The problem of pursuit has been studied mostly in the context of missile guidance and navigation, however, it is also an essential component in biological systems ranging from prey capture to mating and in bio-inspired engineering applications with small, cheap, and agile vehicles. We consider the pursuit problem with a focus on robustness to noisy sensor measurements and efficiency in the control effort. We design a pursuit law based on Lyapunov analysis and establish its robustness to unknown target acceleration and measurement errors using the concept of ultimate boundedness. We also present the results from experiments conducted to study the practical challenges involved in pursuit by lightweight platforms with noisy sensors. These experiments highlight the benefit of using less control effort in the presence of large measurement errors as compared to existing missile guidance laws.