Parallel Implementations of the Kalman Filter for Tracking Applications
The first parallel implementations of the extended covariance Kalman filter (ECKF) and the extended square root covariance filter (ESRCF) for tracking applications are developed in this thesis. The decoupling technique and special properties in the tracking KF are explored to reduce computational requirements and to increase parallelism.
The use of the decoupling technique to the ECKF eliminates the need for a matrix inversion, and results in the time and measurement updates of m decoupled (n/m)-dimensional state esimate error covariance P₀(k)'s instead of 1 coupled n-dimensional covariance matrix P(k), where m denotes the tracking dimension and n denotes the number of state elements.
Similarly, the use of the decoupling technique to the ESRCF separates the time and measurement updates of 1 coupled P½(k) into those of m decoupled P₀½(k)'s.
The updates of m decoupled matrices are found to require less computation than those of 1 coupled matrix, and they may be performed for each axis in parallel.
In the parallel implementation of time and measurement updates of P(k) in the ECKF, the updates of m decoupled P₀(k)'s are found to require approximately m times less number of processing elements and clock cycles than the updates of 1 coupled P(k). Similarly, the parallel implementation of the updates of m decoupled P₀½(k)'s in the ESRCF requires approximately m time less number of processing elements and clock cycles than that for 1 coupled P½(k).
The transformation of the Kalman gain which accounts for the decoupling of P(k) and P½(k) is found easy to implement.
The sparse nature of the measurement matrix and the sparse, band nature of the transition are explored to simplify matrix multiplications.