a random finite set, so the mathematical tools provided by finite set statistics (FISST) can be used in the MTT problem based on the Bayesian framework [7]. However, the multi-targets Bayesian recursion proposed by [PERSON] is difficult to apply in practice. Hence, the Probability Hypothesis Density (PHD) algorithm is proposed by [PERSON], which is a recursion algorithm that propagates the first-order statistical moment associated with the multi-targets posterior [8]. Also, a new Cardinalized Probability Hypothesis Density (CPHD) [9] algorithm introduced by [PERSON], which is different with PHD in that it jointly propagates the intensity function and the cardinality distribution. Compared with the traditional algorithm, the PHD and CPHD algorithms not only avoid the data association problem in MTT, but also can realize the estimation of the target number and their state. In MTT system, the PHD and CPHD algorithms operate on the single target state space and avoid the data association problem. However, the PHD and CPHD algorithms include multiple integrals that have no closed form solution in general. To implement the PHD and CPHD algorithms, the sequential Monte Carlo (SMC) method and the Gaussian mixture (GM) method have been introduced in [10; 11; 12]. Also, a new generalization of multi-Bernoulli filter has been proposed by Vo B-T and Vo B-N, which is called the generalized labeled multi-Bernoulli (GLMB) filter [13]. Some improved versions of the GLMB filter are used to track extend target [14] and multi-target [15]. Also, [PERSON] et al. proposed a Second-Order PHD (SO-PHD) filter [16]. During the past decade, the PHD and CPHD algorithms have been applied to many practical problems, such as bi-static radar tracking [17] and sonar target tracking [18]. In underwater MTT systems, we have to handle the uncertainty of measurement and detection probability. Clutter is a kind of measurement that does not belong to any targets, while the accurate detection probability refers to the phenomena that sensors can detect the targets. Significant mismatched parameters between clutter and detection probability parameters inevitably lead to erroneous estimates in MTT. Usually, the conventional PHD and CPHD algorithms assume the detection probability is known a priori, which is not suitable in many applications. With the help of the Monte Carlo method, the SMC-PHD algorithm works well on real data of sonar tracking systems, but the detection probability is not analyzed [19]. So some improved methods have been proposed to estimate the detection probability. The GM-PHD algorithm with variable probability of detection is used in sonar tracking scenario [20]. Here, the detection probability is modeled as the segmented function of distance, which is lacking the basis of sonar equation and acoustic theory. So the tracking performance needs to be further improved. [PERSON] proposed the Beta distribution in order to model the detection probability and apply it to GM-CPHD (Beta-GM-CPHD) [21]. This algorithm can automatically adjust the detection probability, while there will be a certain delay when the detection probability varies with time, which will result in a decrease of filter accuracy. This paper is aimed at active Sonar target tracking systems. We propose to model the detection probability through the active sonar equation, and get the analytic expression of the detection probability, which relates to target location when fixed the false detection probability. This novel detection probability is used in PHD and CPHD algorithms and applied to underwater active sonar tracking systems. At same time, the CPHD filter jointly propagates the intensity function and the cardinality distribution, which leads to a higher computational complexity than the PHD filter. The gating strategy is an effective way to reduce the computational burden of the CPHD filter [22; 23]. The proposed adaptive gating strategy mentioned in literature [22] outperforms the standard elliptical gating strategy in literature [23].