State estimation with measurement error compensation using neural network

For a system with redundant sensors, the estimated state from the Kalman filter is biased if sensor mounting error existed. To remove this bias, the mounting errors must be compensated first before using the Kalman filter. It is shown that only the projection part of the sensors errors in the measurement space needs to be compensated. If the state of a system is unavailable, a neuro-fuzzy network can be used to estimate the compensation term. This method is simpler, as it does not require a model for the errors as proposed by Hall et al. (1983). A sub-optimal Kalman filter with measurement compensation that restrains each row of the Kalman gain matrix to be in the measurement space is also derived. An example is presented to illustrate the performance of the proposed method.