GPS Satellite Surveying, 4th Edition

Chapter 3Recursive Least Squares

In many applications of least-squares adjustments the measurements are taken sequentially at discrete epochs in time. Five arrangements are addressed in this chapter: The first case deals with estimation of static parameters. A static parameter represents a time-invariant quantity. In sequential estimation, each new measurement improves the previous estimate of the static parameters. Other cases include parameters that depend on time. Two types of time-dependent parameters are considered. First, we consider time-varying parameters that are not constrained by a dynamic model. They can vary arbitrarily and take independent values at two adjacent epochs. Parameters of the other type represent sequential states of a discrete dynamic process that is subject to a dynamic model. The dynamic model can be of linear or nonlinear functional relationship connecting two sequential states representing parameters at two adjacent time instances. The sequential measurements and estimated parameters are used to update the sequential estimates. For example, in some applications the physical nature of the problem imposes dynamic constraints on the rover coordinates. Another example is across-receiver difference ionospheric delays. Since they do not completely vanish for long baselines, the residual ionospheric delays are slow time-varying parameters that can be constrained by a dynamic model.

The second case discussed in this chapter refers to the mixed problem ...