Showing papers on "Adaptive filter published in 2014"

The Labeled Multi-Bernoulli Filter

Abstract: This paper proposes a generalization of the multi- Bernoulli filter called the labeled multi-Bernoulli filter that outputs target tracks. Moreover, the labeled multi-Bernoulli filter does not exhibit a cardinality bias due to a more accurate update approximation compared to the multi-Bernoulli filter by exploiting the conjugate prior form for labeled Random Finite Sets. The proposed filter can be interpreted as an efficient approximation of the $\delta$ -Generalized Labeled Multi-Bernoulli filter. It inherits the advantages of the multi-Bernoulli filter in regards to particle implementation and state estimation. It also inherits advantages of the $\delta$ -Generalized Labeled Multi-Bernoulli filter in that it outputs (labeled) target tracks and achieves better performance.

A Novel Grid Synchronization PLL Method Based on Adaptive Low-Pass Notch Filter for Grid-Connected PCS

Abstract: The amount of distributed energy resources (DERs) has increased constantly worldwide. The power ratings of DERs have become considerably high, as required by the new grid code requirement. To follow the grid code and optimize the function of grid-connected inverters based on DERs, a phase-locked loop (PLL) is essential for detecting the grid phase angle accurately when the grid voltage is polluted by harmonics and imbalance. This paper proposes a novel low-pass notch filter PLL (LPN-PLL) control strategy to synchronize with the true phase angle of the grid instead of using a conventional synchronous reference frame PLL (SRF-PLL), which requires a d-q-axis transformation of three-phase voltage and a proportional-integral controller. The proposed LPN-PLL is an upgraded version of the PLL method using the fast Fourier transform concept (FFT-PLL) which is robust to the harmonics and imbalance of the grid voltage. The proposed PLL algorithm was compared with conventional SRF-PLL and FFT-PLL and was implemented digitally using a digital signal processor TMS320F28335. A 10-kW three-phase grid-connected inverter was set, and a verification experiment was performed, showing the high performance and robustness of the proposal under low-voltage ride-through operation.

An Adaptive Prefiltering Method to Improve the Speed/Accuracy Tradeoff of Voltage Sequence Detection Methods Under Adverse Grid Conditions

Abstract: This paper deals with the improvement of the transient response and harmonic, subharmonic, and dc-offset voltage rejection capability of a grid voltage sequence detection scheme based on a second-order generalized integrator (SOGI). To perform that, the SOGI structure is first analyzed in deep, emphasizing both its tradeoff limits between settling time and harmonic attenuation and the sensitivity to grid subharmonics and dc-offset voltage. Then, a study of the effect of grid voltage harmonics and subharmonics in SOGI and in the SOGI-FLL and MSOGI-FLL structures is introduced. Hence, to overcome these problems, a new structure based on the use of the SOGI filter as prefilter for the previous structures is proposed to achieve a faster time response and higher harmonic rejection. This structure is used in a sequence detection scheme for the detection of the grid voltage components in the αβ-frame and it is applied in a three-phase PV system. Experimental and comparative results are shown to validate this proposal.

A Motion-Tolerant Adaptive Algorithm for Wearable Photoplethysmographic Biosensors

Abstract: The performance of portable and wearable biosensors is highly influenced by motion artifact. In this paper, a novel real-time adaptive algorithm is proposed for accurate motion-tolerant extraction of heart rate (HR) and pulse oximeter oxygen saturation (SpO2) from wearable photoplethysmographic (PPG) biosensors. The proposed algorithm removes motion artifact due to various sources including tissue effect and venous blood changes during body movements and provides noise-free PPG waveforms for further feature extraction. A two-stage normalized least mean square adaptive noise canceler is designed and validated using a novel synthetic reference signal at each stage. Evaluation of the proposed algorithm is done by Bland-Altman agreement and correlation analyses against reference HR from commercial ECG and SpO2 sensors during standing, walking, and running at different conditions for a single- and multisubject scenarios. Experimental results indicate high agreement and high correlation (more than 0.98 for HR and 0.7 for SpO2 extraction) between measurements by reference sensors and our algorithm.

Adaptive Compensation Method of Position Estimation Harmonic Error for EMF-Based Observer in Sensorless IPMSM Drives

Abstract: To improve the performance of sensorless interior permanent magnet synchronous motor (IPMSM) drives, a quadrature phase-locked loop (PLL) with an adaptive notch filter (ANF) is proposed for the model-based sliding-mode observer (SMO). The position estimation error with the sixth harmonic distortion caused by the inverter nonlinearity and the flux spatial harmonics is analyzed. The ANF based on adaptive noise canceling principle combined with the quadrature PLL is proposed to diminish the estimation harmonic error. This method can adaptively compensate the harmonics in the estimated electromotive force to eliminate the corresponding position estimation error. The estimated harmonic coefficients from the ANF can be continuously self-tuned using the least-mean-squares algorithm according to the estimated position information. The effectiveness of the proposed method is verified with the experimental results at a 2.2-kW IPMSM sensorless drive.

A Novel Design and Optimization Method of an $LCL$ Filter for a Shunt Active Power Filter

Abstract: Compared with the L filter, the LCL filter is more suitable for high-power low-switching-frequency applications due to its better attenuation characteristics on high frequencies. However, the parameter design for the LCL filter is more complex since both the inhibiting effect of the high-frequency harmonic current and the influence to the controller response performance of the converter should be considered. In this paper, the model of the LCL filter and the design criteria of the LCL filter for a shunt active power filter (SAPF) are analyzed in the beginning. Then, the impacts of all parameters of the LCL filter on SAPF are intuitively drawn on a graph by theoretical derivation. Finally, a novel parameter design and optimization method for the LCL filter is proposed. The validity and effectiveness of the proposed method are proved by simulated and experimental results of a single-phase SAPF prototype at the end of this paper.

Adaptive Vectorial Filter for Grid Synchronization of Power Converters Under Unbalanced and/or Distorted Grid Conditions

Abstract: This paper presents a new synchronization scheme for detecting multiple positive-/negative-sequence frequency harmonics in three-phase systems for grid-connected power converters. The proposed technique is called MAVF-FLL because it is based on the use of multiple adaptive vectorial filters (AVFs) working together inside a harmonic decoupling network, resting on a frequency-locked loop (FLL) which makes the system frequency adaptive. The method uses the vectorial properties of the three-phase input signal in the αβ reference frame in order to obtain the different harmonic components. The MAVF-FLL is fully designed and analyzed, addressing the tuning procedure in order to obtain the desired and predefined performance. The proposed algorithm is evaluated by both simulation and experimental results, demonstrating its ability to perform as required for detecting different harmonic components under a highly unbalanced and distorted input grid voltage.

Position Estimation Error Reduction Using Recursive-Least-Square Adaptive Filter for Model-Based Sensorless Interior Permanent-Magnet Synchronous Motor Drives

Abstract: To improve the performance of sensorless interior permanent-magnet synchronous motor (IPMSM) drives, an adaptive filter (AF) using recursive-least-square (RLS) algorithm is proposed for the electromotive force (EMF) model-based sliding-mode observer with a quadrature phase-locked loop (PLL) tracking estimator. The inverter nonlinearities and flux spatial harmonics, which cause the position estimation error with the sixth harmonic, are analyzed. An AF based on the adaptive noise-cancelling principle in cascade with a quadrature PLL is adopted to remove the harmonic estimation error. According to the harmonic characteristics of the estimation error from the quadrature PLL, the AF coefficients can be continuously updated by the RLS algorithm. The application of the RLS algorithm guarantees the fast convergence rate of the AF. Through the AF using the RLS algorithm, the harmonics of the estimated EMF can be effectively compensated. Therefore, the selected position estimation harmonic error can be eliminated. The effectiveness of the proposed method is verified with the experimental results at a 2.2-kW sensorless IPMSM drive.

Removal of High-Density Salt-and-Pepper Noise in Images With an Iterative Adaptive Fuzzy Filter Using Alpha-Trimmed Mean

Abstract: Suppression of impulse noise in images is an important problem in image processing. In this paper, we propose a novel adaptive iterative fuzzy filter for denoising images corrupted by impulse noise. It operates in two stages-detection of noisy pixels with an adaptive fuzzy detector followed by denoising using a weighted mean filter on the “good” pixels in the filter window. Experimental results demonstrate the algorithm to be superior to state-of-the-art filters. The filter is also shown to be robust to very high levels of noise, retrieving meaningful detail at noise levels as high as 97%.

Motion artifact removal from photoplethysmographic signals by combining temporally constrained independent component analysis and adaptive filter

Abstract: The calculation of arterial oxygen saturation (SpO2) relies heavily on the amplitude information of the high-quality photoplethysmographic (PPG) signals, which could be contaminated by motion artifacts (MA) during monitoring. A new method combining temporally constrained independent component analysis (cICA) and adaptive filters is presented here to extract the clean PPG signals from the MA corrupted PPG signals with the amplitude information reserved. The underlying PPG signal could be extracted from the MA contaminated PPG signals automatically by using cICA algorithm. Then the amplitude information of the PPG signals could be recovered by using adaptive filters. Compared with conventional ICA algorithms, the proposed approach is permutation and scale ambiguity-free. Numerical examples with both synthetic datasets and real-world MA corrupted PPG signals demonstrate that the proposed method could remove the MA from MA contaminated PPG signals more effectively than the two existing FFT-LMS and moving average filter (MAF) methods. This paper presents a new method which combines the cICA algorithm and adaptive filter to extract the underlying PPG signals from the MA contaminated PPG signals with the amplitude information reserved. The new method could be used in the situations where one wants to extract the interested source automatically from the mixed observed signals with the amplitude information reserved. The results of study demonstrated the efficacy of this proposed method.

Distributed Sparse Recursive Least-Squares Over Networks

Abstract: Distributed estimation over networks has received much attention in recent years due to its broad applicability. Many signals in nature present high level of sparsity, which contain only a few large coefficients among many negligible ones. In this paper, we address the problem of in-network distributed estimation for sparse vectors, and develop several distributed sparse recursive least-squares (RLS) algorithms. The proposed algorithms are based on the maximum likelihood framework, and the expectation-maximization algorithm, with the aid of thresholding operators, is used to numerically solve the sparse estimation problem. To improve the estimation performance, the thresholding operators related to l0- and l1-norms with real-time self-adjustable thresholds are derived. With these thresholding operators, we can exploit the underlying sparsity to implement the distributed estimation with low computational complexity and information exchange amount among neighbors. The sparsity-promoting intensity is also adaptively adjusted so that a good performance of the sparse solution can be achieved. Both theoretical analysis and numerical simulations are presented to show the effectiveness of the proposed algorithms.

Adaptive room equalization using a speaker and a handheld listening device

Abstract: A loudspeaker that measures the impulse response of a listening area is described. The loudspeaker may output sounds corresponding to a segment of an audio signal. The sounds are sensed by a listening device proximate to a listener and transmitted to the loudspeaker. The loudspeaker includes an adaptive filter that estimates the impulse response of the listening area based on the signal segment. An error unit analyzes the estimated impulse response together with the sensed audio signal received from the listening device to determine the accuracy of the estimate. New estimates may be generated by the adaptive filter until an accuracy level is achieved for the signal segment. A processor may utilize one or more estimated impulse responses corresponding to various signal segments that cover a defined frequency spectrum for adjusting the audio signal to compensate for the impulse response of the listening area. Other embodiments are also described.

Convex Combination of Adaptive Filters under the Maximum Correntropy Criterion in Impulsive Interference

Abstract: A robust adaptive filtering algorithm based on the convex combination of two adaptive filters under the maximum correntropy criterion (MCC) is proposed. Compared with conventional minimum mean square error (MSE) criterion-based adaptive filtering algorithm, the MCC-based algorithm shows a better robustness against impulsive interference. However, its major drawback is the conflicting requirements between convergence speed and steady-state mean square error. In this letter, we use the convex combination method to overcome the tradeoff problem. Instead of minimizing the squared error to update the mixing parameter in conventional convex combination scheme, the method of maximizing the correntropy is introduced to make the proposed algorithm more robust against impulsive interference. Additionally, we report a novel weight transfer method to further improve the tracking performance. The good performance in terms of convergence rate and steady-state mean square error is demonstrated in plant identification scenarios that include impulsive interference and abrupt changes.

Active actuator fault-tolerant control of a wind turbine benchmark model

Abstract: SUMMARY This paper describes the design of an active fault-tolerant control scheme that is applied to the actuator of a wind turbine benchmark. The methodology is based on adaptive filters obtained via the nonlinear geometric approach, which allows to obtain interesting decoupling property with respect to uncertainty affecting the wind turbine system. The controller accommodation scheme exploits the on-line estimate of the actuator fault signal generated by the adaptive filters. The nonlinearity of the wind turbine model is described by the mapping to the power conversion ratio from tip-speed ratio and blade pitch angles. This mapping represents the aerodynamic uncertainty, and usually is not known in analytical form, but in general represented by approximated two-dimensional maps (i.e. look-up tables). Therefore, this paper suggests a scheme to estimate this power conversion ratio in an analytical form by means of a two-dimensional polynomial, which is subsequently used for designing the active fault-tolerant control scheme. The wind turbine power generating unit of a grid is considered as a benchmark to show the design procedure, including the aspects of the nonlinear disturbance decoupling method, as well as the viability of the proposed approach. Extensive simulations of the benchmark process are practical tools for assessing experimentally the features of the developed actuator fault-tolerant control scheme, in the presence of modelling and measurement errors. Comparisons with different fault-tolerant schemes serve to highlight the advantages and drawbacks of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.

Adaptive Widely Linear Reduced-Rank Beamforming Based on Joint Iterative Optimization

Abstract: We propose a reduced-rank beamformer based on the rank- D Joint Iterative Optimization (JIO) of the modified Widely Linear Constrained Minimum Variance (WLCMV) problem for non-circular signals. The novel WLCMV-JIO scheme takes advantage of both the Widely Linear (WL) processing and the reduced-rank concept, outperforming its linear counterpart as well as the full-rank WL beamformer. We develop an augmented recursive least squares algorithm and present an improved structured version with a much more efficient implementation. It is shown that the improved adaptive scheme achieves the best convergence performance among all the considered methods with a low computational complexity.

Sparse Adaptive Filtering by an Adaptive Convex Combination of the LMS and the ZA-LMS Algorithms

Abstract: In practice, one often encounters systems that have a sparse impulse response, with the degree of sparseness varying over time. This paper presents a new approach to identify such systems which adapts dynamically to the sparseness level of the system and thus works well both in sparse and non-sparse environments. The proposed scheme uses an adaptive convex combination of the LMS algorithm and the recently proposed, sparsity-aware zero-attractor LMS (ZA-LMS) algorithm. It is shown that while for non-sparse systems, the proposed combined filter always converges to the LMS algorithm (which is better of the two filters for non-sparse case in terms of lesser steady state excess mean square error (EMSE)), for semi-sparse systems, on the other hand, it actually converges to a solution that produces lesser steady state EMSE than produced by either of the component filters. For highly sparse systems, depending on the value of a proportionality constant in the ZA-LMS algorithm, the proposed combined filter may either converge to the ZA-LMS based filter or may produce a solution which, like the semi-sparse case, outperforms both the constituent filters. A simplified update formula for the mixing parameter of the adaptive convex combination is also presented. The proposed algorithm requires much less complexity than the existing algorithms and its claimed robustness against variable sparsity is well supported by simulation results.

Sparsity-Aware Data-Selective Adaptive Filters

Abstract: We propose two adaptive filtering algorithms that combine sparsity-promoting schemes with data-selection mechanisms. Sparsity is promoted via some well-known nonconvex approximations to the l 0 norm in order to increase convergence speed of the algorithms when dealing with sparse/compressible signals. These approximations circumvent some difficulties of working with the l 0 norm, thus allowing the development of online data-selective algorithms. Data selection is implemented based on set-membership filtering, which yields robustness against noise and reduced computational burden. The proposed algorithms are analyzed in order to set properly their parameters to guarantee stability. In addition, we characterize their updating processes from a geometrical viewpoint. Simulation results show that the proposed algorithms outperform the state-of-the-art algorithms designed to exploit sparsity.

Sparsity-Aware Adaptive Algorithms Based on Alternating Optimization and Shrinkage

Abstract: This letter proposes a novel sparsity-aware adaptive filtering scheme and algorithms based on an alternating optimization strategy with shrinkage The proposed scheme employs a two-stage structure that consists of an alternating optimization of a diagonally-structured matrix that speeds up the convergence and an adaptive filter with a shrinkage function that forces the coefficients with small magnitudes to zero We devise alternating optimization least-mean square (LMS) algorithms for the proposed scheme and analyze its mean-square error Simulations for a system identification application show that the proposed scheme and algorithms outperform in convergence and tracking existing sparsity-aware algorithms

A New Algorithm for Wire Fault Location Using Time-Domain Reflectometry

Abstract: In time domain reflectometry (TDR) attenuation and dispersion of the reflected signal limit the reachable accuracy for wire faults location. Because time of flight is evaluated, the wire faults with small impedance changing are difficult to locate. In this paper, a novel method for the TDR-based wire fault detection is presented by transfer function analysis in the time domain. For the determination of the transfer function, a deconvolution should be carried out. Thereby, an inverse problem is to be solved by an adaptive filter approach. Adaptive filters are able to reduce spurious noise of the deconvolution and lead to an acceptable deconvolution estimate. Therefore, a high signal-to-noise-ratio can be reached. The filter's stopband characteristics are optimized by optimization technique to reduce the noise components of the transfer function in the frequency domain. For that a nonlinear fitting procedure is proposed using the Riad-Parruck optimization criterion. The developed method can locate both hard faults (open and short circuits) and soft faults with small impedance changes, and identify the type of wire faults simultaneously in a controlled laboratory environment (without the impedance changes from mechanical vibration, movement, and moisture). The algorithm using adaptive filters and optimization techniques is proposed in this paper for the traditional TDR method, but it is general for most other reflectometry approaches. The estimated wirings are coaxial cables and twisted pair cables, which are used in electrical and power distribution systems.

A Frequency-Locked-Loop Filter for Biased Multi-Sinusoidal Estimation

Abstract: In this paper, an adaptive filter, based on a third-order generalized integrator, is proposed to estimate all the parameters of a biased sinusoid The averaging theory is used to prove that the filter identifies the unknown frequency of the signal, in the case of a pure biased sinusoid in input Moreover, in the case of a generic periodic signal, the method provides an estimate of the fundamental frequency by converging to a limit cycle in its vicinity The robustness of the proposed approach with respect to noise in the input signal is analyzed A filter bank is also presented to deal with the reconstruction problem of a generic multi-sinusoidal signal Simulation results are also provided to compare the performances of the method with existing ones

Sparsity-Aware Adaptive Algorithms Based on Alternating Optimization with Shrinkage

Abstract: This letter proposes a novel sparsity-aware adaptive filtering scheme and algorithms based on an alternating optimization strategy with shrinkage. The proposed scheme employs a two-stage structure that consists of an alternating optimization of a diagonally-structured matrix that speeds up the convergence and an adaptive filter with a shrinkage function that forces the coefficients with small magnitudes to zero. We devise alternating optimization least-mean square (LMS) algorithms for the proposed scheme and analyze its mean-square error. Simulations for a system identification application show that the proposed scheme and algorithms outperform in convergence and tracking existing sparsity-aware algorithms.

Critical-Path Analysis and Low-Complexity Implementation of the LMS Adaptive Algorithm

Abstract: This paper presents a precise analysis of the critical path of the least-mean-square (LMS) adaptive filter for deriving its architectures for high-speed and low-complexity implementation. It is shown that the direct-form LMS adaptive filter has nearly the same critical path as its transpose-form counterpart, but provides much faster convergence and lower register complexity. From the critical-path evaluation, it is further shown that no pipelining is required for implementing a direct-form LMS adaptive filter for most practical cases, and can be realized with a very small adaptation delay in cases where a very high sampling rate is required. Based on these findings, this paper proposes three structures of the LMS adaptive filter: (i) Design 1 having no adaptation delays, (ii) Design 2 with only one adaptation delay, and (iii) Design 3 with two adaptation delays. Design 1 involves the minimum area and the minimum energy per sample (EPS). The best of existing direct-form structures requires 80.4% more area and 41.9% more EPS compared to Design 1. Designs 2 and 3 involve slightly more EPS than the Design 1 but offer nearly twice and thrice the MUF at a cost of 55.0% and 60.6% more area, respectively.

Automatic Identification and Removal of Ocular Artifacts in EEG—Improved Adaptive Predictor Filtering for Portable Applications

Abstract: Electroencephalogram (EEG) signals have a long history of use as a noninvasive approach to measure brain function. An essential component in EEG-based applications is the removal of Ocular Artifacts (OA) from the EEG signals. In this paper we propose a hybrid de-noising method combining Discrete Wavelet Transformation (DWT) and an Adaptive Predictor Filter (APF). A particularly novel feature of the proposed method is the use of the APF based on an adaptive autoregressive model for prediction of the waveform of signals in the ocular artifact zones. In our test, based on simulated data, the accuracy of noise removal in the proposed model was significantly increased when compared to existing methods including: Wavelet Packet Transform (WPT) and Independent Component Analysis (ICA), Discrete Wavelet Transform (DWT) and Adaptive Noise Cancellation (ANC). The results demonstrate that the proposed method achieved a lower mean square error and higher correlation between the original and corrected EEG. The proposed method has also been evaluated using data from calibration trials for the Online Predictive Tools for Intervention in Mental Illness (OPTIMI) project. The results of this evaluation indicate an improvement in performance in terms of the recovery of true EEG signals with EEG tracking and computational speed in the analysis. The proposed method is well suited to applications in portable environments where the constraints with respect to acceptable wearable sensor attachments usually dictate single channel devices.

PAPR-Constrained Pareto-Optimal Waveform Design for OFDM-STAP Radar

Abstract: We propose a peak-to-average power ratio (PAPR)-constrained Pareto-optimal waveform-design approach for an orthogonal frequency division multiplexing (OFDM) radar signal to detect a target using the space-time adaptive processing (STAP) technique. The use of an OFDM signal does not only increase the frequency diversity of our system but also enable us to adaptively design the OFDM coefficients in order to further improve the system performance. First, we develop a parametric OFDM-STAP measurement model by considering the effects of signal-dependent clutter and colored noise. Then, we observe that the resulting STAP performance can be improved by maximizing the output signal-to-interference-plus-noise ratio (SINR) with respect to the signal parameters. However, in practical scenarios, the computation of output SINR depends on the estimated values of the spatial and temporal frequencies and target-scattering responses. Therefore, we formulate a PAPR-constrained multiobjective-optimization problem to design the OFDM spectral parameters by simultaneously optimizing four objective functions: maximizing the output SINR, minimizing two separate Cramer-Rao bounds (CRBs) on the normalized spatial and temporal frequencies, and minimizing the trace of the CRB matrix on the target-scattering coefficient estimations. We present several numerical examples to demonstrate the achieved performance improvement due to the adaptive waveform design.

Variable Step-Size Affine Projection Sign Algorithm

Abstract: This brief proposes a novel variable step-size affine projection sign algorithm (APSA), which is characterized by its robustness against impulsive noises. To obtain a step size reasonably, the proposed algorithm investigates the mean-square deviation (MSD) of APSA. Because it is impossible to accurately compute the MSD of APSA, the proposed algorithm derives the upper bound of the MSD using the upper bound of the L1-norm of the measurement noise. The optimal step size is calculated at each iteration by minimizing the upper bound of the MSD, which improves the filter performance, with respect to the convergence rate and the steady-state estimation error. The simulation results demonstrate that the proposed algorithm improves the filter performance in a system-identification scenario in the presence of impulsive noises.

Area-Delay-Power Efficient Fixed-Point LMS Adaptive Filter With Low Adaptation-Delay

Abstract: In this paper, we present an efficient architecture for the implementation of a delayed least mean square adaptive filter. For achieving lower adaptation-delay and area-delay-power efficient implementation, we use a novel partial product generator and propose a strategy for optimized balanced pipelining across the time-consuming combinational blocks of the structure. From synthesis results, we find that the proposed design offers nearly 17% less area-delay product (ADP) and nearly 14% less energy-delay product (EDP) than the best of the existing systolic structures, on average, for filter lengths N=8, 16, and 32. We propose an efficient fixed-point implementation scheme of the proposed architecture, and derive the expression for steady-state error. We show that the steady-state mean squared error obtained from the analytical result matches with the simulation result. Moreover, we have proposed a bit-level pruning of the proposed architecture, which provides nearly 20% saving in ADP and 9% saving in EDP over the proposed structure before pruning without noticeable degradation of steady-state-error performance.

Filter chains with associated multipath views for exploring large data sets

Abstract: A multipath explorer may allow a user to quickly visualize an entire population of data hierarchically in a tree-like structure. For example, a user can select a first filter to be applied to a data set, and the multipath explorer can display data in the data set that satisfies the first filter requirements and data in the data set that does not satisfy the first filter requirements. A second filter can be applied to the data in the data set, and the multipath explorer can display data in the data set that satisfies the first and second filter requirements, data in the data set that satisfies the first filter requirements and not the second filter requirements, data in the data set that satisfies the second filter requirements and not the first filter requirements, and data in the data set that does not satisfy the first or second filter requirements.