Exact Filtering of Measurement Errors in Dynamical Systems

Abstract

Measurements of values in dynamical systems are often incomplete or accompanied by error. Incomplete measurements occur when not all of the relevant quantities in the system are measured. We provide a technique which recovers the full state of a dynamical system given an incomplete measurement. One type of error we consider is constant shifting, caused by systematic bias in the measuring device. Two other types of measuring device errors are amplification and attenuation, both of which result in a constant multiplicative rescaling of a measurement. Lastly, we consider periodic noise, which occurs when a measured signal is obscured by another signal. For each kind of error, we provide a filtering method which recovers the full state of the dynamical system.