Initialization of the Kalman filter without assumptions on the initial state

In absence of covariance data, Kalman filters are usually initialized by guessing the initial state. Making the variance of the initial state estimate large makes sure that the estimate converges quickly and that the influence of the initial guess soon will be negligible. If, however, only very few measurements are available during the estimation process and an estimate is wanted as soon as possible, this might not be enough. This paper presents a method to initialize the Kalman filter without any knowledge about the distribution of the initial state and without making any guesses.