The problem of computing estimates of the state vector in a non-stationary dynamic linear model is considered. Such estimates cannot be obtained with the usual Kalman filter because it fails, on finite precision computing machines, when seeded with the infinite variances associated with the required diffuse or partially diffuse prior probability distribution. The response in the literature has been the development of a number of relatively complex hybrid filters specifically designed to avoid the problem. However, it is argued in this paper that this response has been largely unwarranted. Rather, it is established that any square root implementation of the Kalman filter is capable of producing satisfactory results, so long as the required triangular orthogonalisation calculations are undertaken with standard fast Givens transformations, rather than the more usual Householder or Gram-Schmidt procedures.