Weak target recognition, tracking and track management with a low signal-to-noise ratio (SNR) are always tricky problems. Probability hypothesis density (PHD) filtering propagates the first-order multi-target moment to obtain the best Poisson approximation to multi-target density. The PHD filtering does not consider explicit associations between measurements and targets, which is computationally efficient. But it cannot distinguish different targets or extract the time series of track states. Based on track-before-detect (TBD) strategies, this paper proposes labeled PHD (LPHD) filtering and derives its close-form solution, which identifies targets with a unique label. It is derived based on rigorous Bayes criteria, finite set statistics and Kullback-Leibler divergence minimization approximation. The separable TBD-based observation likelihood is conjugate to the Poisson mixture prior for LPHD filtering. Under the point-target assumption, the multi-hypothesis assignments of pixel-to-target are implemented with Murty's K-shortest path algorithm for LPHD filtering. Additionally, sequential Monte Carlo (SMC) implementations under the nonlinear non-Gaussian assumption are devised. Finally, simulations exhibit good performance in low SNR scenarios.