Localization systems and methods for transmitting timestampable localization signals from anchors according to one or more transmission schedules. The transmission schedules may be generated and updated to achieve desired positioning performance. For example, one or more anchors may transmit localization signals at a different rate than other anchors, the anchor transmission order can be changed, and the signals can partially overlap. In addition, different transmission parameters may be used to transmit two localization signals at the same time without interference. A self-localizing apparatus is able to receive the localization signals and determine its position. The self-localizing apparatus may have a configurable receiver that can select to receive one of multiple available localization signals. The self-localizing apparatuses may have a pair of receivers able to receive two localization signals at the same time. A bridge anchor may be provided to enable a self-localizing apparatus to seamlessly transition between two localization systems.