Estimation of the Time-Variant Velocity of a Single Walking Person in Two-Dimensional Non-Stationary Indoor Environments Using Radio-Frequency Techniques

Accurate estimation of the time-variant (TV) velocity of moving persons/objects in indoor spaces is of crucial importance for numerous wireless indoor applications. This article introduces a novel iterative procedure to estimate the TV velocity, i.e., TV speed and TV angle-of-motion (AOM), of a single moving person in 2D indoor environments by using radio-frequency (RF) techniques. The indoor area is equipped with a distributed $2\times 2$ multiple-input multiple-output (MIMO) system. The proposed method is divided into two parts. In the first part, we estimate the path gains and the instantaneous Doppler frequencies by fitting the exact spectrograms of the complex channel gains of a 2D non-stationary channel model to the spectrograms obtained from the received radio signals. In the second part of this work, another estimation procedure is proposed to deduce the desired TV velocity from the estimated TV Doppler frequencies. Although, the primary objective of the proposed iterative estimation techniques is to determine the TV velocity, i.e., TV speed and TV AOM, of the walking person, it computes all channel parameters including the path gains, the TV angles-of-arrival, and the TV angles-of-departure. Closed-form solutions are derived for the path gains, the TV Doppler frequencies, the TV speed, and the TV angles, which in turn reduces considerably the complexity of the optimization methods. Numerical results are provided to demonstrate the validity and robustness of the proposed algorithms against noise. This is accomplished by analyzing the agreement between the estimated parameters of interest with the corresponding exact values, which are known from computer generated test signals. The estimation accuracy of the proposed method is evaluated for different values of the signal-to-noise (SNR) ratio. It is shown that this technique estimates the TV Doppler frequencies and TV speed with an accuracy between 70% and 97% for SNR values ranging from 0 dB to 20 dB.