There has been increased interest in the detection of adversarial security attacks on the control functions of autonomous systems. In this research, we propose the use of low cost state space checks for detection of security attacks on sensors, actuators and control software of autonomous systems. These attacks are assumed to be initiated by intrusions, malware or embedded hardware Trojans. The checks consist of predicting sensor (actuator) values from prior values of actuators (sensors) and external control inputs. The associated nonlinear predictors are learned in real time using Gaussian Process regressors (GPs). Recovery from sensor and actuator attacks is performed by sensor-actuator data restoration. Recovery from control software attacks is performed by reverting to a lightweight linearized controller that prevents short-term catastrophic system malfunction. Experimental results on a brake-by-wire, steer-by-wire system and a traveling robot (hardware) prove the viability of the proposed approach.