Multi-Target Tracking Based On Improved PF Algorithms

The tracking of multiple targets is a problem that arises in a wide variety of fields, But the multi-target tracking technique got a rapidly develop with the widely application of the Kalman Filter and its combination with data association technique until 1970's. There are two problems for multi-targets tracking: the association of measurements and the estimation of each target. Because the target model uncertainty and incomplete measurements in the real world multi-target tracking, it's necessary to give the non-linear and non-Gaussian models for the target dynamics and measurement likelihood. Traditional linear methods can't satisfy the increasingly precision demand, so its need to study the multi-target tracking algorithms for general non-linear and non-Gaussian models.For general non-linear and non-Gaussian models, Particle Filtering has become a practical and popular numerical technique to approximate the Bayesian tracking recursions. This is due to its efficiency, simplicity, flexibility and ease of implementation. D. Avitzour and Neil Gordon first give the feasibility of using Particle Filter to track multiple targets. However, such a straightforward implementation of the particle filter suffers greatly from the curse of dimensionality. As the number of targets increases an exponentially increasing number of particles is required to maintain the same estimation accuracy, Also the resample leads to a rapid depletion of the Monte Carlo representation. This paper we will give the improved particle filtering strategies to combat this problem.The data association problem is very important in multi-target tracking problem. A large number of strategies are available to solve the data association problem. The JPDAF is probably the most widely applied and successful strategy formulti-target tracking under data association uncertainty. However the original formulation of the JPDAF assumes linear and Gaussian models. And the main shortcoming of the JPDAF is that, to maintain tractability, the final estimate is collapsed to a single Gaussian, thus discarding pertinent information. Recently strategies have been proposed to combine the JPDAF with particle techniques to accommodate general non-linear and non-Gaussian models. We will study these strategies in this paper.According to the analysis above, we determine the main work of this paper as follows: based on description of the elements of the multi-target tracking model. We present improved algorithms for multi-target tracking to address the shortcomings of Standard Particle Filter and JPDAF. And finally we evaluate and compare the algorithms on a synthetic tracking problem. The following gives the main work of this paper in detail.1. Description of the multi-target tracking model.First the individual targets are assumed to evolve independently according to Markovian dynamic models, this implies that the dynamics for the combined state can factorises over the individual targets, so we can develop the State-Space and Dynamics. Then describes the measurement process and the data association problem, and formulates the likelihood conditional on a known association hypothesis. A prior for the association hypothesis is also developed. We will assume the prior for the association hypothesis to be independent of the state and past values of the association hypothesis. Note further that the prior for the target is implicitly captured by the factorisation of the association vector. This factorisation will aid in the design of efficient sampling strategies to combat the curse of dimensionality with an increase in the number of targets.2. Improved Particle Filters for multi-target trackingAs the particle filter suffers from the curse of dimensionality. We propose improved particle filtering strategies to solve the multi-target tracking problem. The first strategy samples the individual targets sequentially by utilizing a factorisation of the importance weights, if the association hypothesis were known, the filtering distribution would factorise completely over the individual targets. Each of the targets could then be treated independently, thus defeating the curse of dimensionality, so it's possible to construct a proposal for the associations that factorises sequentially over the individual target associations. This facilitates a strategy where the targets and their associations can be sampled sequentially, conditionally on each other. We will refer to this algorithm as the Sequential Sampling Particle Filter (SSPF). The second strategy assumes the associations to be independent over the individual targets. So the Posterior dependencies between the targets can be removed. Such an assumption facilitates an efficient component-wise sampling strategy to construct new joint particles. We will refer to this algorithm as the Independent Partition Particle Filter (IPPF). From the simulation we can see that the performance for the all the strategies decreases as the number of target increase and the problem becomes more difficult, in that more particles are required to achieve the same estimation accuracy. The standard particle filter is consistently outperformed by the other algorithms. But IPPF are not always able to disambiguate all the targets.3. MC-JPDAF for multi-target trackingWe combine the JPDAF with particle techniques to accommodate general non-linear and non-gaussian models. It aims to represent the marginal filtering distributions for each of the targets with particles, instead of a Gaussian, as is the case for the standard JPDAF. This algorithm we will refer to as the Monte Carlo JPDAF (MC-JPDAF).Compare the simulation we can see that the MC-JPDAFconsistently outperforms other particle filtering algorithms, and its performance does not appear to degrade significantly with an increase in the difficulty of the problem or the number of targets.4. State proposal distributionAll the algorithms in this paper require the specification of a proposal distribution for the individual target states. The most state proposal distribution was taken to be the target dynamics, since it leads to an intuitively simple strategy. It can, however, lead to inefficient algorithms, since the state-space is explored without any knowledge of the observations. Another proposal distribution is the optimal in the sense that it minimises the variance of the importance weights. For models with non-linearities, non-Gaussian noise and data association uncertainty it is generally not possible to obtain a closed-form expression for the optimal proposal distribution. As a compromise between the prior proposal and the optimal proposal we use a mixture proposal.