Online LTI system identification and time delay estimation

Model order selection for linear time-invariant (LTI) systems is an important system modeling concern and has been widely investigated through past decades. Different approaches of order selection such as Akaike information criterion (AIC), Bayesian information criterion (BIC), minimum description length (MDL) and reconstruction error LTI system identification (RE-LTI) propose different criteria to select the optimum order of a system. In many real life applications of model order selection the size of an observed data set is increasing. Thus, order selection methods need to adopt the best fit of a model as the data set size is increasing. This is our motivation to extend RE-LTI order selection for online application of order selection with lower computational cost and complexity. It has been shown previously that AIC, BIC, two-stage MDL and many existing order selection criteria are special cases of RE-LTI method. Our online order selection approach reduces the computational complexity of the offline approach from O(N3) to O(N2). It should be noted that RE-LTI and MNDL order selection methods have same fundamentals and consequently extending RE-LTI to online RE-LTI also extends MNDL to online MNDL. Another crucial issue in system identification and modeling is estimating the time delay of a system’s impulse response (or determining the start of its non-zero part). This problem is addressed in various areas including radar, sonar, acoustic source tracking, multipath channel identification, as well as many automatic control applications. Utilizing fundamentals of RE-LTI approach, here we introduce a new time-delay estimator. Simulation results show advantages of the proposed method and its superiority to existing approaches in accuracy and robustness in terms of the FIT index.