This paper develops estimators for locating a rigid body using the time measurements, and the Doppler as well if it is moving, between the sensors in the rigid body and a few landmarks outside. The challenge of rigid body localization is that in addition to the position, we are also interested in obtaining the rotation parameters of the rigid body that must belong to the special orthogonal group. The proposed estimators are non-iterative and have two steps: preliminary and refinement. The preliminary step provides a coarse estimate and the refinement step improves the first step estimate to yield an accurate solution. When the rigid body is stationary, we are able to locate the body with accuracy higher than the solutions of comparable complexity found in the literature. When the rigid body is moving, we develop an estimator that contains the additional unknowns of angular and translational velocities. Simulations show that the proposed estimators, in both stationary and moving cases, can approach the Cramer-Rao Lower Bound performance under Gaussian noise over the small error region.

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This paper presents a human walking speed estimation algorithm using a Doppler radar system for in-home passive gait assessment of elderly adults. The Fast Fourier Transform (FFT) has been a common approach to obtain the gait speed estimation. The proposed algorithm analyzes the received radar signal by counting its zero-crossing periods in the time domain and applies an interquartile range filter to improve its robustness with respect to the gait signature dynamics in the radar data. The proposed algorithm provides better accuracy and does not seem to produce extreme incorrect speed estimates compared to the previously developed FFT method. It has been applied to the Doppler radar system that is deployed in in-home environments to continuously monitor the daily activities of the senior residences and estimate their gait speeds. Improving the accuracy of gait parameters can better facilitate the assessment of the physical conditions of the seniors.

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