Kalman's optimum linear filter has proved to be immensely popular in the field of computer vision. A less often quoted contribution of Kalman's to the control theory literature is that of the concepts of controllability and observability which may be used to analyse the state transition and observation equations and give insights into the filter's viability. This paper aims to highlight the usefulness of these two ideas during the design stage of the filter and, as well as presenting the standard solutions for linear systems, uses a practical vision application (that of tracking plants for an autonomous crop protection vehicle) to illustrate a useful special case where these methods may be applied to a non-linear system. The application of tests for controllability and observability to the practical non-linear system give not only confirmation that the filter will be able to produce stable estimates, but also gives a lower bound on the number of features required from each image for it to do so.
