Fundamental aspects of a method for virtual navigation of a sound field within an array of ambisonics microphones, wherein the subset of microphones to be used for interpolation is determined parametrically, are presented. An existing, weighted-average-based navigational method serves as a benchmark due to its simplicity and its applicability to arbitrary sound fields but introduces comb-filtering and, for near-field sources, degrades localization. A critical review of existing methods is presented, through which a number of issues are identified. In the proposed method, those microphones that are nearer to the desired listening position than to any source are determined based on the known or inferred positions of sources. The signals from only those microphones are then interpolated using a regularized least-squares matrix of filters. Spectral distortions and source localization errors are characterized for the benchmark and proposed methods via numerical simulations of a two-microphone array, and an experimental validation of these simulations is presented. Results show that, for near-field sources, the proposed method significantly outperforms the benchmark in both spectral and localization accuracy due to the exclusion of the second microphone. For far-field sources, the proposed method achieves slightly decreased spectral distortions due to the flattened response of the interpolation filters.

Metrics are presented that assess spectral coloration and localization errors incurred by navigational techniques for higher-order ambisonics. Previous studies on the coloration induced by such navigational techniques have been largely qualitative, and the accuracy of previously-used localization models in this context is unclear. The presented metrics are applied in numerical simulations of navigation over a range of translation distances. Coloration is predicted using an auditory filter bank to compute the spectral energy differences between the test and reference signals in critical bands, and localization is predicted using a precedence-effect-based localization model. Coloration and localization errors are also measured through corresponding binaural-synthesis-based listening tests, wherein subjects are first asked to rate the induced coloration relative to reference and low-pass-filtered “anchor“ signals, and subsequently judge source position. Relationships are drawn between the metrics and the results of the listening tests in order to validate the predictive capabilities of the metrics.

Performance errors are characterized for two representative linear extrapolation methods for virtual navigation of higher-order ambisonics sound fields. For such methods, navigation is theoretically restricted to within the so-called region of validity, which spherically extends from the recording ambisonics microphone to its nearest source, but the precise consequences of violating that restriction have not been previously established. To that end, the errors introduced by each method are objectively evaluated, in terms of metrics for sound level, spectral coloration, source localization, and diffuseness, through numerical simulations over a range of valid and invalid conditions. Under valid conditions, results show that the first method, based on translating along plane-waves, accurately reproduces both the level and localization of a source, whereas the second method, based on ambisonics translation coefficients, incurs significant errors in both level and spectral content that increase steadily with translation distance. Under invalid conditions, two common features of the performance of both methods are identified: significant localization errors are introduced and the reproduced level is too low. It is argued that these penalties are inherent to all methods that are bound by the region of validity restriction, including all linear extrapolation methods.

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Suitable domains are established for the practical application of two state-of-the-art parametric interpolation methods for virtual navigation of ambisonics-encoded sound fields. Although several navigational methods have been developed, existing studies rarely include comparisons between methods and, significantly, practical assessments of such methods have been limited. To that end, the errors introduced by both methods are objectively evaluated, in terms of metrics for sound level, spectral coloration, source localization, and diffuseness, through numerical simulations. Various practical domains are subsequently identified, and guidelines are established with which to choose between these methods based on their intended application. Results show that the first method, which entails a time-frequency analysis of the sound field, is preferable for large-area recordings and when spatial localization accuracy is critical, as this method achieves superior localization performance (compared to the second method) with sparsely distributed microphones. However, the second method, which parametrically excludes from the interpolation any microphones that are farther from the listening position than is any source, is shown to be more suitable for applications in which sound quality attributes such as coloration and diffuseness are critical, since this method achieves smaller spectral errors with sparsely distributed microphones and smaller diffuseness errors under all conditions.