A modified adaptive Kalman filtering algorithm considering the system matrix uncertainty and data instability of the state space theory for Positron emission tomography(PET) reconstruction was proposed. Based on tracer kinetic theory

an evolution equation of the tracer is introduced as a prior to constrain the reconstruction. Along with the observation equation of the detectors

the two equations constitute a state spatial model. After introducing virtual noise to represent the error of the system matrix

the modified adaptive Kalman filter is applied to estimate the process and the observation noise and meantime completes the PET reconstruction. The performance of the algorithm was verified by computer simulations

which show that modified adaptive Kalman filter is more robust than the traditional maximum likelihood expectation maximization method and filtered back projection methods. The results are meaningful and particularly suitable for the real positron emission tomography system.