Kalman Filtering and Smoothing to Estimate Real-Valued States and Integer Constants

slowing the execution speed of the solution algorithm. Alternative approximate methods for filtering and smoothing are proposed and tested; these are methods that bound the sizes of the integer linear least-squares problems. Bounded problem sizes are achieved by treating integers from remote-in-time measurements as real-valued unknowns, which allows them to be dropped from explicit consideration. The resulting algorithms have been tested using a truth-model simulation. Their accuracies can be very near to optimal, and they reduce the computational costs of the filter and the smoother.