Linear Prediction Approaches to Compensation of Missing Measurements in Kalman Filtering

Kalman filter relies heavily on perfect knowledge of sensor readings, used to compute the minimum mean square error estimate of the system state. However in reality, unavailability of output data might occur due to factors including sensor faults and failures, confined memory spaces of buffer registers and congestion of communication channels. Therefore investigations on the effectiveness of Kalman filtering in the case of imperfect data have, since the last decade, been an interesting yet challenging research topic. The prevailed methodology employed in the state estimation for imperfect data is the open loop estimation wherein the measurement update step is skipped during data loss time. This method has several shortcomings such as high divergence rate, not regaining its steady states after the data is resumed, etc. This thesis proposes a novel approach, which is found efficient for both stationary and nonstationary processes, for the above scenario, based on linear prediction schemes. Utilising the concept of linear prediction, the missing data (output signal) is reconstructed through modified linear prediction schemes. This signal is then employed in Kalman filtering at the measurement update step. To reduce the computational cost in the large matrix inversions, a modified Levinson-Durbin algorithm is employed. It is shown that the proposed scheme offers promising results in the event of loss of observations and exhibits the general properties of conventional Kalman filters. To demonstrate the effectiveness of the proposed scheme, a rigid body spacecraft case study subject to measurement loss has been considered.