Demonstrated trajectory selection by hidden Markov model

Abstract

This paper proposes an automatic selection scheme to choose the most consistent trajectory among a number of human-demonstrated ones. The consistency-determination is based on the hidden Markov model (HMM) technique. There are three stages involved. The first stage is preprocessing of the human-generated trajectories. It includes short-time Fourier transform and vector quantization. The former maps the trajectories from the time domain to the frequency domain, and the latter quantizes a list of frequency spectra to a finite number of prototype spectrum-vectors, called symbols. The second stage is training of the HMM. The unknown model parameters in the HMM are tuned by the concept of counting event occurrences. The quantized symbols are counted so that probabilities of occurrences are applied to train the HMM. The third stage is measurement of the consistency of every trajectory. Each trajectory is sent through the trained HMM. A probability-based likelihood index is evaluated which reflects the consistency of the trajectory with the HMM. The trajectory giving the largest likelihood index is considered to be the most consistent one and will be selected.