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Identification and tracking of time- variant systems is relevant in many applications, such as acoustic echo cancellation, active noise control, or in acoustics, e.g., for fast acquisition of head-related transfer functions (HRTFs) via dynamic measurements. Unlike in many other applications, for acoustic measurements the excitation signals can be chosen and optimized for the specific measurement scenario. So far, for this optimization the impact of the group delay on the tracking behavior has not been explicitly considered as a design criterion. In this paper, the influence of time-variance in combination with the temporal properties (envelope, group delay) of the excitation signal is addressed. In simulations and in dynamic binaural room impulse response measurements it is shown how the group delay of the excitation sequence affects the progression in tracking.

Research in static and time-variant system identification has brought up a broad variety of identification algorithms. In acoustics, e.g., static measurements of transfer functions are commonly conducted using Inverse Cyclic Convolution (ICC) with Exponential Sweep excitation. Identification and tracking of time-variant systems, however, often employ adaptive filter algorithms, such as the Normalized Least Mean Square (NLMS) algorithm. An interesting implementation variant is the so-called Efficient NLMS (eNLMS) algorithm for arbitrary periodic excitation. ICC and the eNLMS algorithm originate from different fields and have so far evolved independently. This paper bridges the gap using a theoretical analysis of both algorithms to prove that they can be transferred into each other. This understanding provides a joint perspective, such that know-how from both fields can be combined to further optimize the system identification process.

In system identification one problem is the autocorrelation of the excitation signal which often crucially affects the adaptation process. This paper focuses on the Kalman filter based adaptation working in the frequency domain and the implication due to correlated signal input. Principle simulations and the introduction of a reference model indicate to which extent correlation take effect. The experimental results demonstrate that even though the Kalman approach already takes advantage from a certain level of inherent decorrelation, it also benefits from additional decorrelation. To address this issue, we derive a new realizable efficient structure combining the Kalman filter based adaptation with linear prediction techniques. The performance gains of the proposed approach are confirmed via experiments for an acoustic echo cancellation application for different scenarios.

In stereo or multi-channel system identification, the most critical problems regarding online identification, e.g., for acoustic echo control, are the correlation properties of the excitation signals of the different audio channels. In this paper the impact of both the auto- and cross-correlation properties is considered and investigated. A new system combining appropriate decorrelation techniques with a Kalman filter driven adaptation algorithm in the frequency domain is presented. For the auto-decorrelation a new structure is proposed where the signals in the adaptation paths are decorrelated via linear prediction without affecting the acoustic signals. A small non-linearity is added into each channel for the reduction of the cross-correlation between channels. The performance evaluation clearly shows the influence of the different countermeasures and the effectiveness of the combined approach.