This paper is generally concerned with multiple target tracking with possibly unresolved or merged measurements, and is motivated by recent advances in signal processing, particularly radar signal processing, that enable the extraction of two or more targets from a single merged detection, under certain conditions. The output of such signal processing can be viewed as a result of a process of estimating an unknown number of objects with no particular meaningful ordering, i.e., mathematically best characterized as a simple finite point process or, equivalently, a random finite set, and a priori and a posteriori statistics can be described as a set of Janossy measures. However, since a sensor generally observes only a subspace of a target state space, it may not be possible to express the target detection results as a full-dimensional probability distribution on a target state space. In this paper, we will try to extend the concept of the Janossy measure density function to express information pertaining only to an instantaneously observable part of target state space, to formulate what we tentatively called the generalized Janossy density function, which may be viewed as an unnormalized or improper probability distribution. Based on this concept of the generalized Janossy measure, or the likelihood function concept, a tracking process can be formulated as a process of recursively updating, by the measurement likelihood functions, the a posteriori probability distribution expressed as a set of Janossy measure density functions.