Estimation with Multitemporal Measurements
Adam M. Fosbury · Journal of Guidance Control and Dynamics · 2010
This paper studies measurements that are mathematical functions of states at more than one time instance where the exact time instances may not be known. For consistency of discussion, they are referred to as multitemporal measurements. Many sensors that rely on received light waves, sound waves, or other transmitted physical phenomena can have measurements that are classified as multitemporal. Even though there is a finite time between the sending and receiving of these signals, measurement estimates are commonly written as if these actions occurred simultaneously. The application of lasers for communication across large distances has provided a system where ignoring this phenomenon results in numerically significant errors. After mathematically describing the measurements, the overall multitemporal problem is discussed in the context of time-delay measurement, out-of-sequence measurement, relative state measurement, and Global-Positioning-System problems. While some research has explored the use of Global-Positioning-System signals as a means for Global-Positioning-System satellites to estimate their own orbits, that research has made simplifying assumptions that allow the multitemporal problem to be avoided. A solution using Taylor-series approximations within an extended Kalman filter is developed and shown to provide filter convergence, whereas a filter ignoring the multitemporal problem does not.