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Filtering Algorithm Based on Innovations Theory

for White Gaussian Plus Colored Observation Noise

**Seiichi Nakamori**

Kagoshima University

1-20-6, Kohrimoto, Kagoshima 890, Japan

This paper presents a new filtering algorithm based on the innovations theory for white Gaussian noise plus colored observation noise. The autocovariance function of the signal plus colored noise, the variance of the white Gaussian observation noise and the crosscovariance function between the signal and the observed value are assumed known. The presented algorithm is quite different from the previous one in the point that the current approach does not assume an uncorrelated property between the signal and the colored noise. The autocovariance function of the signal plus colored noise is calculated by subtracting the variance of the white Gaussian observation noise from the autocovariance function of the observed value.

Keywords: estimation problems, filtering algorithm, Wiener-Hopf integral equation, Wiener process, colored noise

Received February 16, 1989; revised April 25, 1989.

Communicated by Jun S. Huang.