Abstract
Abstract. Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.
Highlights
A common problem in signal estimation theory is the estimation of objects’ direction (DOA, direction of arrival) using an array of sensors
We use a general version of the gcd function in order to write the problem as a polynomial
A Pulse-Doppler or frequency modulated continuous wave radar deals most of the time with the single object case, because all objects are first separated in range and velocity
Summary
A common problem in signal estimation theory is the estimation of objects’ direction (DOA, direction of arrival) using an array of sensors. The Cramr-Rao bound only takes local DOA errors into account (Athley, 2005). Athley (2005) approximated the global errors analytically and calculated an error probability per side lobe of the so called beampattern. This allows the analytical calculation of the variance of DOA estimates, which can be used as a cost function for array optimization. Larger errors can even be advantageous, as they are easier to classify as outliers and to reject over time by using tracking These considerations lead to a minimization of global errors, where only the height of the side lobes is important and not their position. If Eq the characteristics are completely different, the proposed al- ter b u;(0 0.4 1.7 4.3)T u0 b u;(0 0.4 1.7 4.3)T
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