**Statistical Filter – updated 2024-05-19**

In concept, filters remove noise from signals, so that you can see the true value. However, really, the filter only tempers the noise, it cannot remove uncertainty. And, in any of several approaches to “averaging”, the filter creates a lag or delay in recognizing when a signal changes value.

In digital control applications, new data comes every time interval. We have the past values and the current value, all noisy, and wish to use that information to get a best estimate of the actual process variable value at the current time. These filter applications are different from post processing of data (auditory or visual) in which filtering at one point in time or space has both the before and the after data. In control, we only have the current and past values.

Most filtering in process control applications assumes that the true signal is at steady state. The article “Data Filtering in Process Automation Systems” (__InTECH,__ 2018, Vol. 65, No. 4, pp. 14-19, by Alford, Hrankowsky, and Rhinehart), reviews several classic methods and their attributes.

A favorite approach of mine is grounded in a Statistical Process Control (SPC) concept of preventing tampering, of only permitting change when there is adequate statistical evidence. This filter is a procedure for triggering change. I have used it for both control and coefficient value adjustment in both batch and continuous processes. It is summarized here and in my book Nonlinear Model-Based Control.

“Tampering” is the SPC label for implementing change in response to noise in data. If a process is at set point, then there should be no control action. But, if the vagaries of measurement noise make it appear to be off of target, then a controller will take action, and that action will drive the process away from set point. This is termed tampering. A famous example is W. Edwards Demming’s funnel thought-experiment.

In the filter method, the statistic is the cumulative sum of deviations from target since the last change. The sum is normalized by the signal variability. When there is 95% statistical confidence that change is justified, make a change in the filtered value, otherwise keep the output unchanged. The method is described here r3eda site SPC Filter 2016-06-29 and demonstrated here with a VBA simulator r3eda SPC Filter 2017-04-23 and user guide r3eda site SPC Filter user Manual 2016-06-29.

The original publication on the method is Rhinehart, R. R., “A CUSUM-Type On-Line Filter,” __Process Control and Quality__, Vol. 2, No. 2, February, 1992, pp. 169-176.

Application publications include: Mahuli, S. K., R. R. Rhinehart, and J. B. Riggs, “pH Control Using a Statistical Technique for Continuous On-Line Model Adaptation,” __Computers & Chemical Engineering__, Vol. 17, No 4, 1993, pp 309-317; Rhinehart, R. R. “A Statistically Based Filter”, __ISA Transactions__, Vol. 41, No. 2, April 2002, pp 167-175; and Muthiah, N., and R. Russell Rhinehart, “Evaluation of a Statistically-Based Controller Override on a Pilot-Scale Flow Loop”, __ISA Transactions__, Vol. 49, No. 2, pp 154-166, 2010. Those are pilot- or lab-scale demonstrations. I have been a part of several successful industrial applications.