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As the number of snapshots decreased, the signal power (variance matrix) estimation error are accordantly increased.
As SAM does not require the characterization of the background, it can avoid the inaccuracy of the comparison result caused by the noise covariance matrix estimation error.
They present what they call an oracle approximating shrinkage (OAS) estimator, which is an iterative method presented in Algorithm 2. In Algorithm 2, δtarget represents a specified threshold for the covariance matrix estimation error.
where x ^ k and x ̃ k are the state estimate matrix and state prediction matrix, respectively; P ^ k, P ̃ k and K k are the estimation error covariance matrix, prediction error covariance matrix, and Kalman Gain, respectively; e k|j, e ^ k, and e ̃ k are the state error matrix, estimation error matrix, and prediction error matrix, respectively.
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Such effects lead to covariance matrix estimation errors, adaptive filter mismatch, and consequently, performance loss in GMTI processing.
However, in this method, the receiver's performance is considerably degraded in the presence of channel and data correlation matrix estimation errors [21, 22].
Figure 1 Matrix estimation errors, with a random tensor of size 8 × 8 × 8 and rank 5. (a) Matrix A. (b) Matrix B. (c) Matrix S. Figure 2 Sum of matrix estimation errors, with a random tensor of size 3 × 3 × 3 and rank 5. Note the asymptote depending on the maximum number of iterations executed.
In this study, we study the noise free IVA problem as defined in (2), and neglect the cross covariance matrix estimation errors due to the finite sample size effect.
Since cognitive RSS-WLS estimator is unbiased, covariance matrix of estimation error of (36) is also covariance matrix of the estimator.
And the autocorrelation matrix of estimation error is (15).
Finally, by substituting (26) and (34) into (23), the closed form of the 3 by 3 covariance matrix of estimation error is obtained as, C V = ( H - 2 1 M v T D ) T Ω - 1 ( H - 2 1 M v T D ) - 1 (36).
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