The focus of the work in this thesis is concerned with the investigation and development of indirect measurement techniques. The methodology adopted is a combination of practical experimental, analytical deductive reasoning and simulation studies. This has led to proposals for a number of indirect tyre pressure monitoring systems, which are able to detect pressure loss under specific circumstances. The outcome overall is a proposal for a new supervisory system comprising of a modular framework, allowing various algorithms and techniques to be implemented in a complementary manner as they emerge and data sources become available. A number of contributions to the field have been made, which to the knowledge of the author, provide potential for further algorithm development and are imminently applicable given the above. The methods include a tyre pressure diagnosis via a wheel angular velocity comparator, the development of a model-based tyre pressure diagnosis via application of an unknown input observer and a parameter estimation scheme, a model-based tyre pressure diagnosis approach via an enhanced Kalman filter configured to estimate states including the input, a model-based tyre pressure diagnosis via cautious least squares, an investigation and critique of the effects of the choice of sampling interval on discrete-time models and estimation thereof. It is considered, that the extensive literature review provides a valuable historic insight into the tyre fault detection problem. It is clear, from the development and testing of the algorithms (and also the literature), that no single indirect pressure detection method is able to reliably detect changes in all driving scenarios which the regulations typically stipulate (depending on jurisdiction). In the absence of any information about the road input, the majority of the detection work must be shouldered by the wheel angular velocity comparator algorithm. As image recognition and sensor technology develops, it becomes possible to make estimates about the road surface and this removes some of the uncertainty on the input of the model-based parameter estimation approaches. Further work is detailed which goes some way towards realising the next steps in a development cycle suitable for a vehicle manufacturer to take through to the implementation stage.