Real-Time Implementation of the Optimal Predictor and Optimal Filter: Accuracy Versus Latency [Lecture Notes]

Although the Kalman filter is often presented within a continuous-time context [1]-[4], the original derivation was provided in discrete time [5]. In practice, controllers and observers are invariably implemented digitally; thus discrete-time algorithms deserve special attention. This article focuses on the real-time implementation of the discrete-time Kalman filter and its relation to the discrete-time Kalman predictor. These algorithms differ in subtle ways, as highlighted in this article. Equations for the discrete-time Kalman filter and predictor are given in [6]. Unfortunately, the covariance matrix becomes indefinite after a few steps, which shows that those equations are erroneous. The present article corrects and extends the results from [6].