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Starting from the 3D recording space receiver-source-frequency, they estimate observables in the 3D estimation space DOA-DOD-TOA.
The signal projector (respectively the noise projector) is deduced from the L first (respectively the N e M r F − L last) eigenvectors: π s = ∑ i = 1 L v i v i H (resp. π n = ∑ i = L + 1 N e M r F v i v i H ). The D-MUSICAL estimator, in the 3D DOA-DOD-TOA estimation space, is then: P D-MUSICAL ( θ r, θ e, T ) = 1 d ( θ r, θ e, T ) H π n ̂ d ( θ r, θ e, T ) (16).
It is shown that the sliding mode in the estimation space can be attained in finite time.
In the 1D case, narrowband signals recorded on a receiver array lead to a DOA estimation space [7, 14, 15].
The two arrivals might not be separated on the 2D DOA TOA estimation space (see Figure 2-left).
The main interest of this 3D estimation space is its capability for the separation of acoustic arrivals that usually interfere in the recording space, due to multipath propagation.
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These different paths lead to arrivals that interfere in the traditional recording space, and also in the traditional estimation spaces (e.g. the direction of arrival [DOA] space).
A non-fragile observer is designed to estimate the system states, and an observer-based SMC is synthesized to ensure the reachability of the sliding surfaces in the state-estimation space.
Furthermore, the reachability of sliding surfaces is also investigated in state-estimate space and estimation error space, respectively.
It is shown that the reachabilities of the proposed sliding mode surfaces can be guaranteed in both the state estimate space and the estimation error space simultaneously under the designed control schemes.
It is shown that the proposed SMC scheme guarantees the reachability of the sliding surfaces defined in both the state estimate space and the state estimation error space, respectively.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com