This study deals with the design of a load sensorless multi-loop control system for the stand-alone inverter. In the proposed strategy, only the inverter current is measured, which is practically required for both control and protection purposes, then the load voltage and current are both estimated using the linear Kalman filter algorithm, and the gradient descent adaptive control method, respectively. The estimated quantities are used as feedback signals of an inner-outer double-loop controller, which uses a proportional-resonant outer-controller to regulate the output voltage with minimum steady-state error and a simple proportional inner-controller to provide active damping and improve the transient performance. The controller parameters are designed in the frequency domain based on the required bandwidth and stability margin. Furthermore, the controllability and observability, as well as the stability of overall digital control system, including the dynamics of estimators, are analytically investigated. Simulation and experimental results, with a 600 VA prototype, confirm the theoretical achievements and illustrate the excellent performance of the proposed estimation and control scheme.