Adaptive Kalman filtering has attracted a lot of attention during the last 15 years; perusal of the published literature shows the diversity of the techniques that have been proposed in this context. In this note, we present an adaptive Kalman filtering scheme, based on the quantization of the parameter space; this quantization is performed in order to generate a state estimate with a prescribed degree of suboptimality. The philosophy is to shift, as much as possible, the computational burden to off-line calculations, and perform the real time computations with algorithms of reduced complexity. This filtering scheme can be integrated into a control loop, so that an efficient adaptive controller is obtained.