Abstract
In this chapter we introduce and illustrate the application of the Kalman filter. The basis for the Kalman filter is the combination/fusion of measurements with model-based predictions. This combination/fusion procedure consists of a recursive sequence of steps. First, based on previous knowledge and a model of the system dynamics, an a priori estimate of the state of the system is produced. Next, a measurement is made, and an a posteriori estimate is computed by fusing the a priori prediction with this measurement. This a posteriori estimate is used to provide a new a priori estimate preceding the next measurement. The combination algorithm that realizes the ongoing fusion of the a priori prediction and the measurement is based on the uncertainties associated with both the prediction and measurement. This is accomplished by using a blending factor that is determined by the variance of the noise in both the process that is being examined as well as the measurement noise. An example of the application of the Kalman filter to estimation of a neuron's resting potential is discussed.
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