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This paper investigates the problem of state estimation incorporating infrequent, delayed and integral measurements. In chemical process, there often exist two types of measurements. On one hand, the measurements for process variables such as flow rates and pressures are sampled frequently and are available nearly instantaneously. On the other hand, the measurements for quality variables such as concentration are sampled infrequently and are available with a delay due to long analysis time involved. Moreover, due to the interval time taken by chemical sample collection, the measurements for some quality variables have another important characteristic: it is a function of the states of the compositions over a period of time. This paper formulates the process with infrequent, delayed and integral measurements as an equivalent variable dimension system, whose measurements are both delay and integration free. Based on the new model, a variable dimension unscented Kalman filter (VD-UKF) is proposed to estimate the states. Furthermore, the stability of the proposed VD-UKF is analyzed. Compared with the existing results, the proposed stability condition is significantly relaxed and the invertibility condition of Jacobian matrices is no longer needed. Finally, a simulation example demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

As a recursive state estimation algorithm, the Kalman filter (KF) assumes initial state distribution is known a priori , while in practice the initial distribution is commonly treated as design parameters. In this paper, we will answer three questions concerning initialization: (1) At each time step, how does the KF respond to measurements, control signals, and more importantly, initial states? (2) What is the price (in terms of accuracy) one has to pay if inaccurate initial states are used? and (3) Can we find a better strategy rather than through guessing to improve the performance of KF in the initial estimation phase when the initial condition is unknown? To these ends, the classical recursive KF is first transformed into an equivalent but batch form, from which the responses of the KF to measurements, control signal, and initial state can be clearly separated and observed. Based on this, we isolate the initial distribution by dividing the original state into two parts and reconstructing a new state-space model. An initialization algorithm is then proposed by employing the Bayesian inference technique to estimate all the unknown variables simultaneously. By analyzing its performance, an improved version is further developed. Two simulation examples demonstrate that the proposed initialization approaches can be considered as competitive alternatives of various existing initialization methods when initial condition is unknown. [ABSTRACT FROM AUTHOR]