Batch State Estimation
The previous chapter allows estimation of the states in the model of a dynamicsystem using sequential measurements. We found that the sequential estimation results of §1.3 and the probability concepts introduced in Chapter 2, developed for estimation of algebraic systems, remain valid for estimation of dynamic systems upon making the appropriate new interpretations of the matrices involved in the estimation algorithms. Specifically, taking a measurement at the current time and an estimate of the state at the previous time with knowledge of its error properties, the methods of Chapter 3 are used to produce a state estimate of the dynamic system at the current time. In this chapter the results of the previous chapter are extended to batch state estimation. The disadvantage of batch estimation methods is they cannot be implemented in real time; however, they have the advantage of providing state estimates with a lower error-covariance than sequential methods. This may be extremely helpful when accuracy is an issue, but real time application is not required. We also remark that classical batch methods have no convenient means for accommodating model uncertainty, whereas model uncertainty is readily accommodated in sequential algorithms. Even though all of the data are available in a batch, we find the recursive Kalman structure to be useful in this setting, to accommodate process noise.