13.3 A More Practical Approach to Utilizing the Family of Kalman Filters

A close examination of the dynamic and observation models given by (3.17) and (3.18) for the various case studies reveal that a hierarchy of models exists This hierarchy is presented in Table 13.4.

Table 13.4 Hierarchy of Dynamic and Observation Models.

Combination Dynamic Model Observation Model
Linear/linear xn = Fxn−1 + vn−1 zn = Hxn + wn
Linear/nonlinear xn = Fxn−1 + vn−1 img
Nonlinear/linear img zn = Hxn + wn
Nonlinear/nonlinear img img

Based on this model hierarchy, it is almost obvious that the dynamic prediction process can be considered to be completely independent of the observation prediction process. This enables one to use the Kalman filter method that is most suited for each model. For example, for the linear/nonlinear case, one can use the linear Kalman filter equations for dynamic prediction and one of the nonlinear Kalman filter methods for observation prediction. Similarly, for the nonlinear/nonlinear case, when the state vector xn is of high dimension and the observation vector zn is of low dimension, ...

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