Recovering Observability via Active Sensing

Observability is a formal property of a system that ensures the ability to estimate the system's states from output measurements and knowledge of the inputs. In engineering, sensors are typically designed and deployed to guarantee observability irrespective of the control input, thereby simplifying control systems design. Here, we consider a class of nonlinear sensors that require `persistently exciting' control inputs to maintain observability. This choice of sensor models is motivated by biological sensing systems which `adapt' to constant stimuli, giving them a very high dynamic range, but leading to a phenomenon known as perceptual fading. To prevent perceptual fading, animals employ active sensing in the form of time-varying motor commands that continually stimulate sensory receptors. To capture this phenomenon, we introduce a simplified sensor model that requires active sensing inputs to maintain observability. Under certain assumptions, the input-output characteristics of the active sensing system is shown to be equivalent to an observable linear time-invariant (LTI) system. Using the framework of Harmonic Transfer Functions, the equivalent system is identified by (1) modulating the system via a sinusoidal active input, (2) demodulating the resulting output, and (3) low-pass filtering. This relatively simple framework for active sensing may pave the way for the design and deployment of adaptive sensory systems for engineering applications.