Detecting jumplike parameter changes and optimal evaluation of the state of discrete dynamical systems

An optimal algorithm is determined for evaluating the states of a digital dynamic system and detection of jerk-like variation of its parameters and, observations. Interrelated equations are provided for a posteriori probability of a jerk and a posteriori probability density of the dynamic system state. Solution of these equations by approximate methods provides current evaluation of the system state in real time and finding the median estimate of the jerk time. An example is considered with reference to a system which is described by an autoregression process with a jerk of the correlation coefficient at a random time.