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A general discrete-time Kalman filter (KF) for state matrix estimation using matrix measurements is presented. The new algorithm evaluates the state matrix estimate and the estimation error covariance matrix in terms of the original system matrices. The proposed algorithm naturally fits systems which are most conveniently described by matrix process and measurement equations. Its formulation uses a compact notation for aiding both intuition and mathematical manipulation. It is a straightforward extension of the classical KF, and includes as special cases other matrix filters that were developed in the past. Beyond the analytical value of the matrix filter, it is shown through various examples arising in engineering problems that this filter can he computationally more efficient than its vectorized version.

A novel missile guidance law that is dependent on the conditional probability density function of the estimated states is presented. The guidance law is derived by analyzing an interception scenario in the framework of an linear quadratic Gaussian (LQG) terminal control problem with bounded acceleration command. The nonlinear saturation function is represented by the equivalent random input describing function. Since for the investigated problem the certainty equivalence property is not valid, the resulting controller depends on the measurement noise level and on the saturation limit. In comparison to the classical optimal guidance law (OGL), the maximal value of the effective navigation gain is achieved during the engagement instead of near the terminal time. Thus, the saturation limit is reached earlier so as to have enough time to reduce the guidance errors. Using Monte-Carlo simulations, the superiority of the new guidance law over the classical OGL is shown. This validates the new approach of designing an estimation statistics dependent guidance law by using a random input describing function to approximate the missile's acceleration saturation.

The Simple Adaptive Control (SAC) controls an augmented plant that comprises the true plant with Parallel Feedforward . The Almost Strictly Positive Real (ASPR) property of the augmented plant guarantees the stability of the tracking loop and leads to asymptotic following. Prior publications have shown that, based only on the prior knowledge on stabilizability properties of systems (usually available), the Parallel Feedforward Configuration (PFC) allows adaptive control of realistic systems, even if they are both unstable and non-minimum phase. However, it was commonly thought that the addition of the PFC requires a price when compared with good linear time invariant (LTI) designs that do not use any addition to the plant. The paper shows that the use of a properly designed SAC with PFC, as Add-On to LTI system design, improves the performance. Although SAC doesn't directly control the true plant tracking error, it always gives smaller tracking error and reduced sensitivity to plant disturbance and output measurement noise with respect to the best LTI controller. [ABSTRACT FROM AUTHOR]