Multivariable Nyquist plot of discrete-time stationary optimal linear filters

The behaviour of the locus of the determinant of the optimal discrete-time stationary Kalman filter return difference matrix, as the z-transform variable traverses the unit circle, is considered. It is found that this locus does not enter a circle which is centered at the origin and whose radius is determined by the signal/noise ratio. This radius increases from zero, in the case where the measurements are free of noise, to one, in the case where all the components of the measurement noise vector have unbounded intensities.