Synthesis of Filter Structures in Finite Wordlength Kalman Filters

Abstract

When Kalman filters are implemented with microprocessors or signal processors, quantization errors (rounfoff errors and coefficient quantization errors) due to finite wordlength implementation affect the state estimate. This paper studies analysis of quantization errors in Kalman filters and synthesis of minimum quantization error Kalman filter structures.
Infinite wordlength Kalman filters are described by the state and output equations, and filter structures are introduced to Kalman filters by the state transformation, since quantization effects of digital systems highly depend on structures. Finite wordlength Kalman filters are also described by the equations. Roundoff errors and coefficient quantization errors are analyzed for any structures of Kalman filters. The results of error analysis are in agreement with the results of simulation. Minimum quantization error Kalman filters are synthesized by using minimization method of quantization errors in state-space digital filters. Synthesis method of minimum quantization error Kalman filters is very effective to reduce quantization errors.