**1. Introduction**

The objective of Multi-Target Tracking (MTT) is to jointly estimate the number of targets and their individual states, and to provide target tracks or trajectories, from a sequence of measurements provided by sensing devices such as radar [1], sonar [2], or cameras [3]. Traditional MTT algorithms, including Joint Probabilistic Data Association Filter (JPDAF) [4] and Multiple Hypothesis Tracking (MHT) [5], always transform the multi-target tracking problem into multiple independent single-target tracking problems by data association processing according to a certain distance criterion. Association error resulting from complex scene deteriorates the tracking performance of JPDAF and MHT.

In recent years, multi-source multi-target information fusion theory based on Random Finite Sets (RFS) provides a unified and scientific mathematical basis for multi-sensor multi-target tracking problem [6,7]. Different from traditional heuristic methods, multi-target tracking methods based on RFS strictly describe target birth, death, spawning, miss detection and clutters in multi-target tracking process, directly estimate number and state of targets, and even provide target tracks or trajectories by modeling multi-target states and sensor measurements as RFS or labeled RFS, which has the best performance in Bayesian sense.

The multi-target Bayes filter is difficult to implement. Fortunately, some advanced approximations have been proposed, such as the Probability Hypothesis Density (PHD) filter [8–10], the Cardinalized PHD (CPHD) filter [11,12], the Multi-target Multi-Bernoulli (MeMBer) filter [13] and the Cardinality Balanced MeMBer (CBMeMBer) filter [14]. More recently, multi-target tracking algorithms based on labeled random finite sets have been proposed [15–23], and it can obtain track-valued estimates of individual targets without the need for post-processing, such as the Generalized Labeled Multi-Bernoulli (GLMB) filter [15] and Labeled Multi-Bernoulli (LMB) filter [16].

Since Sequential Monte Carlo (SMC) implementation and Gaussian Mixture (GM) implementation of PHD filter were proposed, the PHD filter has attracted significant attention in multi-target tracking research. To reduce the computational complexity of the PHD filter, several gating strategies were introduced to exclude clutter observation participating in filter updating [24,25]. To obtain target states from posterior PHD, several multi-target state extraction algorithms have been proposed, such as clustering [26,27] and data-driven methods [28–31]. To fuse information from multiple observation system, multi-sensor multi-target tracking filters based on PHD were proposed [32–34]. To track maneuvering targets, traditional multi-model method was introduced to PHD filter [35]. Faced with unknown backgrounds, such as unknown detection probability, unknown clutter parameter, several improved PHD filters can estimate background parameters while tracking [36,37]. In non-standard target observation model, several improved PHD filters were proposed to track extended target [38,39].

The standard PHD filter has considered the influence of the detection probability on multi-target tracking, but its performance degrades significantly under low detection probability in practice, especially when continuous miss detection occurs. For example, the posterior particle weights of a SMC-PHD filter will become small under continuous miss detection, and corresponding particles may be eliminated from the particle pool and then the undetected target will be lost.

Several recent works have made some attempts [40,41]. Based on the GM-PHD filter, the Refined GM-PHD (RGM-PHD) filter [40] was proposed to improve the performance of the GM-PHD filter under continuous miss detection. This method is effective in terms of various detection probabilities, false alarm rates and continuous miss detection rates. However, some key parameters of the RGM-PHD filter, including the penalty coefficient and the reward coefficient, are determined without explicit formula, which is difficult to be generalized to other applications. Also based on GM implementation of PHD filter, a novel target state estimate method was integrated into three improved GM-PHD filters [41], which results in better tracking performance in imperfect detection probability scenarios. However, lower bound of detection probability in simulations is set as 0.8, which can't sufficiently illustrate the effectiveness of the method under low detection probability.

In this paper, based on SMC implementation of PHD filter, we propose a heuristic method called Refined PHD (R-PHD) filter to improve multi-target tracking performance under low detection probability. First, survival probability dependent on target state is defined, which is based on the hypothesis that target enter and exit sensor Fields of View (FoV) usually occur at the boundary. Then, individual target and particle are assigned a unique label, which is utilized to confirm if miss detection occurs for each target and identify particles representing the undetected target. When miss detection occurs, posterior weights will be revised according to the prediction step. The key of the proposed method is to distinguish real targets and false alarms. This paper binarizes the likelihood function of individual extracted target, which is approximated as a random variable obeying two-point distribution. When extracted target is a real target, success probability of the two-point distribution is approximatively the detection probability. When extracted target is a false alarm, the success probability is approximatively a very small value. Then this paper transforms target confirmation problem into a hypothesis test problem, and utilizes Sequential Probability Ratio Test (SPRT) [42] to confirm real targets in real time. After target extraction at each time, we mark each extracted target as a real target or a false alarm, or make no decision according to test statistic.

The rest of the paper is organized as follows. Section 2 reviews probability hypothesis density filter and corresponding SMC implementation. Section 3 proposes the refined PHD filter in detail. Computer simulations illustrating the effectiveness and the performance of the proposed method are provided in Section 4. Finally, Section 5 presents the conclusion.
