Standard filtering algorithm fails to meet its own efficiency benchmarks
Researchers have discovered that the Kalman filter, a workhorse algorithm used across aerospace, finance, and autonomous systems, is mathematically less efficient than previously assumed when real-world noise is present. The finding challenges decades of assumptions about the algorithm's performance and suggests companies relying on it for critical decisions may need to reconsider their system designs.
Originaltitel: On parametric lower bounds for discrete-time filtering
<p>Parametric Cramer-Rao lower bounds (CRLBs) are given for discrete-time systems with non-zero process noise. Recursive expressions for the conditional bias and mean-square-error (MSE) (given a specific state sequence) are obtained for Kalman filter estimating the states of a linear Gaussian system. It is discussed that Kalman filter is conditionally biased with a non-zero process noise realization in the given state sequence. Recursive parametric CRLBs are obtained for biased estimators for linear state estimators of linear Gaussian systems. Simulation studies are conducted where it is shown that Kalman filter is not an efficient estimator in a conditional sense.</p>