Optimal and Robust State Estimation

11Applications of FIR State Estimators

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This chapter is the last, and it is now a proper place to give examples of practical applications of FIR state estimators. As the approach suggests, many useful FIR engineering algorithms can be developed to solve filtering, smoothing, and prediction problems on data finite horizons under diverse operation conditions in different environments. For Gaussian processes, the batch OFIR state estimator has proven to be the most accurate in the MSE sense, and the supporting recursive KF algorithm and its various modifications have found a huge number of applications. The OUFIR state estimator and RH MVF are commonly used in the canonical ML FIR batch form, since the recursive forms for these batches are more complex than Kalman recursions. The UFIR state estimator is blind on optimal horizons (has no other tuning factors) and is thus robust, unlike the OFIR and OUFIR estimators. Therefore, the iterative UFIR filtering algorithm using recursions has found practical applications as an alternative to KF in uncertain environments. It is worth noting that there has been no further development of the original LMF idea, because LMF is nothing more than KF operating on data finite horizons. In recent decades, there has appeared a big class of norm‐bounded , , ‐to‐, , and hybrid FIR state estimators. Such estimators are called robust, ...