Physical sensors, such as nitrogen oxides (NOx) sensors, are widely used in many products, such as modem vehicles, to measure and monitor various parameters associated with motor vehicles. Physical sensors often take direct measurement of the physical phenomena and convert these measurements into measurement data to be further processed by control systems. Although physical sensors take direct measurements of the physical phenomena, physical sensors and associated hardware are often costly and, sometimes, unreliable. Further, when control systems rely on physical sensors to operate properly, a failure of a physical sensor may render such control systems inoperable.
Instead of direct measurements, virtual sensors are developed to process various physically measured values and to produce values that are previously measured directly by physical sensors. For example, U.S. Pat. No. 5,386,373 (the '373 patent) issued to Keeler et al. on Jan. 31, 1995, discloses a virtual continuous emission monitoring system with sensor validation. The '373 patent uses a back propagation-to-activation model and a monte-carlo search technique to establish and optimize a computational model used for the virtual sensing system to derive sensing parameters from other measured parameters.
Other techniques try to establish complex mathematical models to be used as virtual sensors. For example, Michael L. Traver et al., “A Neural Network-Based Virtual NOx Sensor for Diesel Engines,” discloses an in-cylinder combustion model using in-cylinder combustion-pressure-based variables to predict values of NOx emissions.
However, these conventional techniques involve a large amount of run-time computation, often in floating-point representation, and may be computationally impractical for real-time applications. In particular, when virtual sensor models are implemented on an embedded computer platform without floating-point arithmetic hardware, the large amount of streaming floating-point math conversion may significantly decrease performance of the embedded computer platform.
Methods and systems consistent with certain features of the disclosed systems are directed to solving one or more of the problems set forth above.