Comparison of the Cusum, First-Order, Self-Tuning and Kalman Filters

Abstract

This work involved the comparison of the CUSUM filter, the first-order filter, the self-tuning filter and the Kalman filter. The filters were compared on the basis of the minimization of the integral sum of errors (ISE), the relative cost and the relative ease of understanding. The ISE was compared for processes involving a step change, a ramp change and an oscillatory process change. These three processes were simulated using Visual Basic for Applications (VBA). The four filters were also compared based on the relative ease of human understanding based on the complexity of equations. The relative cost of the filters was based on the number of operations and the required number of storage variables. The CUSUM filter is the best filter to use in a steady state process involving no change. In a process that involves a step change, the Kalman filter is the best filter to use. A process that involves a ramp change is best filtered using the Kalman filter. And, an oscillatory process is best filtered using the self-tuning filter. First-order filter is the easiest to understand, while the Kalman filter is the most complex to understand. The first-order filter is the cheapest to operate in terms of arithmetic operations, while the Kalman filter is the most expensive in terms of arithmetical operations. The first-order filter is the least expensive considering required number of variables, while the CUSUM filter requires the most number of variables and is thus the most expensive in terms of the required number of variables.