Theoretical radar-Doppler models for pivoting mechanical and biological objects-of-interest

Abstract

A set of approximate theoretical equations for the Doppler response of monostatic radar signals due to slowly pivoting objects are derived. The treatment is based on physical models extracted from the mechanical engineering community. Potential applications include analysis of load-based vehicle classification and detection of biological movements such as human joint rotations. Several example calculations are presented based on the resulting theoretical formulas. These examples include Doppler calculations for notional first-order vehicle suspension models and first-order human joint (arm/leg) rotation models. Each set of example calculations includes two sets of notional radar parameters in order to provide insight into potential Doppler pivot detection capabilities as a function of basic radar parameters such as frequency and PRF (pulse repetition frequency).

Remote vibrometry recognition of nonlinear eigen-states for object coverage of randomly large size

“…This model of a "welded-together" panel system 19 uses the parameters in Equation 3. A "manual," analytical calculation [7, App C] helped validate the FEA results for the simulated vibration created before application of the laser vibrometry model.…”

“…[35] 18 The extent to which the literature supports the Central Limit Theorem can be found in papers from 1937 through 2003 with Uspensky [37], Landon and Norton [38], Khinchin [39], North [40], and Le Cam [41]. 19 The term welded assumes the plate deflections at both points are the same using an infinitely stiff connection. The closed gap stiffness used in this work is more like hard rubber [7, App B.2.5], but the effect is the same.…”

“…In the full analysis, the structure is a free-floating system using D'Alembert reactions, an analysis technique common to vehicle engineering. See, for example, the numerous "quarter-panel models" in the literature [18,19], which are mostly meant to show how to model some features for reasons stated previously 6 .…”

“…Eq. (18) shows the format of the system matrix for submission to an eigen-solver. Some of the terms in , and , were kind enough to cancel:…”

Local Information from Range-Speed Radar Sequences

“…If the micro-motion has a range dependency the range information is added, this is the 3-D range-speed-time space referred as the 3-D cubic micro-motion feature space, see [17], [12] and [10]. A theoretical study of micro-motion of simple objects like cubes and rods is given by Chen [3] and Mitra [13]. Chen derived a mathematical framework solving the micro-motion modulations induced by vibration, rotation, tumbling and coning motions and applied to point scatterers target models.…”