The Kalman Filter
Richard J. Smythe · Apress eBooks · 2021
Kalman filters reportedly came to prominence in the early years of the space program as a result of their success in definitively tracking space exploration vehicles. Kalman filters are mathematical processes first applied to extract vehicular courses or trajectories from noise-filled, measured radio-telemetry navigational data. Navigational data involves numerous degrees of freedom, such as roll, pitch, and yaw combined with forward, sideways, and vertical motions. Following a vehicle motion involves simultaneous application of the Kalman filter to each spatial dimension. Simultaneous, multiple filtering requires the application of advanced high-speed matrix algebra that goes beyond the introductory nature of this work. Kalman filtering is often taught by the application of mathematics to models of motion in a single dimension in which the uncertainty in position as a function of time is significantly reduced. The mathematical modeling of an error in a one-dimensional position as a function of time is equivalent to that of errors in a time-based sensor data stream. (See Prof. M. van Biezen presenting the first six lectures of “The Kalman Filter” for an excellent qualitative and quantitative demonstration of the filter theory and practical single-dimension application to the smoothing of a temperature sensor data stream.)