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This paper presents a simplified recursive filtering approach to noise removal process in modern accelerometers. The noise at the end of sensor output stems from the motion of the spacecraft during launch and orbital corrections plus thermal noise of the transistors. These two factors provide the ideal conditions for the application of the recursive filter where measurement and process noises are involved. The process noise covariance and measurement noise covariance matrices are the key variables of the filter. The resolution of the accelerometer is raised to a few mili G's which provides the requested conditions for the application of autonomous spacecraft.