Online models of pipelines almost always suffer from a surfeit of data: while a hydraulic model only requires one pressure or flow measurement at each boundary, real pipelines have pressure and flow meters all over the place. One would ideally like to make the best possible use of all the measurements. This process is called "state estimation". Over the last thirty years, several schemes have been developed for state estimation. Two of the more popular ones, a simple pressure-based scheme that discards many of the measurements and the Equal Error Fractions approach, will be examined here and compared with a new maximum-likelihood scheme and, for reference, with no state estimation at all. Comparisons will be performed on simple simulated gas and liquid pipelines in the presence of meter noise, quantization errors, and hydraulic transients. The performance of the various approaches will be examined, as well as the complexity of implementation and run speed.


A hydraulic model of a pipeline requires that one boundary condition, either pressure or flow, be specified at every place fluid enters or leaves the line. Pipelines tend to have much more instrumentation than this; for example, there are often both pressure and flow measurements available at supply and delivery locations. The extra data from these additional instruments can improve the estimate of the pressures and flows in the system (that is, the hydraulic state of the line). Techniques for doing this are called "state estimation". There is no industry standard technique for state estimation. While hydraulic models themselves now largely belong to two schools - method-of-characteristics models and implicit finite difference models - there are almost as many types of state estimation around as there are modelers. The goal of this paper is to describe and compare some of the more popular state estimation techniques with an eye to providing recommendations for which schemes to use in which circumstances. There are several desirable properties of a state estimator; it's not enough to say "it should produce the best possible estimate of the state", because a method that works well in steady state might do something spectacularly wrong during a transient, or a method that works for certain types of instrument errors might have trouble with other sorts. Also, it's nice if a state estimator produces some form of output that can drive hydraulic tuning.

Methods of State Estimation

We will examine three approaches to state estimation: two that are widely used in online models and a new approach developed by the author. In this section we discuss the qualitative advantages and disadvantages of the different methods, and then in the Results section below we will compare their performance - how accurate an

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