Kalman Filters – Errors and Correction

Many navigation systems today rely on the use of Kalman filters.  The Kalman filter is an algorithm that uses a series of measurements over time, even those containing “noise” and other errors, and produces estimates that tend be more accurate than those based on a single measurement. The Kalman filter was developed back in the early 1960s by Rudolph Kalman.  In his seminal paper titled “A new approach to linear filtering and prediction problems”, he outlined the optimal solution of a linear control problem.  What he accomplished is phenomenal and revolutionized real-time control applications.

One problem in the perception of the Kalman filter is that people tend to view it as accurate when it is, in fact, only just optimal in a mean-squared sense.  A properly tuned Kalman filter with a well-behaved system will combine sensors using their variances such that the mean-squared error is minimized.  This optimal merging of sensors does not necessarily imply overall system accuracy.

Improper “tuning” of the Kalman filter as well as improper modeling of system dynamics are often the cause of poor performance.  External influences can also change the behavior of a sensor in an unpredictable way.  For instance, a magnetometer that is used to measure magnetic fields will produce two different means with the same variance depending on whether or not a permanent magnet is placed nearby.  As you can see with this example, there are times when we need to consider more than just variances when merging data.  What is needed is a smart algorithm than can make intelligent decisions when the system acts in an unpredictable way.  Sparton has accomplished this with a unique algorithm called AdaptNavTM.

Sparton AdaptNavTM

Sparton’s AdaptNavTM adaptive algorithms outperform traditional Kalman filter-based approaches by providing real-time optimization of product performance when used in varying magnetic and dynamic operating environments. AdaptNav™ opens the door to optimized sensor system performance and a simplified approach to platform-specific customization.

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