Search

This paper theoretically analyzes the Mean Square Error (MSE) on the steady-state frequency estimation realized by the all-pass-based adaptive notch filtering algorithms with the normalized lattice structure. The adaptive algorithms to be considered are the Simplified Lattice Algorithm (SLA) proposed by Regalia and the Affine Combination Lattice Algorithm (ACLA) proposed by the authors. For these two algorithms, we derive the frequency estimation MSE in closed-form. The derivation is based on construction of a linear time-invariant model for generation of frequency estimation error, and division of this model into two submodels of which output signals are statistically uncorrelated to each other. This strategy leads to more accurate theoretical MSE expressions than the direct use of the existing analysis methods. Simulation results demonstrate that our theoretical MSE expressions are in very good agreement with the simulated MSE values. HighlightsThe frequency estimate MSEs are derived in closed-form for SLA and ACLA.The proposed MSE expressions show higher accuracy than the conventional methods.The key point in MSE derivation is division of error generation models.

Sparse subspace clustering (SSC) clusters $n$ points that lie near a union of low-dimensional subspaces. The SSC model expresses each point as a linear or affine combination of the other points, using either $\ell_1$ or $\ell_0$ regularization. Using $\ell_1$ regularization results in a convex problem but requires $O(n^2)$ storage, and is typically solved by the alternating direction method of multipliers which takes $O(n^3)$ flops. The $\ell_0$ model is non-convex but only needs memory linear in $n$, and is solved via orthogonal matching pursuit and cannot handle the case of affine subspaces. This paper shows that a proximal gradient framework can solve SSC, covering both $\ell_1$ and $\ell_0$ models, and both linear and affine constraints. For both $\ell_1$ and $\ell_0$, algorithms to compute the proximity operator in the presence of affine constraints have not been presented in the SSC literature, so we derive an exact and efficient algorithm that solves the $\ell_1$ case with just $O(n^2)$ flops. In the $\ell_0$ case, our algorithm retains the low-memory overhead, and is the first algorithm to solve the SSC-$\ell_0$ model with affine constraints. Experiments show our algorithms do not rely on sensitive regularization parameters, and they are less sensitive to sparsity misspecification and high noise., This paper is accepted for publication in Signal Processing

This paper introduces an optimal variable step-size affine projection algorithm for the modified filtered-x active noise control systems. First, the recursion form of the error covariance from the tap weight update equation is constructed, not ignoring the dependency between the estimation error and the secondary noise signal. Such consideration has not been concerned previously for the analysis of the modified filtered-x affine projection algorithm. Second, a recursion form of the mean square deviation is derived from that of the error covariance. From the recursion form, an optimal step size is decided to get the fastest convergence rate. Both the recursion forms of the mean square deviation and the optimal step size require scalar additions and multiplications that do not contribute to the overall complexity seriously. The simulation results on the active noise control environments show both fast convergence rate and low steady-state error.

In this paper, a new affine projection sign algorithm with a variable step-size, robust in impulsive noise environments, is proposed. For that purpose, l1-norm of the a posteriori error vector is minimized under a box constraint on the step-size. Since the proposed l1-norm minimization problem is non-differentiable convex one, an efficient numerical procedure is developed for the affine projection structure algorithm. Finally, it is demonstrated that the proposed algorithm, not requiring any a priori knowledge, yields more robust convergence in various impulsive noise environments than conventional algorithms with robustness to outliers and recent variable step-size algorithms with a priori information.

In this paper we present a general formalism for the establishment and mean-square performance analysis of the family of selective partial update affine projection (SPU-AP), selective regressor affine projection (SR-AP), and selective partial update subband adaptive filter (SPU-SAF) algorithms. This analysis is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. We demonstrate through simulations that the results are useful in predicting the performance of these adaptive filter algorithms.