The suspension system of a ground vehicle moving on or off road can be improved by so called "active control" using control strategies which require feedback of all or some of the system states. A stochastic state estimator, or "Kalman filter", can be used to estimate these states. Various Kalman filters suited to this problem are developed, and optimal control strategies suited to these Kalman filters are specified and assessed. It turns out that there are basic problems of unobservability and uncontrollability inherent in the behaviour of such suspension systems, and original solutions to these problems are suggested and explored. A laboratory equipment is designed and constructed to reveal the behaviour of hydraulic actuators in this context, and this is used to ensure that the strategies suggested are realistic. An Intel 8086 microprocessor based circuit in which a practical Kalman filter can be realized is designed. A considerable number of computer simulations are also used to test and assess the estimation and control strategies. All these represent original work by the author.