Super-resolution processing technique for vector sensors

Vector sensors are used in radar, sonar and communications applications. Vector sensors use measurements from multiple, co-located sensors to achieve improved spatial resolvability. Vector sensors obtain multi-variate measurements at a point by measuring the signal in multiple polarizations or the spatial derivatives of the signal. This study focuses on vector sensors which measure the spatial derivatives of the signal. The measurement of the spatial derivatives allows one to extrapolate the signal over an aperture significantly greater than the real aperture of the sensors themselves. The degree to which the signal can be extrapolated will depend on the number of spatial derivatives which are measured. In practice, the vector sensors measure only the lowest order spatial derivatives of a signal. This limits the size of the aperture over which the signal can be extrapolated. In this paper, a super-resolution processing technique is developed for extending the aperture by estimating the higher order spatial derivatives from the measured lower order derivatives. A linear prediction (LP) model is used to write the higher order derivatives in terms of the lower order derivatives. The coefficients of the LP model are estimated using the measurements. The Least Mean Square (LMS) algorithm is used to estimate the LP coefficients from the vector sensor measurements. The LP model is then used to estimate the higher order spatial derivatives. Using the higher order derivatives, the signal can be extrapolated over a larger aperture. The LP model that relates the higher order spatial derivatives to the measured lower order derivatives is formulated. For the purpose of clarity, the study focuses on one-dimensional vector sensors. Simulations are used to study the effectiveness of this technique. The improvement in the spatial resolution is studied as a function of the order of the LP process and signal-to-noise ratio.