Study on Navigation Accuracies

Part 1: Theoretical Approach for a Height Finding Radar by a New Method

Abstract

This paper describes a theoretical approach for estimating the cruising altitude of an aircraft using a conventional pulse radar with a rotating fan beam antenna. Under the assumption that an aircraft maintains her altitude and speed while she traverses the fan beam, a method for estimating the height of the aircraft from the data taken by each scan is described.

The data obtained by several scans are assumed to be processed by a mini-computer and the height of the aircraft is estimated by a least square method and sequential approximation. Between the items of information obtained for each scan (the distance, the elevation angle and the data aquisition time) a theoretical relationship is established as the following observation equation, and one of the coefficients contains the height information.

R_i²=(c₁t_i+c₂)²+c₃/cos²β_i

where R_i: distance

β_i: elevation angle

t_i: data acquisition time (i=1, 2,....., n)

c₃=h² h: height n: number of data set

The coefficient is determined by a curve fitting method. This paper describes the method of analysis first, and then an accuracy of the method by a computer simulation.