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Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook by Bruce P. Gibbs

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CHAPTER 9

FILTERING FOR NONLINEAR SYSTEMS, SMOOTHING, ERROR ANALYSIS/MODEL DESIGN, AND MEASUREMENT PREPROCESSING

This chapter covers extensions of Kalman filtering that are routinely used. Specific topics considered in this chapter are:

1. Kalman filtering for nonlinear systems: The standard techniques include linearization about a reference trajectory (linearized filtering), linearization about the current estimate (extended Kalman filtering), and iterated linearized filtering (iterated extended Kalman filter or iterated linear filter-smoother). The extended Kalman filter is probably the most frequently used Kalman filter implementation.

2. Smoothing: Smoothers compute the minimum mean-squared error (MMSE) estimate of a state in past time based on measurements up to a later time. Smoothing options include fixed point, fixed lag, and fixed interval.

3. Error analysis and model state selection: Error analysis should be a necessary step in most Kalman filter implementations. As with least-squares estimation, Monte Carlo and covariance error analysis can be used. Options for linear covariance error analysis include perturbation analysis of independent error sources (measurement noise, process noise, and errors in unadjusted or “considered” model parameters), error analysis for reduced-order models (ROMs) defined as transformations on detailed models, and error analysis for truth and filter models that are structurally different but a subset of important states are common to both. ...

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