This work studies the feasibility of a novel two-step algorithm for infrastructure and object positioning, using pairwise distances. The proposal is based on the optimization algorithms, Scaling-by-Majorizing-a-Complicated-Function and the Limited-Memory-Broyden-Fletcher-Goldfarb-Shannon. A qualitative evaluation of these algorithms is performed for 3D positioning. As the final stage, smoothing filtering techniques are applied to estimate the trajectory, from the previously obtained positions. This approach can also be used as a synthetic gesture data generator framework. This framework is independent from the hardware and can be used to simulate the estimation of trajectories from noisy distances gathered with a large range of sensors by modifying the noise properties of the initial distances. The framework is validated, using a system of ultrasound transceivers. The results show this framework to be an efficient and simple positioning and filtering approach, accurately reconstructing the real path followed by the mobile object while maintaining low latency. Furthermore, these capabilities can be exploited by using the proposed algorithms for synthetic data generation, as demonstrated in this work, where synthetic ultrasound gesture data are generated.
Keywords: infrastructure positioning; multidimensional scaling; object positioning; synthetic data generation; trajectory optimization; ultrasound.