Gyroscopic tracking systems in the presence of multidimensional random disturbances

Abstract

Gyroscopic tracking systems may be designed to follow multidimensional input signals. Thus, for example, on the basis of a three-axis gyroscope system [1] it is possible to construct a tracking system to follow a three-dimensional signal on three axes properly oriented in a three-dimensional space. It is possible to follow two-dimensional input signals with a two-axis gyroscope system. On the basis of the theory of multidimensional random processes [2–5], we treat below the problem of constructing an optimal gyroscopic tracking system for following a two-dimensional input signal in the presence of not only noise in the input, but also disturbances caused by the motion of the object on which the tracking system is mounted. As is shown in the paper, these disturbances cause intercorrelation of the reduced input signals which determine the optimal weighting function, even in the case when the input signals themselves are uncorrelated. The correlation function of the reduced input signals is determined both by the statistical characteristics of the disturbances and by the structure and parameters of the transfer function matrix of the gyroscope system. Hence, the optimal weight function of the entire tracking system as a unit, and not only its correction circuit, depends to a large extent on the dynamic characteristics of the gyroscope system.