**3. LM-IPDA Algorithm for Multi-Target Tracking**

In a cluttered environment, multi-target tracking algorithms with data association such as global nearest neighbor (GNN) [26,27] and joint probabilistic data association (JPDA) [28–30] have been widely used. However, these algorithms in general do not include an FTD procedure that can distinguish the true tracks generated by the target measurements from the false tracks generated by the clutter measurements. JIPDA and LM-IPDA are multi-target tracking algorithms with FTD functions for autonomous track management. JIPDA has optimal target tracking performance for single scan data association since it probabilistically takes into account all possible events between measurements and tracks in the cluster for each scan. However, it has heavy computational loads as the number of feasible joint events to be considered increases combinatorially depending on the number of measurements and the number of tracks. In this paper, LM-IPDA instead of JIPDA is used for multi-target tracking as the computation time increases linearly commensurate with the number of targets. In LM-IPDA, the state of track *τ* is represented as a hybrid state that consists of the target existence event (discrete event) and the trajectory state (continuous variable) such as:

$$p[\mathbf{x}\_{k-1}^{\mathsf{T}}, \boldsymbol{\chi}\_{k-1}^{\mathsf{T}} | \mathbf{Z}^{k-1}] = P\left\{\boldsymbol{\chi}\_{k-1}^{\mathsf{T}} | \mathbf{Z}^{k-1}\right\} p(\mathbf{x}\_{k-1}^{\mathsf{T}} | \boldsymbol{\chi}\_{k-1}^{\mathsf{T}}, \mathbf{Z}^{k-1}),\tag{9}$$

where *χ<sup>τ</sup> <sup>k</sup>*−<sup>1</sup> represents the existence event of target *<sup>τ</sup>* at scan *<sup>k</sup>* <sup>−</sup> 1, and the probability density function of the target state at scan *k* satisfies:

$$p(\mathbf{x}\_{k-1}^{\tau}|\chi\_{k-1}^{\tau}, \mathbf{Z}^{k-1}) = N(\mathbf{x}\_{k-1}^{\tau}; \mathbf{\hat{x}}\_{k-1|k-1}^{\tau}, \mathbf{P}\_{k-1|k-1}^{\tau}).\tag{10}$$

The track recursion is composed of the following steps:

