection in a PIR-based Wireless Sensor Network
- 2009
-
Ingår i: Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), 2009, Melbourne, Australia. - 9781424435173 ; , s. 337 - 342
-
Konferensbidrag (refereegranskat)abstract
- We present a low-complexity algorithm for intrusion detection in the presence of clutter arising from wind-blown vegetation, using passive infra-red (PIR) sensors in a wireless sensor network (WSN). The algorithm is based on a combination of Haar transform (HT) and support-vector-machine (SVM) based training and was field tested in a network setting comprising of 15-20 sensing nodes. Also contained in this paper is a closed-form expression for the signal generated by an intruder moving at a constant velocity. It is shown how this expression can be exploited to determine the direction of motion information and the velocity of the intruder from the signals of three well-positioned sensors.
|
|
| 5. |
- Rahmathullah, Abu Sajana, 1986
(författare)
-
Data association algorithms and metric design for trajectory estimation
- 2016
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is concerned with trajectory estimation, which finds applications in various fields such as automotive safety and air traffic surveillance. More specifically, the thesis focuses on the data association part of the problem, for single and multiple targets, and on performance metrics. Data association for single-trajectory estimation is typically performed using Gaussian mixture smoothing. To limit complexity, pruning or merging approximations are used. In this thesis, we propose systematic ways to perform a combination of merging and pruning for two smoothing strategies: forward-backward smoothing (FBS) and two-filter smoothing (TFS). We present novel solutions to the backward smoothing step of FBS and a likelihood approximation, called smoothed posterior pruning, for the backward filtering in TFS. For data association in multi-trajectory estimation, we propose two iterative solutions based on expectation maximization (EM). The application of EM enables us to independently address the data association problems at different time instants, in each iteration. In the first solution, the best data association is estimated at each time instant using 2-D assignment, and given the best association, the states of the individual trajectories are immediately computed using Gaussian smoothing. In the second solution, we average the states of the individual trajectories over the data association distribution, which in turn is approximated using loopy belief propagation. Using simulations, we show that both solutions provide good trade-offs between accuracy and computation time compared to multiple hypothesis tracking.For evaluating the performance of trajectory estimation, we propose two metrics that behave in an intuitive manner, capturing the relevant features in target tracking. First, the generalized optimal sub-pattern assignment metric computes the distance between finite sets of states, and addresses properties such as localization errors and missed and false targets, which are all relevant to target estimation. The second metric computes the distance between sets of trajectories and considers the temporal dimension of trajectories. We refine the concepts of track switches, which allow a trajectory from one set to be paired with multiple trajectories in the other set across time, while penalizing it for these multiple assignments in an intuitive manner. We also present a lower bound for the metric that is remarkably accurate while being computable in polynomial time.
|
|
| 6. |
- Rahmathullah, Abu Sajana, 1986, et al.
(författare)
-
Generalized optimal sub-pattern assignment metric
- 2017
-
Ingår i: 20th International Conference on Information Fusion, Fusion 2017, Xian, China, 10-13 July 2017. - 9780996452700 ; , s. 182-189
-
Konferensbidrag (refereegranskat)abstract
- This paper presents the generalized optimal sub-pattern assignment (GOSPA) metric on the space of finite sets of targets. Compared to the well-established optimal sub-pattern assignment (OSPA) metric, GOSPA is not normalised by the cardinality of the largest set and it penalizes cardinality errors differently, which enables us to express it as an optimisation over assignments instead of permutations. An important consequence of this is that GOSPA allows us to penalize localization errors for detected targets and the errors due to missed and false targets, as indicated by traditional multiple target tracking (MTT) performance measures, in a sound manner. In addition, we extend the GOSPA metric to the space of random finite sets, which is important to evaluate MTT algorithms via simulations in a rigorous way.
|
|
| 7. |
- Rahmathullah, Abu Sajana, 1986, et al.
(författare)
-
Merging-based forward-backward smoothing on Gaussian mixtures
- 2014
-
Ingår i: 17th International Conference on Information Fusion, FUSION 2014; Salamanca; Spain; 7 July 2014 through 10 July 2014. - 9788490123553 ; , s. -
-
Konferensbidrag (refereegranskat)abstract
- Conventional forward-backward smoothing (FBS) for Gaussian mixture (GM) problems are based on pruning methods which yield a degenerate hypothesis tree and often lead to underestimated uncertainties. To overcome these shortcomings, we propose an algorithm that is based on merging components in the GM during filtering and smoothing. Compared to FBS based on the N-scan pruning, the proposed algorithm offers better performance in terms of track loss, root mean squared error (RMSE) and normalized estimation error squared (NEES) without increasing the computational complexity.
|
|
| 8. |
- Rahmathullah, Abu Sajana, 1986
(författare)
-
Practical methods for Gaussian mixture filtering and smoothing
- 2014
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In many applications, there is an interest in systematically and sequentially estimating quantities of interest in a dynamical system, using indirect and inaccurate sensor observations. There are three important sub-problems of sequential estimation: prediction, filtering and smoothing. The objective in the prediction problem is to estimate the future states of the system, using the observations until the current point in time. In the filtering problem, we seek to estimate the current state of the system, using the same information and in the smoothing problem, the aim is to estimate a past state. The smoothing estimate has the advantage that it offers the best performance on average compared to filtering and prediction estimates. Often, the uncertainties regarding the system and the observations are modeled using Gaussian mixtures (GMs). The smoothing solutions to GMs are usually based on pruning approximations, which suffer from the degeneracy problem, resulting in inconsistent estimates. Solutions based on merging have not been explored well in the literature. We address the problem of GM smoothing using both pruning and merging approximations. We consider the two main smoothing strategies of forward-backward smoothing (FBS) and two-filter smoothing (TFS), and develop novel algorithms for GM smoothing which are specifically tailored for the two principles. The FBS strategy involves forward filtering followed by backward smoothing. The existing literature provides pruning-based solutions to the forward filtering and the backward smoothing steps involved. In this thesis, we present a novel solution to the backward smoothing step of FBS, when the forward filtering uses merging methods. The TFS method works by running two filtering steps: forward filtering and backward filtering. It is not possible to apply the pruning or merging strategies to the backward filtering, as it is not a density function. To the best of our knowledge, there does not exist practical approximation techniques to reduce the complexity of the backward filtering. Therefore, in this thesis we propose two novel techniques to approximate the output of the backward filtering, which we call intragroup approximation and smoothed posterior pruning. We also show that the smoothed posterior pruning technique is applicable to forward filtering as well. The FBS and TFS solutions based on the proposed ideas are implemented for a single target tracking scenario and are shown to have similar performance with respect to root mean squared error, normalized estimation error squared, computational complexity and track loss. Compared to the FBS based on N-scan pruning, both these algorithms provide estimates with high consistency and low complexity.
|
|
| 9. |
- Rahmathullah, Abu Sajana, 1986, et al.
(författare)
-
Smoothed probabilistic data association filter
- 2013
-
Ingår i: FUSION 2013, 9-12 July 2013, Istanbul, Turkey. - 9786058631113 ; , s. 1296 - 1303
-
Konferensbidrag (refereegranskat)abstract
- This paper presents the Smoothed Probabilistic Data Association Filter (SmPDAF) that attempts to improve the Gaussian approximations used in the Probabilistic Data Association Filter (PDAF). This is achieved by using information from future measurements. Newer approximations of the densities are obtained by using a combination of expectation propagation, which provides the backward likelihood information from the future measurements, and pruning, which uses these backward likelihoods to reduce the number of components in the Gaussian mixture. Performance comparison between SmPDAF and PDAF shows us that the root mean squared error performance of SmPDAF is significantly better than PDAF under comparable track loss performance.
|
|
| 10. |
- Rahmathullah, Abu Sajana, 1986, et al.
(författare)
-
Two-filter Gaussian mixture smoothing with posterior pruning
- 2014
-
Ingår i: 17th International Conference on Information Fusion, FUSION 2014, Salamanca, Spain, 7-10 July 2014. - 9788490123553 ; , s. Art. no. 6916249-
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we address the problem of smoothing on Gaussian mixture (GM) posterior densities using the two-filter smoothing (TFS) strategy. The structure of the likelihoods in the backward filter of the TFS is analysed in detail. These likelihoods look similar to GMs, but are not proper density functions in the state-space since they may have constant value in a subspace of the state space. We present how the traditional GM reduction techniques can be extended to this kind of GMs. We also propose a posterior-based pruning strategy, where the filtering density can be used to make further approximations of the likelihood in thebackward filter. Compared to the forward–backward smoothing(FBS) method based on N-scan pruning approximations, the proposed algorithm is shown to perform better in terms of track loss, normalized estimation error squared (NEES), computational complexity and root mean squared error (RMSE).
|
|
