Using the Kalman Algorithm to Correct Data Errors of a 24-Bit Visible Spectrometer

To reduce cost, increase resolution, and reduce errors due to changing light intensity of the VIS SPEC, a new technique is proposed which applies the Kalman algorithm along with a simple hardware setup and implementation. In real time, the SPEC automatically corrects spectral data errors resulting from an unstable light source by adding a photodiode sensor to monitor the changes in light source intensity. The Kalman algorithm is applied on the data to correct the errors. The light intensity instability is one of the sources of error considered in this work. The change in light intensity is due to the remaining lifetime, working time and physical mechanism of the halogen lamp, and/or battery and regulator stability. Coefficients and parameters for the processing are determined from MATLAB simulations based on two real types of datasets, which are mono-changing and multi-changing datasets, collected from the prototype SPEC. From the saved datasets, and based on the Kalman algorithm and other computer algorithms such as divide-and-conquer algorithm and greedy technique, the simulation program implements the search for process noise covariance, the correction function and its correction coefficients. These components, which will be implemented in the processor of the SPEC, Kalman algorithm and the light-source-monitoring sensor are essential to build the Kalman corrector. Through experimental results, the corrector can reduce the total error in the spectra on the order of 10 times; for certain typical local spectral data, it can reduce the error by up to 60 times. The experimental results prove that accuracy of the SPEC increases considerably by using the proposed Kalman corrector in the case of changes in light source intensity. The proposed Kalman technique can be applied to other applications to correct the errors due to slow changes in certain system components.