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# The “Go-Free” Concept, Complementary Filter, and Aided Inertial Examples

In the usual form of Kalman filtering we are forced to make assumptions about the probabilistic character of the random variables under consideration. However, in some applications we would like to avoid such demanding assumptions, to some extent at least. There is a methodology for accomplishing this, and it will be referred to here as the go-free concept.

The examples used here are taken from modern navigation technology, especially those involving satellite navigation systems such as GPS. (A detailed description of GPS is given in Chapter 9.) All such systems operate by measuring the transit times of the signal transmissions from each of the satellites in view to the user (usually earthbound). These transit times are then interpreted by the receiver as ranges via the velocity-of-light constant c. However, the receiver clock may not be in exact synchronism with the highly-stable satellite clocks, so there is a local clock offset (known as clock bias) that has to be estimated as well as the local position in an earth-fixed xyz coordinate frame. So, for our purposes here, after linearization as discussed in Chapter 7, we simply pick up the estmation problem as one where we need to estimate three unknown position coordinates and a clock bias based on n measurements where n≥4. Normally n is greater than 4. So, in its simplest form, we have an overdetermined linear system of noisy measurements to work with ...

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