Bounded constrained filtering for GPS/INS integration

This paper considers estimation problems where inequality constraints are imposed on the outputs of linear systems and can be modeled by nonlinear functions. In this case, censoring functions can be designed to constrain measurements for use by filters and smoothers. It is established that the filter and smoother output estimates are unbiased, provided that the underlying probability density functions are even and the censoring functions are odd. The Bounded Real Lemma is employed to ensure that the output estimates satisfy a performance criterion. A global positioning system (GPS) and inertial navigation system (INS) integration application is discussed in which a developed solution exhibits improved performance during GPS outages when a priori information is used to constrain the altitude and velocity measurements

Iterative Smoother-Based Variance Estimation

The minimum-variance smoother solution for input estimation is described and it is shown that the resulting estimates are unbiased. The smoothed input and state estimates are used to iteratively identify unknown process noise variances. The use of smoothed estimates, as opposed to filtered estimates, leads to improved approximate Cramér-Rao lower bounds for the unknown parameters. It is also shown that the sequence of iterates are monotonic and asymptotically approach the actual values under prescribed conditions. A nonlinear mining navigation application is described in which unknown parameters are estimated