###### Abstract  
The random finite set (RFS) approach for multi-target tracking is widely researched because it has a rigorous theoretical basis. However, many prior parameters such as the clutter density, survival probability and detection probability of the target, pruning threshold, merging threshold, initial state of the birth object and its error covariance matrix are required in the standard RFS-based filters. In real application scenes, it is difficult to obtain these prior parameters. To address this problem, an adaptive marginal multi-target Bayes filter without the need for clutter density is proposed. This filter obviates the need for prior clutter density and survival probability. Instead of using the prior initial states of newborn targets and their error covariance matrices, it uses two scans of observations to generate the initial states of potential birth targets and their error covariance matrices according to the least squares technique. Simulation results reveal that the proposed adaptive filter has smaller OSPA and OSPA\({}^{(2)}\) errors as well as less cardinality error than the adaptive RFS-based filters. The OSPA and OSPA\({}^{(2)}\) errors have been reduced by more than 20% compared to those of  
predicted and updated intensity or density, the clutter density, survival probability and detection probability of the target are assumed to be known in these three RFS-based filters. Because each potential target (or Gaussian item) is associated with each observation at each time step in these three RFS-based filters, severely combinatorial explosion arises as the filtering recursion increases. The pruning threshold and merging threshold must be applied in these filters to restrict the combinatorial explosion [1]. In addition, the three RFS-based filters assume that the birth intensity or density is known a priori. This assumption also implies that initial states and error covariance matrices of targets are known in advance. To obviate the need for the prior initial states or error covariance matrices of birth targets, the adaptive methods for forming the birth object intensity or density are discussed in [16; 17; 18; 19; 20; 21; 22]. The adaptive methods in [16; 20; 21] use the measurements of previous time steps to form the birth intensity or birth filtering density. In order to avoid the repeated use of measurements, the gating technique is needed in these approaches to remove the measurements near the current multi-target states [16; 20]. However, these adaptive methods still require the known error covariance of birth targets. To obviate the need for the prior error covariance of birth targets, the adaptive methods in [17; 18; 19] use the measurements of the previous two time steps to build the potential birth track and then use the potential birth track to form the birth intensity or density. The adaptive \(\delta\)-GLMB (AGLMB) filter [22] uses the measurements of the previous three time steps to build the tentative track based on the rule-based track initiation technique [23], and estimates the state of the tentative track and its error covariance according to the least squares technique. However, the adaptive RFS-based filters still require that the clutter density and survival probability are known in advance. The clutter density and survival probability play important roles in obtaining the predicted and updated densities or intensities in the adaptive RFS-based filters, but it can be challenging to accurately estimate them in real-world scenarios. To track multiple objects in the presence of unknown clutter density, unknown survival probability, and unknown initial state and error covariance, we propose an adaptive marginal multi-target Bayes (AMTB) filter without the need for clutter density and survival probability in this paper. The filter delivers the probability density function (PDF), track label and existence probability of the object in the filtering recursion. Two data association steps are required in the recursion of this filter.