Advances in the control of autonomous systems have accompanied an expansion in the potential applications for autonomous robotic swarms. The success of applications involving humans depends on the quality of interaction with the swarm, particularly the trust that the commander places in the swarm. Absent from the literature is the design of commander trust dynamics that incorporate asymmetric responses to swarm performance. This paper focuses on developing an estimated trust model that employs a switched linear system structure. The identified model is used in a model-based observer that eliminates the need for self-reported trust measurements. Results from a recent user study with 51 participants illustrate considerations during the estimation of population parameters for such nonlinear model-based observers. It is anticipated that such a trust observer can be used to augment communication interfaces for human-swarm interactions in complex environments, leading to better performing systems incorporating humans in the loop.