This technical note (TN) develops Bayesian track extraction algorithms for targets modeled as hidden reciprocal chains (HRC). HRC are a class of finite-state random process models that generalize the familiar hidden Markov chains (HMC). HRC are able to model the "intention" of a target to proceed from a given origin to a destination, behavior that cannot be properly captured by an HMC. While Bayesian estimation problems for HRC have previously been studied, this TN focuses principally on the problem of track extraction, that is, confirming target existence in a set of observations of uncertain origin. Simulation examples are presented, which show that the additional model information contained in an HRC, measured in terms of Kullback-Leibler divergence, improves detection performance when compared to HMC models.