Improvement of trigonometric function reproduction methods in radar data processing systems
Abstract
Various methods of trigonometric function reproduction are widely used in computational procedures of primary and secondary radar data processing systems, radar control and diagnostics systems. This paper deals with search for Chebyshev polynomials of best approximation of varying degrees based on integrated optimization criterion, which minimize the maximum possible approximation error within 3...64 significant output figures. The algorithm efficiency estimation was evaluated by the maximized gain at the limited costs not exceeding a certain value, and the cost was the sum denoting the number of mathematical operations and the number of invariables extracted from memory. Chebyshev polynomials from zero power to eleventh power are obtained; their corresponding values of approximation accuracy are calculated and computational costs for approximation of standard trigonometric functions of sine, tangent and inverse trigonometric functions – arcsine and arctangent- are derived. To improve approximation accuracy of trigonometric and arc trigonometric functions in the specified interval of values, a method of splitting into two subintervals is proposed, which ensures twofold increase of approximation accuracy with a slight gain in algorithm complexity. A pool of trigonometric functions with the range of given rate errors of order [0.2; 10–8] was created for the first time. Improved reproduction algorithms are developed when ensuring the rise of discrete increment of two or three or more significant result figures with a fixed increase in algorithm complexity of no more than for 2-3 operations in representation range for output data of 2-32 and more binary bits. Result error reduction is provided via cancellation effect of component errors, bit grids of special-purpose matchers are reduced by 2-5 binary bits.
