I went throught the main reference [1] in my following project, as well as studied the corresponding area, which is called optimal scheduling in sensor networks.

In [1], the main work can be decomposed into 4 steps:

  1. Discrete time Riccati equation: With observation and propagation, the localization process can reach a steady state, which is characterized by the discrete time Riccati equation.

  2. Continuous time Riccati equation: Frequency is introduced by transforming the discrete-time version to the continuous time version, while the steady state is preserved.

  3. Convex optimization problem: The Riccati equation in previous two steps is regarded as a constrain in the optimization problem, in order to minimize the steady state covariance. One should argue that the freqency in the Riccati equation is convex.

  4. Semidefinite optimization problem: The original optimization problem does not have good numerical behavior. Thus, an equivalent semidefinite optimization problem is derived to achieve better numerical solution.

    The study of optimal scheduling in sensor networks try to guarantee the estimation performance in sensor networks with least action as possible. The works vary in system modeling, scheduling types, and optimization methods.


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