1 Preface
The Kalman Filter (KF) is a recursive optimal estimation algorithm that provides the best possible estimate of a system’s internal state in the presence of process and measurement uncertainties. From the state estimation viewpoint, it serves as a mathematical framework to combine noisy sensor data with a predictive dynamic model, yielding a statistically optimal estimate of the underlying state variables. This ability to fuse information from different sources in a principled manner makes it indispensable in navigation, guidance, and control applications.
In the context of system identification, the Kalman Filter offers a structured way to estimate not only the states but also the parameters governing system dynamics. By augmenting the state vector with unknown parameters, one can formulate an extended state-space model, allowing the filter to adaptively learn model coefficients as new data become available. This makes the Kalman Filter a powerful online identification tool for time-varying or uncertain systems.
The recursive nature of the algorithm eliminates the need to store all past data, enabling real-time estimation even in high-dimensional systems. The filter maintains two key processes: the prediction step, which propagates the state and its uncertainty forward in time using the system model, and the update step, which corrects this prediction based on new measurements. This cycle of prediction and correction ensures that the estimates continuously converge toward the true system behavior as observations accumulate.
Overall, the Kalman Filter bridges the gap between model-based and data-driven approaches, making it a cornerstone in the fields of optimal filtering, adaptive estimation, and modern system identification. This motivated to understand the Kalman Filter.
The link for documentation on understanding Kalman Filter is here.