Showing papers on "Impulse response published in 2000"
Journal Article•
TL;DR: A novel measurement technique of the transfer function of weakly not-linear, approximately time-invariant systems is presented, based on an exponentially-swept sine signal, applicable to loudspeakers and other audio components, but also to room acoustics measurements.
Abstract: A novel measurement technique of the transfer function of weakly not-linear, approximately time-invariant systems is presented. The method is implemented with low-cost instrumentation; it is based on an exponentially-swept sine signal. It is applicable to loudspeakers and other audio components, but also to room acoustics measurements. The paper presents theoretical description of the method and experimental verification in comparison with MLS.
794 citations
TL;DR: The authors show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of MAP reconstruction for priors with quadratic energy functions, and describe how these analytical results can be used to achieve near-uniform contrast recovery throughout the reconstructed volume.
Abstract: Derives approximate analytical expressions for the local impulse response and covariance of images reconstructed from fully three-dimensional (3-D) positron emission tomography (PET) data using maximum a posteriori (MAP) estimation. These expressions explicitly account for the spatially variant detector response and sensitivity of a 3-D tomograph. The resulting spatially variant impulse response and covariance are computed using 3-D Fourier transforms. A truncated Gaussian distribution is used to account for the effect on the variance of the nonnegativity constraint used in MAP reconstruction. Using Monte Carlo simulations and phantom data from the microPET small animal scanner, the authors show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of MAP reconstruction for priors with quadratic energy functions. They also describe how these analytical results can be used to achieve near-uniform contrast recovery throughout the reconstructed volume.
389 citations
TL;DR: For the identification of the time-variant, directional structure of the mobile radio channel impulse response (CIR), a broadband vector channel sounder is described and results from measurements in the 5.2 GHz frequency range in an industrial environment are presented.
Abstract: For the identification of the time-variant, directional structure of the mobile radio channel impulse response (CIR), a broadband vector channel sounder is described. The measurement procedure relies on periodic multifrequency excitation signals, correlation processing, and joint delay-azimuth super-resolution based on the two-dimensional (2-D) unitary ESPRIT algorithm. Problems of imperfect receiver and antenna performance as well as antenna array calibration methods are discussed. Correlation analysis of the directional impulse response records is performed in the time-frequency-spatial domain and the corresponding Doppler-delay-angular domain. Results from measurements in the 5.2 GHz frequency range in an industrial environment are presented.
244 citations
TL;DR: An analog-circuit fault diagnostic system based on backpropagation neural networks using wavelet decomposition, principal component analysis, and data normalization as preprocessors that performs significantly better in fault diagnosis of analog circuits due to the proposed preprocessing techniques.
Abstract: We have developed an analog-circuit fault diagnostic system based on backpropagation neural networks using wavelet decomposition, principal component analysis, and data normalization as preprocessors. The proposed system has the capability to detect and identify faulty components in an analog electronic circuit by analyzing its impulse response. Using wavelet decomposition to preprocess the impulse response drastically reduces the number of inputs to the neural network, simplifying its architecture and minimizing its training and processing time. The second preprocessing by principal component analysis can further reduce the dimensionality of the input space and/or select input features that minimize diagnostic errors. Input normalization removes large dynamic variances over one or more dimensions in input space, which tend to obscure the relevant data fed to the neural network. A comparison of our work with that of Spina and Upadhyaya (see ibid., vol. 44, p. 188-196, 1997), which also employs backpropagation neural networks, reveals that our system requires a much smaller network and performs significantly better in fault diagnosis of analog circuits due to our proposed preprocessing techniques.
231 citations
TL;DR: In this article, the standard linear technique of impulse response function analysis is extended to the nonlinear case by defining a generalized impulse response functions and measures of persistence and asymmetry in response are constructed for a wide class of time series.
144 citations
Book•
01 Jan 2000
TL;DR: In this article, the authors present a model of continuous-time signals as sum of Discrete-Time Sine Waves, where the signal is modelled as a sum of sine waves.
Abstract: The Nature of Biomedical Signals. Memory and Correlation. The Impulse Response. Frequency Response. Modeling Continuous-Time Signals as Sums of Sine Waves. Responses of Linear Continuous-Time Filters to Arbitrary Inputs. Modeling Signals as Sums of Discrete-Time Sine Waves. Noise Removal and Signal Compensation. Modeling Stochastic Signals as Filtered White Noise. Scaling and Long-Term Memory. Nonlinear Models of Signals. Assessing Stationarity and Reproducibility. Appendix.
137 citations
01 Feb 2000
TL;DR: In this paper, the class of continuous-time linear systems is enlarged with the inclusion of fractional linear systems described by fractional differential equations, and it is shown how to compute the impulse, step, and frequency responses from the transfer function.
Abstract: In the paper, the class of continuous-time linear systems is enlarged with the inclusion of fractional linear systems. These are systems described by fractional differential equations. It is shown how to compute the impulse, step, and frequency responses from the transfer function. The theory is supported by definitions of fractional derivative and integral, generalisations of the usual. An introduction to fractal signals as outputs of fractional differintegrators is presented. It is shown how to define a stationary fractal.
121 citations
TL;DR: A mixed ray-tracing-deterministic algorithm is developed that assures that each ray contributes to the final channel response function as many times as it rebounds with an obstacle and increases dramatically the number of contributions and reduces the time required for an accurate simulation.
Abstract: A modified Monte Carlo algorithm for the calculation of the impulse response on infrared wireless indoor channels is presented. As is well known, the characteristics of the room where the IR diffuse channel is implemented can lead to problems in communication, such as a multipath penalty on the maximum baud rate or hidden-station situations. Classical algorithms require large computational effort to calculate the impulse response in an ordinary-size room. Monte Carlo offers the possibility of validating the assumptions made for these classic algorithms (basically, the Lambertian nature of all reflections) with a computational complexity that is determined by the accuracy desired by the user. We have developed a mixed ray-tracing-deterministic algorithm that assures that each ray contributes to the final channel response function as many times as it rebounds with an obstacle. It increases dramatically the number of contributions and reduces, to the same extent, the time required for an accurate simulation. Extensive simulation results are presented and are compared with those of other simulation methods. We demonstrate that the method presented here is much faster than Monte Carlo classical simulation schemes. It can be used as a method of simulation in itself or as a validation algorithm for other comparative studies of pulse broadening.
121 citations
TL;DR: Details about intensity effects for noise stimulation, in particular, the way the BM impedance varies with stimulus intensity, are reported, which illustrate the predictive power of the underlying model.
Abstract: Mechanical responses in the basal turn of the guinea-pig cochlea were measured with broad-band noise stimuli and expressed as input–output cross-correlation functions. The experiments were performed over the full range of stimulus intensities in order to try to understand the influence of cochlear nonlinearity on frequency selectivity, tuning, signal compression and the impulse response. The results are interpreted within the framework of a nonlinear, locally active, three-dimensional model of the cochlea. The data have been subjected to inverse analysis in order to recover the basilar-membrane (BM) impedance, a parameter function that, when inserted into the (linearized version of that) model, produces a model response that is similar to the measured response. This paper reports details about intensity effects for noise stimulation, in particular, the way the BM impedance varies with stimulus intensity. In terms of the underlying cochlear model, the decrease of the “activity component” in the BM impedanc...
105 citations
IBM1
TL;DR: The method comprises calculating a first moment and a second moment of impulse response for an RC circuit and analyzing each node to determine if the delay at that node is at a desired optimization condition for optimizing the circuit response.
Abstract: An efficient method for optimizing RC circuit design to reduce delay. The method comprises: calculating a first moment and a second moment of impulse response for an RC circuit; (2) computing a delay value for each node of the RC circuit utilizing the first and second moments by multiplying the natural logarithm of 2 with a division of the squared power of the first impulse moment by the square root of the second impulse moment; and (3) analyzing each node to determine if the delay at that node is at a desired optimization condition for optimizing the circuit response.
99 citations
01 Feb 2000
TL;DR: In this article, the class of discrete linear systems is enlarged with the inclusion of discrete-time fractional linear systems, which are described by fractional difference equations and fractional frequency responses.
Abstract: In the paper, the class of discrete linear systems is enlarged with the inclusion of discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how io compute the impulse response and transfer function. Fractal signals are introduced as output of special linear systems: fractional differaccumulators, systems that can be considered as having fractional poles or zeros. The concept of fractional differaccumulation is discussed, gencralising the notions of fractal and lif noise, and introducing two kinds of fractional differaccumulated stochastic proccss: hyperbolic, resulting from fractional accumulation (similar to the continuous-time casc), and parabolic noise, resulting from fractional differencing.
22 Oct 2000
TL;DR: In this article, the same spatial impulse response is calculated for each of the image lines, and making 100 lines, thus, gives 100 calculations of the same impulse response delayed differently for the different lines.
Abstract: Realistic B-mode and flow images can be simulated with scattering maps based on optical, CT, or MR images or parametric flow models. The image simulation often includes using 200,000 to 1 million point scatterers. One image line typically takes 1800 seconds to compute on a state-of-the-art PC, and a whole image can take a full day. Simulating 3D images and 3D flow takes even more time. A 3D image of 64 by 64 lines can take 21 days, which is not practical for iterative work. This paper presents a new fast simulation method based on the Field II program. In imaging the same spatial impulse response is calculated for each of the image lines, and making 100 lines, thus, gives 100 calculations of the same impulse response delayed differently for the different lines. Doing the focusing after this point in the simulation can make the calculation faster. This corresponds to full synthetic aperture imaging. The received response from each element is calculated, when emitting with each of the elements in the aperture, and then the responses are subsequently focused. This is the approach taken in this paper using a modified version of the Field II program. A 64 element array, thus, gives 4096 responses. For a 7 MHz 64 element linear array the simulation time for one image line is 471 seconds for 200,000 scatterers on a 800 MHz AMD Athlon PC, corresponding to 17 hours for one image with 128 lines. Using the new approach, the computation time is 10,963 seconds, and the beamforming time is 9 seconds, which makes the approach 5.5 times faster. For 3D images with 64 by 64 lines, the total conventional simulation time for one volume is 517 hours, whereas the new approach makes the simulation in 6,810 seconds. The time for beamforming is 288 seconds, and the new approach is, thus, 262 times faster. The simulation can also be split among a number of PCs for speeding up the simulation. A full 3D one second volume simulation then takes 7,500 seconds on a 32 CPU 600 MHz Pentium III PC cluster.
Journal Article•
TL;DR: A methodology is introduced for smoothing the complex transfer function of measured responses using well-established or arbitrary fractional-octave profiles, based on a novel time-frequency mapping framework that has reduced complexity but conforms to perceptual principles.
Abstract: A methodology is introduced for smoothing the complex transfer function of measured responses using well-established or arbitrary fractional-octave profiles, based on a novel time-frequency mapping framework. A corresponding impulse response, also derived analytically, has reduced complexity but conforms to perceptual principles. The relationship be tween complex smoothing and traditional power spectral smoothing is also discussed.
01 Dec 2000
TL;DR: In this paper, the authors describe a method for measuring the normalised IR experimentally, using a vector network analyser, and compare different air and dielectric-filled TEM horn antennas.
Abstract: A common way of describing antennas in the time domain is by means of their impulse response. When the time-domain antenna equations are expressed in terms of the normalised impulse response (normalised IR), they become very simple to use, because all frequency-dependent antenna characteristics are included in the normalised IR. This paper describes a method for measuring the normalised IR experimentally, using a vector network analyser. The normalised IRs of different air and dielectric-filled TEM horn antennas are compared and discussed. The normalised IR is found to be a powerful tool for simulating antenna behaviour directly in the time domain. Thanks to the introduction of the virtual source, (i.e. an apparent point in the antenna from which the radiated field degrades by a factor 1/r), the time-domain antenna equations can also be used near the TEM horns, although still in the far field of the antenna. Some examples of time-domain simulations and system modelling using the normalised IR are presented. In each example, the simulations are compared with measured data.
TL;DR: A continuous-time Hammerstein system, i.e., a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one, is identified and an algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown.
Abstract: A continuous-time Hammerstein system, i.e., a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one, is identified. The system is driven and disturbed by white random signals. The a priori information about both subsystems is nonparametric, which means that functional forms of both the nonlinear characteristic and the impulse response of the dynamic subsystem are unknown. An algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown. The impulse response of the dynamic part is recovered with a correlation method. The algorithms are computationally independent. Results of a simulation example are given.
TL;DR: In this article, an adaptive eigenvalue decomposition algorithm (AEDA) is employed to estimate the channel impulse response from the sound source to each of a pair of microphones, and then uses these estimated impulse responses to determine the time delay of arrival (TDOA) between the two microphones by measuring the distance between the first peaks thereof (i.e., the first significant taps of the corresponding transfer functions).
Abstract: A real-time passive acoustic source localization system for video camera steering advantageously determines the relative delay between the direct paths of two estimated channel impulse responses. The illustrative system employs an approach referred to herein as the “adaptive eigenvalue decomposition algorithm” (AEDA) to make such a determination, and then advantageously employs a “one-step least-squares algorithm” (OSLS) for purposes of acoustic source localization, providing the desired features of robustness, portability, and accuracy in a reverberant environment. The AEDA technique directly estimates the (direct path) impulse response from the sound source to each of a pair of microphones, and then uses these estimated impulse responses to determine the time delay of arrival (TDOA) between the two microphones by measuring the distance between the first peaks thereof (i.e., the first significant taps of the corresponding transfer functions). In one embodiment, the system minimizes an error function (i.e., a difference) which is computed with the use of two adaptive filters, each such filter being applied to a corresponding one of the two signals received from the given pair of microphones. The filtered signals are then subtracted from one another to produce the error signal, which is minimized by a conventional adaptive filtering algorithm such as, for example, an LMS (Least Mean Squared) technique. Then, the TDOA is estimated by measuring the “distance” (i.e., the time) between the first significant taps of the two resultant adaptive filter transfer functions.
07 May 2000
TL;DR: In this paper rigorous theoretical performance bounds are constructively established for the joint transmitter-target-channel-receiver optimization problem in the presence of additive colored noise (ACN), (e.g., interference multipath).
Abstract: Recent advances in linear amplifier and arbitrary waveform generation technology have spawned interest in adaptive transmitter systems as a means for both optimizing target signal gain and enhancing ID. In this paper rigorous theoretical performance bounds are constructively established for the joint transmitter-target-channel-receiver optimization problem in the presence of additive colored noise (ACN), (e.g., interference multipath). For the ACN case, an analytical solution is obtained as an eigenvector (with associated maximum eigenvalue) of a homogeneous Fredholm integral equation of the second type. The kernel function is Hermitian and is obtained from the cascade of the target impulse response with the ACN whitening filter. The theoretical performance gains achievable over conventional transmitter strategies (e.g., chirp) are presented for various simulation scenarios including interference multipath mitigation. Also discussed is the potential effectiveness of an optimal discriminating pulse solution for the N-target ID problem that arises naturally from the theory.
TL;DR: In this paper, a detailed analysis of the methods in current use shows that they are not very reliable in some cases and there are theoretical reasons for them to have actual coverage probabilities which deviate considerably from the nominal level in some situations of practical importance.
Abstract: Confidence intervals for impulse responses computed from autoregressive processes are considered. A detailed analysis of the methods in current use shows that they are not very reliable in some cases. In particular, there are theoretical reasons for them to have actual coverage probabilities which deviate considerably from the nominal level in some situations of practical importance. For a simple case alternative bootstrap methods are proposed which provide correct results asymptotically.
Proceedings Article•
01 Sep 2000TL;DR: This work presents a novel nonlinear structure which exploits the echo path characteristics and thus is more efficient than conventional Volterra filters.
Abstract: Acoustic echo cancellers commonly implement linear filters that have to identify as close as possible the impulse response of the acoustic echo path system. However such a system is highly nonlinear, and thus it is reasonable to suppose that a better system identification could be achieved by a nonlinear filter. Volterra filters are well suited for modelling that system but they need in general too many computational resources for a real time implementation. Here we present a novel nonlinear structure which exploits the echo path characteristics and thus is more efficient than conventional Volterra filters. For this structure we have considered two kinds of adaptive algorithms: standard LMS and Affine Projection (AP) algorithms that we adapted to this structure.
TL;DR: The method is applied to investigate high-frequency dynamics of pulse width modulation (PWM) converters operating in discontinuous conduction mode, and the results are used to compare and validate several existing analytical modeling approaches.
Abstract: The paper describes a method for automated small-signal frequency response analysis based on transient response obtained using a general-purpose simulation tool such as simulation program with integrated circuit emphasis (SPICE). The method is based on using the simulation tool to evaluate the converter impulse response. The main advantage of the proposed method as a design verification tool is that frequency responses can be generated efficiently for any converter configuration and any model complexity supported by the general-purpose simulator. Application examples are included to demonstrate very good correlation between the generated responses and experimental data, and to compare the results with predictions of approximate analytical methods. In particular, the method is applied to investigate high-frequency dynamics of pulse width modulation (PWM) converters operating in discontinuous conduction mode, and the results are used to compare and validate several existing analytical modeling approaches.
TL;DR: In this article, the temporal frequency response of water supplemented with scattering particles was deduced from the measurement of the optical backscattering of a short (100 ps) blue-green (532 nm) optical pulse given by a frequency-doubled Nd:YAG laser.
Abstract: The temporal frequency response of water supplemented with scattering particles was deduced from the measurement of the optical backscattering of a short (100 ps) blue-green (532 nm) optical pulse given by a frequency-doubled Nd:YAG laser. Indeed, this backscattering measurement gave the water impulse response from which the transfer function was computed by taking the power spectrum. This backscattering frequency response had a low-pass filter-like response which enabled us to estimate the medium cut-off frequency. As the backscattered signal shape depends on the value of the water attenuation coefficient, the ocean water cut-off frequency varies with the amount of scattering particles its contains. The aim was to define the variations of the cut-off frequency as a function of the attenuation coefficient.
TL;DR: In this article, a nondestructive quality inspection technique using acoustic impulse response method was developed for the detection of surface cracks in an eggshell. But the results showed that the error rates in estimating cracked eggs as normal and estimating normal eggs as cracked (type II error) were 6% and 4%, respectively.
Abstract: A nondestructive quality inspection technique using acoustic impulse response method was developed for the
detection of surface cracks in an eggshell. An experimental system was built to generate the impact force, measure the
response signal, analyze the frequency spectrum, and classify the eggs as cracked or normal. This system includes an
impulse generating unit, an egg holding seat, a microphone with a preamplifier, and a DSP board installed in a personal
computer. A multivariate discriminant analysis and a multiple regression analysis were used to develop classification
criteria for the detection of surface cracks in the eggshell. The error rates in estimating cracked eggs as normal (type I
error) and estimating normal eggs as cracked (type II error) were found to be 6% and 4%, respectively. The measured
processing time for classification was 200 ms/egg with the online inspection algorithm.
23 Jan 2000
TL;DR: In this paper, the authors present a method for extraction of impulse response parameters with particular emphasis on separation of the modes close in frequency, based on normal operation angle measurements across 1200 km in Queensland and power measurements in Victoria.
Abstract: Oscillation frequency and damping of interconnected power systems have traditionally been determined from line switching or generator tripping. In a competitive environment, scheduling generation and limiting transfers to ensure the system remains stable bring cost impacts for the test. Another factor influencing the test is that the resulting oscillation must be significantly above the noise level from customer load variations. Examination of normal operation angle measurements across 1200 km in Queensland and power measurements in Victoria show that frequencies and damping of the modes can be determined. This paper presents a method for extraction of impulse response parameters with particular emphasis on separation of the modes close in frequency.
TL;DR: In this article, a mathematical relationship between the true and reconstructed impedance log is derived without the assumptions required in an existing derivation of the same result, and analytical expressions are derived for the reconstructed impedance corresponding to any given frequency band for two cases: a simple discontinuity and a bed sandwiched between two similar beds.
Abstract: A seismic approximate impedance log is often the ultimate output in the sequence of seismic data‐processing steps. In principle, the true acoustic impedance is obtainable from the inversion of full‐band impulse response. Because the seismic data necessarily is band limited, its inversion obviously would produce an approximate impedance log. A question addressed is how the true and reconstructed logs are related and a mathematical relationship between the two is derived without the assumptions required in an existing derivation of the same result. The deductions also include the contribution of an individual seismic frequency in the reconstruction of the impedance and, in particular, a simple formula for the contribution of direct‐current (dc) frequency, which never is recorded but is required to supplement the inversion. Analytical expressions are derived for the reconstructed impedance corresponding to any given frequency band for two cases: a simple discontinuity and a bed sandwiched between two similar...
Patent•
13 Dec 2000TL;DR: In this article, a method and an arrangement for generating an estimate of the impulse response of a radio channel is presented. But the method is not suitable for the estimation of the channel impulse response in the presence of interference.
Abstract: A method and an arrangement are provided for generating an estimate of the impulse response of a radio channel. There is generated (202, 406) an initial estimate of the impulse response of a radio channel, and a signal is equalized (203, 407) by using the initial estimate. The equalized signal is decoded (205, 409). There is obtained (411) feedback information from the signal (306) after equalization, an updated channel estimate is generated (304, 412) by using said feedback information, and the signal is equalized (407) again by using said updated channel estimate and said feedback information.
TL;DR: In this article, the authors construct the three-dimensional causal impulse response of the Sun by deconcatenating the Kolmogorov result, which has the same spatial and temporal bandwidth as the original data, rather than the decreased bandwidth obtained by cross-correlating traces.
Abstract: Calculation of time-distance curves in helioseismology can be formulated as a blind-deconvolution (or system identification) problem. A classical solution in one-dimensional space is Kolmogorov’s Fourier domain spectral-factorization method. The helical coordinate system maps two-dimensions to one. Likewise a three-dimensional volume is representable as a concatenation of many one-dimensional signals. Thus concatenating a cube of helioseismic data into a very long 1-D signal and applying Kolmogorov’s factorization, we find we can construct the three-dimensional causal impulse response of the Sun by deconcatenating the Kolmogorov result. Time-distance curves calculated in this way have the same spatial and temporal bandwidth as the original data, rather than the decreased bandwidth obtained obtained by cross-correlating traces. Additionally, the spectral factorization impulse response is minimum phase, as opposed to the zero phase time-distance curves produced by cross-correlation.
01 Jan 2000
TL;DR: In this article, simple procedures based on the Hilbert transform and empirical mode decomposition are proposed to identify MDOF linear structural systems using the measured impulse response time histories, from which natural frequencies, damping ratios and mode shapes as well as the physical mass, stiffness and proportional damping matrices of the structure are identified.
Abstract: In this paper, simple procedures based on the Hilbert transform and Empirical Mode Decomposition are proposed to identify MDOF linear structural systems using the measured impulse response time histories. Measured response data are first decomposed into Intrinsic Mode Functions using the Empirical Mode Decomposition method. These Intrinsic Mode Functions are shown to be the modal responses. Then, the Hilbert transform is applied to each Intrinsic Mode Function to obtain the amplitude and phase angle time histories of each mode, from which natural frequencies, damping ratios and mode shapes as well as the physical mass, stiffness and proportional damping matrices of the structure are identified. The applications of the methodology presented are demonstrated through numerical simulations. Simulation results indicate that the system identification method presented offers a simple and effective tool for parametric identification of linear structures.
TL;DR: An efficient method based on an iterative weighted genetic algorithm approach to obtain a least-squares approximation to the given log magnitude function and the weighting function at each iteration is updated using the result of the previous iteration, which leads to the optimal approximation in the log Chebyshev sense.
TL;DR: Simulated data as well as real corner reflector responses are used to show that the correct topography can be recovered precisely even in the presence of phase bias coming from the squinted geometry.
Abstract: This paper develops an analysis of the SAR impulse response function from the interferometric point of view, with the intention of studying its phase behavior in the presence of high squint angle values. It will be pointed out that in this case, a phase ramp is present in the range direction, which, in combination with a certain degree of misregistration between the two images induces an offset in the generated interferometric phase. This behavior, if not compensated, imposes strong limits on the performance of the interferometric techniques in a squinted case, especially for airborne SAR systems. The article proposes two new techniques, which are appropriate to correct the phase bias coming from this source. The first one is based on a modification of the azimuth compression filter, which cancels the phase ramp of the range impulse response function for one specific squint value. In case the SAR processing is performed with variable squint over range, the authors propose a second method oriented to estimating the expected misregistration and thus, the phase bias by means of an iterative approach. Simulated data as well as real corner reflector responses are used to show that the correct topography can be recovered precisely even in the presence of phase bias coming from the squinted geometry.
TL;DR: The authors' results show that, when a priori information on the unknown model parameters is available, Bayes estimation can be of relevant interest, since it can significantly improve the precision of parameter estimates with respect to Fisher estimation.
Abstract: Maximum-likelihood (ML), also given its connection to least squares (LS), is widely adopted in parameter estimation of physiological system models, i.e., assigning numerical values to the unknown model parameters from the experimental data. A more sophisticated but less used approach is maximum a posteriori (MAP) estimation. Conceptually, while ML adopts a Fisherian approach, i.e., only experimental measurements are supplied to the estimator, MAP estimation is a Bayesian approach, i.e., a priori available statistical information on the unknown parameters is also exploited for their estimation. Here, after a brief review of the theory behind ML and MAP estimators, the authors compare their performance in the solution of a case study concerning the determination of the parameters of a sum of exponential model which describes the impulse response of C-peptide (CP), a key substance for reconstructing insulin secretion. The results show that MAP estimation always leads to parameter estimates with a precision (sometimes significantly) higher than that obtained through ML, at the cost of only a slightly worse fit. Thus, a 3 exponential model can be adopted to describe the CP impulse response model in place of the two exponential model usually identified in the literature by the ML/LS approach. Simulated case studies are also reported to evidence the importance of taking into account a priori information in a data poor situation, e.g., when a few or too noisy measurements are available. In conclusion, the authors' results show that, when a priori information on the unknown model parameters is available, Bayes estimation can be of relevant interest, since it can significantly improve the precision of parameter estimates with respect to Fisher estimation. This may also allow the adoption of more complex models than those determinable by a Fisherian approach.