To Drop or Not to Drop: Design Principles for Kalman Filtering Over Wireless Fading Channels

It is the general assumption that in estimation and control over wireless links, the receiver should drop any erroneous packets. While this approach is appropriate for non real-time data-network applications, it can result in instability and loss of performance in networked control systems. In this technical note we consider estimation of a multiple-input multiple-output dynamical system over a mobile fading communication channel using a Kalman filter. We show that the communication protocols suitable for other already-existing applications like data networks may not be entirely applicable for estimation and control of a rapidly changing dynamical system. We then develop new design paradigms in terms of handling noisy packets for such delay-sensitive applications. We reformulate the estimation problem to include the impact of stochastic communication noise in the erroneous packets. We prove that, in the absence of a permanent cross-layer information path, packet drop should be designed to balance information loss and communication noise in order to optimize the performance.