**1. Introduction**

In a multitarget scenario, the targets set cardinality and their dynamic states randomly vary with time. The objective of tracking multiple targets is to estimate the number of targets and their trajectories using the data collected from sensor(s) in a joint manner [1–4]. Currently, there are three major paradigms for this field of study, namely Joint Probability Data Association (JPDA) [1], Multiple Hypotheses Tracking (MHT) [2] and Random Finite Set (RFS) [3,4]. While the first two formers involve modifying single target tracking filters to accommodate the problem of multitarget tracking, the latter applies estimation theory focusing on Bayesian optimality and provide a top-down formulation for solving the multitarget estimation problem [3,4].

Using RFS leads to the development of a series of multitarget estimation algorithms. Several RFS-based filters has been proposed in both the literature and practical applications, such as the Probability Hypothesis Density (PHD) [5], Cardinalized PHD (CPHD) [6,7], and the multi-Bernoulli filters [8]. While these filters and their extensions can give good estimates of the current target states, they do not produce target trajectories without using heuristics [9,10]. A theoretically rigorous and systematic consideration of the multitarget trajectory estimation based on RFS approach was proposed in [11]. This work also derives an exact closed-form solution to the multitarget tracking problem, known as Generalized Labeled multi-Bernoulli (GLMB) filter. This filter can estimate not only the number of the targets but also their trajectories, simultaneously [12]. It has been applied to several problems as tracking with merged measurements [13], track-before-detect [14,15], extended targets [16], cell biology [17,18], sensor scheduling [19], spawning targets [20], distributed data fusion [21], field robotics [22,23] and computer vision [24]. The GLMB filter for multitarget tracking with two sensors has been developed in [25,26]. An efficient implementation of the GLMB filter based on Gibbs sampling whose complexity depends linearly on the total number of measurements and quadratically on the number of hypothesized targets has been presented in [27]. This method has been extended to the multi-scan GLMB filter [28] and the multi-sensor GLMB filter [9].

In the multitarget tracking problem, clutter and detection profile are notable sources of uncertainty [29]. Clutter is the set of false measurements that do not originate from any true target and detection profile models the ability of the sensor to detect targets. Knowledge of these parameters are essential in Bayesian multitarget estimation. Mismatches in parameters of clutter and detection models lead to poor performance of filtering algorithms. While these parameters are unknown and randomly time-varying, they are normally assumed to be known in advance. This assumption is unrealistic in most practical applications and these parameters need to be estimated from training data or manually tuned [29].

Since the adaptability of the tracker to these unknown parameters are important in practice, several RFS filters have been proposed in the literature to perform multitarget tracking with mismatches in clutter and detection probability. Some of the proposed methods that accommodate the unknown clutter rate are given in [30–33]. A filter which bootstraps the clutter estimator of [29] into the CPHD filter [6] has been proposed in [34]. Several approaches for dealing with unknown detection probability have been presented in the literature, such as [29,35,36]. However, none of these filters can output target tracks. While the GLMB filter can output tracks, and has been applied to several problems without prior knowledge of clutter rate, as in [37–39], it is still computationally expensive. A low computational cost bootstrapping method using GLMB filter has been given in [40] for multisensor multitarget tracking with unknown detection probability.

Multisensor multitarget tracking with jointly unknown clutter rate and detection profile is far more complicated than those with a single unknown parameter. The use of multiple sensors leads to multidimensional ranked assignment problem which is the main hurdle in the implementation of the GLMB filter [9]. Furthermore, exploiting background information from training data for the multitarget estimation at each time frame is insufficient due to the time-varying nature of the two mentioned unknown parameters.

This work is aimed to contribute an efficient method for multitarget tracking that not only produces target trajectories but also estimates the jointly unknown clutter rate and detection profile online with low computational cost. By using a simple combination of the two well-known filters, the CPHD and GLMB filters, this method is not only fast in estimating the unknown parameters but also producing trajectories of the targets. Specifically, these two mentioned unknown parameters would be estimated separately by using the *λ*−CPHD and *pD*−CPHD filters before feeding to the GLMB filter for the purpose of tracking trajectories. The preliminary results of this work are reported in [40]. Particularly, in [40], the unknown detection probability is treated by the *pD*−CPHD filter before boostraped into the GLMB filter with known clutter rate. The soundness and effectiveness of the proposed solution are demonstrated in Section 4 via a multiple marine ships tracking application.

The remainder of this work is presented as follows. The backgrounds on GLMB filtering will be given in Section 2. The proposed bootstrapping method will be introduced in Section 3 followed by numerical studies in Section 4. Some concluding marks in Section 5.
