An HMM Approach with a Quantum Receiver on 2-D Image Field to Identify Footsteps

In this paper a novel method is proposed to detect footsteps by taking 2-D image field that varies with time and is expressed as superposition of two sinusoids whose frequency doublets, phases and amplitudes vary from one time slot to another in accordance with the Markov transition probability law. Apart from this within each time slot there is white measurement noise. The aim is to estimate the states of this Hidden Markov Model (HMM) namely frequency doublets, phases, amplitudes and the 2-D sinusoids with each time slot by taking a noisy measurement of the image field. This has applications wherein footsteps of intruder generate 2-D signal along the ground and estimates of their 2-D frequencies and amplitudes enables one to characterize the signal i. e. whether it is generated by possible target and if so then what type of target, human, animal or vehicle. Finally we present a quantum receiver for estimating the parameter of HMM transition probability. This is useful when the signals are very weak.