Abstract
This paper presents a modified measurement differentiation method for the stochastic control systems with both white and colored measurement noises. The first key point of this method is the use of a first-order shaping filter, i.e., a colored noise to approximate the white measurement noise. In order to preserve the wide-band nature of the white noise, the bandwidth of the shaping filter is set to be 10 times that of the system fastest mode. In addition, the root-mean-square value of the shaping filter output is set to be equal to that of the original white noise. The second key point involves augmenting this new colored noise with the original colored ones. The other processes are similar to the traditional measurement differentiation method. This way the proposed method can take both colored and white measurement noises into consideration without increasing the order of the state equations. However, this advantage cannot be obtained by the measurement differentiation method or the state augmentation method. A stochastic optimal control system with time-varying colored and white measurement noises is given for illustration.
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