Abstract
We consider the problem of determining the order of a parametric model from a noisy signal based on the geometry of the space. More specifically, we do this using the nontrivial angles between the candidate signal subspace model and the noise subspace. The proposed principle is closely related to the subspace orthogonality property known from the MUSIC algorithm, and we study its properties and compare it to other related measures. For the problem of estimating the number of complex sinusoids in white noise, a computationally efficient implementation exists, and this problem is therefore considered in detail. In computer simulations, we compare the proposed method to various well-known methods for order estimation. These show that the proposed method outperforms the other previously published subspace methods and that it is more robust to the noise being colored than the previously published methods.
Highlights
Estimating the order of a model is a central, yet commonly overlooked, problem in parameter estimation, with the majority of literature assuming prior knowledge of the model order
It should be noted that the model selection criteria of the minimum description length (MDL) [13] and the maximum a posteriori (MAP) [4]
The MAP criterion of [4] combined with ESPRIT and the method based on the eigenvalues [19] can be seen to generally perform the best, outperforming the measure based on angles between subspaces when the noise is white Gaussian
Summary
Estimating the order of a model is a central, yet commonly overlooked, problem in parameter estimation, with the majority of literature assuming prior knowledge of the model order. The most commonly used methods for estimating the model order are perhaps the minimum description length (MDL) [1, 2], the Akaike information criterion (AIC) [3], and the maximum a posteriori (MAP) rule of [4] These methods are based on certain asymptotic approximations and on statistical models of the observed signal, like the noise being white and Gaussian distributed. We are concerned with a more specific, yet important, case, namely, that of finding the number of complex sinusoids buried in noise This problem is treated in great detail from a statistical point of view in [4] and is exemplified in [5] and other notable approaches include those of [7,8,9,10,11,12,13]. The most common subspace methods for parameter estimation are perhaps the MUSIC (MUltiple SIgnal Classification) method
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