Reconciling sensor data with astronomical models requires powerful computational resources. One such resource is the numerical algorithm known as the sequential state estimator. The most familiar example is the Kalman filter, which in one form or another is used in just about every computer-controlled device. The basic function is to estimate the "state" of a particular system based on measurements from appropriate sensors. The variables depend on the application, but typically include parameters such as position, velocity, temperature, pressure, and airspeed.
The mathematical derivation of the Kalman filter is quite complicated and requires preliminary knowledge of probability, control theory, and linear-system theory. However, for all this mathematical rigor, the Kalman filter can be described as simply a mathematical expression of the scientific method. In other words, the Kalman filter is an algorithm that describes the sequence of observation, experimentation, and deduction that is the heart of basic science.
The Kalman filter begins by creating a mathematical model that describes the dynamic nature of the system in question. It then guesses the values for relevant variables and quantifies the level of confidence in those guesses. Based on these guesses, the algorithm predicts the state of the system at some time in the future. It then makes observations and compares them to the predictions. If the observations agree with the predictions, then the model is assumed to be correct. If the predicted results disagree with the actual results, the model is adjusted to compensate for the discrepancy. The process can be repeated until the state estimate is consistent with the data.
The Kalman filter is used in several systems that maintain the orbits of artificial Earth satellites. For example, Canada uses a Kalman filter for orbit determination of the Telesat communications satellites. Also, the Air Force uses a Kalman filter to maintain the very accurate ephemerides of GPS satellites.