Template updating kalman filter Omani youngporn
For now let it suffice to point out that the Kalman filter maintains the first two moments of the state distribution, The a posteriori state estimate (1.7) reflects the mean (the first moment) of the state distribution¯ it is normally distributed if the conditions of (1.3) and (1.4) are met.
The a posteriori estimate error covariance (1.6) reflects the variance of the state distribution (the second non-central moment).
Again notice how the time update equations in Table 1-1 project the state and covariance estimates from time step k to step k 1. Initial conditions for the filter are discussed in the earlier references.
The first task during the measurement update is to compute the Kalman gain, .
They are assumed to be independent (of each other), white, and with normal probability distributions The matrix A in the difference equation (1.1) relates the state at time step k to the state at step k 1, in the absence of either a driving function or process noise.
The measurement update equations are responsible for the feedback¯i.e.
for incorporating a new measurement into the a priori estimate to obtain an improved a posteriori estimate.
Notice that the equation given here as (1.11) is the same as (1.8).
The next step is to actually measure the process to obtain , and then to generate an a posteriori state estimate by incorporating the measurement as in (1.12).
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A very "friendly" introduction to the general idea of the Kalman filter can be found in Chapter 1 of [Maybeck79], while a more complete introductory discussion can be found in [Sorenson70], which also contains some interesting historical narrative.