Kalman filter is known as the optimal linear mean-squared error estimator. It has been a hot topic in control theory and has many applications in engineering since 1960s....[ Read more ]

Kalman filter is known as the optimal linear mean-squared error estimator. It has been a hot topic in control theory and has many applications in engineering since 1960s.

In this thesis, the classical Kalman filter has been modified in a way to be suitable for state estimation over unreliable networks. A sensor measures the state of a linear discrete time-invariant system and sends each component of the measurement data via a separate channel to a remote estimator. The remote estimator then computes the minimum mean-squared estimate of the system state upon receiving the data from the sensor. The packets can be lost during transmission due to the quality of the channel. We model this uncertainty that appears in each channel as a multiplicative noise.

With the additional channel-estimator co-design freedom, the main contribution of this thesis work is that we provide a sufficient condition on the minimum capacity required for these channels such that the estimation error covariance at the remote estimator remains stable. The sufficient condition is obtained by sequentially allocating the capacity of each individual channel and is shown to be equal to the topological entropy of the system. Simulation results demonstrate that the obtained sufficient condition is almost necessary as well.