Communication systems and methods employing receivers with estimators

Communications systems and methods employ receivers which utilize estimators, such as extended Kalman filters, to estimate a transmitted information signal based only upon initial parameters in a transmitter and a single transmitted state of the transmitter. This arrangement facilitates the use of inherently secure chaotic modulation schemes in the transmitter. In one embodiment, one or more parameters of nonlinear transmitter elements are modulated with one or more information signals to generate a chaotically varying transmission signal. A communication scheme known as Parameter Division Multiple Access (PDMA) is thus created in which multiple information signals from multiple transmitters can be combined and transmitted to corresponding multiple receivers in a single transmission signal. A special Kalman filter known as a feedback Kalman filter is employed for separating each receiver's corresponding portion of the transmitted signal.