In our scenario, a set of node jointly estimates the state of linear dynamic systems in a distributed way. Without deploying a fusion center, each node will perform local processing and share information with neighbors. Kalman Filter as a common and robust state estimation method is widely used based on the full knowledge of system model. Sometimes, each node may not know exactly the time-varying covariance of the measurement noise. Hence, we want to use a method to jointly estimate the dynamic state and the time varying measurement noise parameters.

In paper [1], a recursive noise adaptive Kalman filtering algorithm was proposed based on variational inference approach (VB-AKF). Variational Bayesian inference is a deterministic approximation method widely used in machine learning to provide an analytical approximation to the posterior probability of the unobserved variables. The main tasks of this work are as follows:

1. Study Kalman filter and variational Bayesian inference approach

2. Verify the algorithm VB-AKF in [1]

3. Considering our distributed scenario, try to investigate a distributed noise adaptive Kalman Filter

Requirements:
MATLAB programming skills, background knowledge on linear estimation, statistics and machine learning will be helpful.

[1] S. Sarkka, and N. Aapo, "Recursive noise adaptive Kalman filtering by variational Bayesian approximations," IEEE Transactions on Automatic Control 54.3 (2009): 596-600.