In the current gas turbine market, the traditional design-test-redesign loop is not a viable solution to deploy new products within short timeframes. Hence, to keep the amount of testing to an absolute minimum, theoretical simulation tools like Finite Element Modelling (FEM) have become a driving force in the design of blades to predict the dynamic behaviour of compressor and turbine assemblies in high-speed and unsteady flows. The predictions from these simulation tools need to be supported and validated by measurements. For the past five years, Rolls-Royce Blade Tip Timing (BTT) technology has been replacing rotating Strain Gauge systems to measure the vibration of compressor blades, reducing development times and costs of new aero engine programmes. The overall aim of the present thesis is to progress the BTT technology to be applied to aero engine turbine modules. To this end, the two main objectives of this project are: i. To improve the current validated Rolls-Royce BTT extraction techniques, through the development of novel algorithms for single/multiple asynchronous and responses. ii. To validate the improved extraction using simulated and real engine test data in order to bring the Turbine BTT technology to a Rolls-Royce Technology Readiness Level (TRL) of 4 (i.e. component and/or partial system validation in laboratory environment). The methodology adopted for the development of the novel algorithms is entirely based on matrix algebra and makes extensive use of singular value decomposition as a means for assessing the degree optimisation achieved through various novel manipulations of the input (probe) raw data. The principle contributions of this thesis are threefold: i. The development of new BTT matrix-based models for single/multiple non-integral and integral engine order responses that removed certain pre-processing assumptions required by the current method. ii. The development of BTT technology to operate under the constraint of having equally spaced probes, which is unavoidable in turbines and renders current BTT methods unusable for turbine applications. iii. The development of methods for extracting measurement uncertainty and signal to noise ratios that are based solely on the raw data, without reliance on simulated reference data. Following the verification and validation of the new processing algorithms against simulated data and against validated software with numerous examples of actual engine test data, a Rolls-Royce's Research & Technology (R&T) Critical Capability Acquisition and Capability Readiness (CCAR) review has accredited the novel techniques with a TRL of 4.