Variance-Constrained Multi-Objective Stochastic Control and Filtering

Chapter 4Robust Variance-Constrained Filtering with Missing Measurements

For several decades, filtering techniques have been playing an important role in many branches of signal processing such as target tracking. A number of filtering approaches, including Kalman filtering, H_∞ filtering, and robust filtering, have been proposed in the literature, most of which are under the assumption that the measurements always contain true signals corrupted by the noises. However, in real-world applications, the measurements may contain missing measurements (or incomplete observations) due to various reasons, such as high maneuverability of the tracked targets, sensor temporal failures or network congestion.

On the other hand, it is quite common in practical engineering that, for a class of filtering problems such as the tracking of a maneuvering target, the performance objectives are naturally described as the upper bounds on the error variances of estimation. This gives rise to the so-called variance-constrained filtering problem, which has been motivated from the well-known covariance control theory. Note that the variance-constrained filtering or control theory has been extensively investigated in a variety of practical situations. The key point of the covariance control theory is that the specified variance constraints may not be minimal, but should meet certain given engineering requirements. Therefore, after assigning to the filtering error dynamics a specified variance upper bound, ...