Intelligent signal processing techniques are required for auto-calibration of sensors, and to take care of nonlinearity compensation and mitigation of the undesirable effects of environmental parameters on sensor output. This is required for accurate and reliable readout of the measurand, especially when the sensor is operating in harsh operating conditions. A novel computationally efficient Chebyshev neural network (CNN) model that effectively compensates for such non-idealities, linearises and calibrates automatically is proposed. By taking an example of a capacitive pressure sensor, through extensive simulation studies it is shown that performance of the CNN-based sensor model is similar to that of a multilayer perceptron-based model, but the former has much lower computational requirement. The CNN model is capable of producing pressure readout with a full-scale error of only plusmn1.0% over a wide operating range of -50 to 200degC.