(184f) A Novel Robust Kalman Filter Algorithm Using Incremental PID Controller for Model Uncertainties

Kalman filter has been recognized as a powerful tool for many control problems. Its performance mainly depends on the accuracy of its dynamic model. In employing the filter in real problem, various sources of uncertainty actually should be considered such as unmodeled dynamics, parameter variations, model reduction, and linearization.

It is inevitable to model such inherent inaccuracy in practical applications. It is therefore difficult for conventional Kalman filter to provide satisfactory performance for such cases with significant model uncertainties. To tackle this difficulty, several approaches tried to modify the conventional Kalman filter algorithm in terms of robust estimation and filtering over the past decades.

Alternately, a simple but powerful method is introduced by incorporating incremental PID controller structure to the standard Kalman filter algorithm in this paper. The calculated estimation error defined as the difference between estimation values and measurements is used to correct the state estimates based on proportional, integral, and derivative terms. It makes errors due to state estimates to be much smaller compared to the standard approach which only uses estimation error as a corrective term.

To illustrate the applicability of the proposed method, two case studies are presented for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. The performance comparison of proposed algorithm versus standard Kalman filter algorithm was conducted by calculating the mean square error (MSE) of the estimation error in each case. The proposed algorithm showed the better tracking performance than standard Kalman filter. The current works are under way to employ the proposed improved Kalman filter in actual control applications.