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In this paper the track initiation problem is formulated as multiple composite hypothesis testing using maximum likelihood estimation with probabilistic data association (ML-PDA). The hypothesis selection is based on the minimum description length (MDL) criterion. We first review some well-known approaches for statistical model selection and the advantage of the MDL criterion. Then we present one-dimensional examples to illustrate the MDL criterion used in multiple composite hypothesis testing and the performance limit of the ML-PDA for track initiation is interpreted in terms of the sharpness of the hypothesis testing. Finally, we apply the MDL approach for the detection and initiation of tracks of incoming tactical ballistic missiles in the exo-atmospheric phase using a surface-based electronically scanned array (ESA) radar. The targets are characterized by low signal-to-noise ratio (SNR), which leads to low detection probability and high false alarm rate. The target acquisition problem is formulated using a batch of radar scans to detect the presence of up to two targets. The ML-PDA estimator is used to initiate the tracks assuming the target trajectories follow a deterministic state propagation. The approximate MDL criterion is used to determine the number of valid tracks in a surveillance region. The detector and estimator are shown to be effective even at 4.4 dB average SNR.