Kalman Canonical Decomposition of Linear Time-Varying Systems

Observability Analysis and Concept of Usage of Air Data Attitude and Heading Reference Systems (AD-AHRS)

“…As expected, combinations (29) and (30) show that in a straight and level flight, a barometric altimeter allows us to observe only those combinations of error states that are related to the vertical channel. During a horizontal turn, information on attitude and on one linear combination of sensor errors appears in the measurement.…”

“…The observable combinations (29), (30), and (31) are summarized in Table 2. The rows of the table denote observable combinations, while the columns denote components of the error state vector.…”

“…Concepts of observability, observable costates, and subspaces, which are used in the article, were originally introduced by Kalman [27,28] and developed further, for example, in [29]. Consider the dynamic system (23).…”

“…In [29], it is proven that observable and unobservable costates form the subspaces D t ð Þ and D ⊥ t ð Þ, which can be determined as follows.…”

Factorizing the Monodromy Matrix of Linear Periodic Systems

“…The conditions (29)-(32) are the necessary and sufficient condition for the existence of the Kalman canonical decomposition for linear time-varying systems [12,13]. However, the conditions (29)-(32) does not immediately imply the existence of the periodic Kalman canonical decomposition for linear periodic systems [8,15].…”