Denoising MAX6675 reading using Kalman filter and factorial design

This paper aims to tune the Kalman filter (KF) input variables, namely measurement error and process noise, based on two-level factorial design. Kalman filter then was applied in inexpensive temperature-acquisition utilizing MAX6675 and K-type thermocouple with Arduino as its microprocessor. Two levels for each input variable, respectively, 0.1 and 0.9, were selected and applied to four K-type thermocouples mounted on MAX6675. Each sensor with a different combination of input variables was used to measure the temperature of ambient-water, boiling water, and sudden temperature drops in the system. The measurement results which consisted of the original and KF readings were evaluated to determine the optimum combination of input variables. It was found that the optimum combination of input variables was highly dependent on the system's dynamics. For systems with relatively constant dynamics, a large value of measurement error and small value of process noise results in higher precision readings. Nevertheless, for fast dynamic systems, the previous input variables' combination is less optimal because it produced a time-gap, which made the KF reading differ from the original measurement. The selection of the optimum input combination using two-level factorial design eased the KF tuning process, resulting in a more precise yet low-cost sensor

Distributed Kalman Estimation with Decoupled Local Filters

We study a distributed Kalman filtering problem in which a number of nodes cooperate without central coordination to estimate a common state based on local measurements and data received from neighbors. This is typically done by running a local filter at each node using information obtained through some procedure for fusing data across the network. A common problem with existing methods is that the outcome of local filters at each time step depends on the data fused at the previous step. We propose an alternative approach to eliminate this error propagation. The proposed local filters are guaranteed to be stable under some mild conditions on certain global structural data, and their fusion yields the centralized Kalman estimate. The main feature of the new approach is that fusion errors introduced at a given time step do not carry over to subsequent steps. This offers advantages in many situations including when a global estimate in only needed at a rate slower than that of measurements or when there are network interruptions. If the global structural data can be fused correctly asymptotically, the stability of local filters is equivalent to that of the centralized Kalman filter. Otherwise, we provide conditions to guarantee stability and bound the resulting estimation error. Numerical experiments are given to show the advantage of our method over other existing alternatives