Estimating Noise Variances by Using Multiple Observers

Unknown variances of the noises that excite a time-invariant, linear dynamic system and/or in the observation of its output can be estimated by use of multiple observers. One observer is needed, in general, for each unknown variance. Each observer is time invariant and has different gains from the others. It is shown that each unknown variance is a linear combination of the variances of the residuals of the observers. The required estimates of the noise variances are obtained by using the measured variances of the residuals. The method presented in this paper is illustrated by an application to determining noise parameters in a ring laser gyro.     

Optimum Steady-State Position and Velocity Estimation Using Noisy Sampled Position Data

The Kalman filtering technique is used to obtain analytical expressions for the optimum position and velocity accuracy that can be achieved in a navigation system that measures position at uniform sampling intervals of T seconds through random noise with an rms value of ?x. A one-dimensional dynamic model, with piecewise-constant acceleration assumed, is used in the analysis, in which analytic expressions for position and velocity accuracy (mean square), before and after observations, are obtained. The errors are maximum immediately before position measurements are made. The maximum position error, however, can be bounded by the inherent sensor error by use of a sufficiently high sampling rate, which depends on the sensor accuracy and acceleration level. The steady-state Kalman filter for realizing the optimum estimates consists of a double integrator, the initial conditions of which are reset at each observation.     

Analysis Strapdown Navigation Using Quaternions

A brief review of the theory of strapdown inertial navigation is presented in which the attitude of the sensor box with respect to inertial space is represented by the four-parameter quaternion vector. . A 4X4 matrix R is defined which aids in relating quaternions to direction cosines and facilitates interpretation of the equations for error propagation, which are also derived. In the interpretation, it is shown that the error in the quaternion vector causes aor-(correctable) scale factor error and an equivalent tilt vector error that propagates the same way as the platform tilt vector in a gimbaled system.     

Noise Injected into Coherent Carrier Signals by Random Phase Changes

The autocorrelation and power spectrum of spurii arising from periodic random phase injections into a coherent backscatter signal are found. Design considerations of appropriate filters to eliminate spurii noise is discussed.