Tag Archives: Fourier Transform

Taking into account explicitly the dynamics of the environment, and in particular the diverse frequencies of changes, for mobile robot mapping

T. Krajník, J. P. Fentanes, J. M. Santos and T. Duckett, FreMEn: Frequency Map Enhancement for Long-Term Mobile Robot Autonomy in Changing Environments, IEEE Transactions on Robotics, vol. 33, no. 4, pp. 964-977, DOI: 10.1109/TRO.2017.2665664.

We present a new approach to long-term mobile robot mapping in dynamic indoor environments. Unlike traditional world models that are tailored to represent static scenes, our approach explicitly models environmental dynamics. We assume that some of the hidden processes that influence the dynamic environment states are periodic and model the uncertainty of the estimated state variables by their frequency spectra. The spectral model can represent arbitrary timescales of environment dynamics with low memory requirements. Transformation of the spectral model to the time domain allows for the prediction of the future environment states, which improves the robot’s long-term performance in changing environments. Experiments performed over time periods of months to years demonstrate that the approach can efficiently represent large numbers of observations and reliably predict future environment states. The experiments indicate that the model’s predictive capabilities improve mobile robot localization and navigation in changing environments.

Performing filtering on graphs instead of individual signals

E. Isufi, A. Loukas, A. Simonetto and G. Leus, “Autoregressive Moving Average Graph Filtering,” in IEEE Transactions on Signal Processing, vol. 65, no. 2, pp. 274-288, Jan.15, 15 2017. DOI: 10.1109/TSP.2016.2614793.

One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogs of classical filters, but intended for signals defined on graphs. This paper brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which are able to approximate any desired graph frequency response, and give exact solutions for specific graph signal denoising and interpolation problems. The philosophy to design the ARMA coefficients independently from the underlying graph renders the ARMA graph filters suitable in static and, particularly, time-varying settings. The latter occur when the graph signal and/or graph topology are changing over time. We show that in case of a time-varying graph signal, our approach extends naturally to a two-dimensional filter, operating concurrently in the graph and regular time domain. We also derive the graph filter behavior, as well as sufficient conditions for filter stability when the graph and signal are time varying. The analytical and numerical results presented in this paper illustrate that ARMA graph filters are practically appealing for static and time-varying settings, as predicted by theoretical derivations.