IntroductIonSpace-borne infrared missile early-warning system is an important component of missile defense systems. By detecting the azimuth and elevation angles of a missile, the early-warning system can provide a real-time report of each occurrence of a missile launch, and estimate launch parameters and trajectory 1 . The estimation of boost-phase trajectory from space-borne line-of-sight (LOS) measurements. Due to the lack of distance information between a missile and observational satellites, the first problem that needs to be settled is the poor-observability 2,3 . There are two solutions to this problem: one is to increase the number of satellites; the other is to incorporate a priori information into estimation. We focus on the later approach in this paper.A priori information in trajectory estimation can be divided into two levels: a priori information about trajectory model and parameters. Generally, a priori information about model is expressed by a parameterless model with high accuracy. A typical parameterless model is the profile-based model 4,5,11 , which assumes that one can build a profile database before launch 6 . Since a profile-based model only contains four launch parameters, it has conquered the problem of poorobservability effectively. However, an accurate profile of an incoming missile is hard to obtain. Hence, the 'full knowledge' profile has to be improved to increase its adaptability. The pseudo-measurement approach, which takes constraints on trajectory as measurements, can also be treated as a priori information about trajectory model. For example, equalityconstraints are considered as pseudo-measurements in state estimation in 7 . In 8 , the constraints of altitude and speed at the first measurement epoch of a ballistic target are considered as pseudo-measurements.A priori information about parameters refers to prior distribution of model parameters. To include this kind of information, one can employ the so-called Bayesian paradigm. It has been pointed out by 9 that the Bayesian paradigm has no difficulty in treating non-identifiable parameters. But one might be misled by a wrong prior distribution, especially in poor-observability scenarios like the current situation.Recently Tharmarasa 10 , et al. proposes a profile-free launch point estimator using smoothing followed by backward prediction. They focus on using less a priori information as far as possible, which makes their method work well only in a multi-sensor scenario. Kim 11 et al. proposes a launch point estimator based-on k-NN search. Their method is a profilebased method too, but with a different kind of profile.An estimator for trajectory estimation from space-borne LOS measurements following the Bayesian paradigm were proposed in the paper. (i) A new kind of boost-phase trajectory profile, which is more adaptable than other existing profiles; (ii) A profile-based maximum penalised likelihood estimator (PMPLE), which can incorporate different kinds of information into trajectory estimation; (iii) A 1 L and log-barrier pe...