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This research effort studies the use of redundant induction coil gauges to reduce state estimation uncertainties for moving Lagrangian points (LPs); e.g. discrete points, moving interfaces, projectiles, etc. The technique embeds a small, high-strength magnet at the LP and simultaneously tracks the magnet continuously with five (5) or more induction coils along a single axis of motion. A calibrated coil gauge model is presented as a function of LP position and velocity. The optimized LP state (position and velocity) estimate based upon redundant LP observations allows direct solution for LP velocity; requiring only one differentiation step to obtain acceleration. A specific experimental implementation (Particulate Materials Meso-scale Diagnostics system) is simulated to evaluate and minimize the expected state estimation errors. Induction coil signals with various levels of noise are simulated based upon a prescribed LP state variation with time. The state optimization algorithm attempts to recover the truth state values. Worst-case position estimation errors of ±0.3 mm and velocity estimation errors of ±0.46 m/s are determined for LPs travelling 0-1,000 m/s at realistic in-lab data noise levels. [ABSTRACT FROM AUTHOR]

The accurate determination of the steering vector of a sensor array that corresponds to a desired signal is often hindered by uncertainties due to array imperfections, such as the presence of a direction-of-arrival (DOA) estimation error, mutual coupling, array sensor gain/phase uncertainties, and senor position perturbations. Consequently, the performance of conventional beamforming algorithms that use the nominal steering vector may be significantly degraded. A new method for recursively correcting possible deterministic errors in the estimated steering vector is proposed here. It employs the subspace principle and estimates the desired steering vector by using a convex optimization approach. We show that the solution can be obtained in closed form by using the Lagrange multiplier method. As the proposed method is based on an extended version of the conventional orthonormal PAST (OPAST) algorithm, it has low implementation complexity, and moving sources can be handled. In addition, a robust beamformer with a new error bound that uses the proposed steering vector estimate is derived by optimizing the worst case performance of the array after taking the uncertainties of the array covariance matrix into account. This gives a diagonally loaded Capon beamformer, where the loading level is related to the bound of the uncertainty in the array covariance matrix. Numerical results show that the proposed algorithm performs well, especially at high signal-to-noise ratio (SNR) and in the presence of deterministic sensor uncertainties. [ABSTRACT FROM PUBLISHER]