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This text provides a self-contained, "no frills," mathematically rigorous derivation from first principles of all basic Kalman filter recursions. This approach relies on a pared-down version of more general state-space models found most often in the literature. Such simplification saves notational complexity without sacrificing conceptual understanding. The rigor found in the book ensures a fundamental understanding of how the Kalman filter actually works, which builds confidence for those employing the filter in their research and writing code to implement it in practice. The author provides implementations of the Kalman filter in Java available for download from his Web site.