Implementing a Kalman Filter in Postgres

Summary

Modern GPS datasets are notoriously noisy: satellites drift, buildings scatter signals, and consumer devices introduce frequent errors. When working with millions of position samples from vehicles, smartphones, or IoT devices, this noise makes analysis unreliable. Routes jump, tracks zigzag, and outliers distort aggregates. The Kalman Filter is the standard technique for smoothing such data. Traditionally, it is applied outside the database in environments like Python or MATLAB. But for large-scale datasets stored in Postgres, filtering directly inside the database has clear advantages: no additional processing pipeline, results available immediately in SQL, and scalable analytics over billions of rows. For our own usage at traconiq, we built an open source project that implements a Kalman Filter in Postgres. You can explore the code and try it yourself here, if you also have GPS data: github.com/traconiq/kalman-filter-neon The Kalman Filter is a recursive algorithm used to estimate the true state of a dynamic system, such as the position of a moving vehicle, from noisy observations. At each step, it combines two parts: Prediction: uses a motion model to project the next position (and optionally velocity). Update: corrects that prediction using the latest observed measurement. What makes the Kalman Filter effective is that it explicitly models uncertainty. Both the process (how the system evolves) and the measurements (GPS fixes) carry noise, represented in a covariance matrix. The filter continually refines its estimates as new data arrives, producing a smoothed track that follows the real trajectory more closely than raw GPS data. Because of this, Kalman Filters are widely used in navigation, robotics, signal processing, and finance. Applied to GPS data, they can turn jittery position samples into realistic paths suitable for analytics or visualization. An artificial GPS track with a very low confidence (high HDOP values). Red track: observations. Purple track: fi...