Minimum Variance Distortionless Response Research Articles

Can all variations within the unified mask-based beamformer framework achieve identical peak extraction performance?

This study investigates mask-based beamformers (BFs), which estimate filters for target sound extraction (TSE) using time-frequency masks. Although multiple mask-based BFs have been proposed, no consensus has been reached on which one offers the best target-extraction performance. Previously, we found that maximum signal-to-noise ratio and minimum mean square error (MSE) BFs can achieve the same extraction performance as the theoretical upper-bound performance, with each BF containing a different optimal mask. However, two issues remained unsolved: only two BFs were covered, excluding the minimum variance distortionless response BF; and ideal scaling (IS) was employed to ideally adjust the output scale, which is not applicable to realistic scenarios. To address these issues, this study proposes a unified framework for mask-based BFs comprising two processes: filter estimation that can cover all possible BFs and scaling applicable to realistic scenarios by employing a mask to generate a scaling reference. Based on the operators and covariance matrices used in BF formulas, all possible BFs can be classified into 12 variations, including two new ones. Optimal masks for both processes are obtained by minimizing the MSE between the target and BF output. The experimental results using the CHiME-4 dataset suggested that 1) all 12 variations can achieve the theoretical upper-bound performance, and 2) mask-based scaling can behave like IS, even when constraining the temporal mean of a non-negative mask to one. These results can be explained by considering the practical parameter count of the masks. These findings contribute to 1) designing a TSE system, 2) improving scaling accuracy through mask-based scaling, and 3) estimating the extraction performance of a BF.

Corrosion Monitoring in Automotive Lap Joints Based on Imaging Methods of Lamb Waves.

Corrosion damage presents significant challenges to the safety and reliability of connected vehicles. However, traditional non-destructive methods often fall short when applied to complex automotive structures, such as bolted lap joints. To address this limitation, this study introduces a novel corrosion monitoring approach using Lamb wave-based weighted fusion imaging methods. First, the Minimum Variance Distortionless Response (MVDR) is utilized to process Lamb wave signals collected under bolt-loosening and bolt-tightening conditions to image the bolt locations. Second, based on the identified bolt positions, the weighted Reconstruction Algorithm for Probabilistic Inspection of Damage (RAPID) is applied to the Lamb wave signals acquired before and after corrosion, enabling precise imaging of the actual positions of the corroded bolts. Experiments are conducted on three-bolt lap joints in cases of single-corrosion and two-corrosion using A0 mode Lamb waves and piezoelectric sensor networks. The results demonstrate that the proposed method effectively images multiple types of damage and achieves maximum location deviations of 7.43 mm. This approach enables precise and visual multi-damage assessment, particularly in hard-to-access regions. When integrated with V2X-enabled (Vehicle-to-Everything) systems, the method offers potential for incorporation into automotive structural health monitoring systems for remote diagnosis in complex structures, thereby enhancing monitoring efficiency and accuracy.

Detecting flying objects in synthetic aperture radar images using Moving Target Indicator methods

AbstractThe growing proliferation of synthetic aperture radar (SAR) sensors brings the tantalising prospect of extending their utility into ‘novel’ applications. One potential extension is the detection of fast moving and accelerating flying objects in SAR imagery. However, since SAR image formation typically assumes the scene to be static over the coherent processing interval, moving objects give rise to blurred point spread functions, significant range migration and even potential aliasing of target signatures. The result is reduced target to clutter ratio (TCR) and poor detection performance. Successful detection of airborne targets thus requires compensation for potentially large target acceleration and velocity values observed over the comparatively long dwell times typical of practical SAR collection paradigms. This paper considers this problem and presents two main ideas to achieve this goal: a carefully constructed Moving Target Indicator (MTI) detection method implemented using real‐world Ingara SAR data, and a theoretical ground clutter suppression method. The MTI detection method combines several well‐known techniques for the flying target detection problem: interferometric processing, clutter suppression, and autofocus, and provides an extended acceleration phase compensation technique for highly accelerating targets such as planes. This proposed processing pipeline has been applied to experimental data of a plane during take off (a challenging Doppler unambiguous moving target), with the goal of continued detecting and tracking of this target. A generalised SAR signal model is presented that parameterises a flying moving target signature in terms of range and azimuthal target velocities and accelerations. Data driven approaches for estimating these motion parameters are examined and applied to experimental data acquired with the Ingara SAR sensor. The detection method was found to improve TCR by around 6 dB, along with superior detection and tracking performance. Following this, a theoretical study into suppressing ground clutter via multi‐channel cross‐track interferometry is investigated. Three separate ground clutter suppression methods, coherent subtraction, conventional beamforming, and minimum variance distortionless response (MVDR) beamformer, are presented then analysed using stochastic simulations. The MVDR adaptive beamformer method was found to provide the best performance for the scenario simulated.

A novel damage localization method of Circular Phased Array using Minimum Variance Distortionless Response Beamforming with Autocorrelation Matrix Diagonal Loading

Damage localization methods based on Acoustic Emission (AE) can be classified into time-based and waveform-based. However, the former requires a large number of sensors while the latter is limited to 2D plane localization. In order to address the challenge of achieving more accurate 3D localization using a reduced number of sensors, this paper proposes a Circular Phased Array using Minimum Variance Distortionless Response (MVDR) Beamforming with Autocorrelation Matrix Diagonal Loading (AMDL) method. Firstly, a sparse circular array is utilized to form multiple beamforming for coherent shear wave signals, decomposing the original 3D localization problem into Direction Of Arrival (DOA) estimation. Secondly, azimuth angle, elevation angle and autocorrelation matrix diagonal loading methods are introduced, working in conjunction with the MVDR beamforming algorithm. Finally, spatial integration is performed through matrix decomposition to solve geometric overdetermined equations. The effectiveness of the proposed method is validated through numerical simulations and experimental verifications under various damage conditions. Results indicate that estimation errors for azimuth and elevation angles are both less than 2 %, while 3D damage source localization errors remain within a range of less than 3 %. This proposed method extends beamforming technology from 2D plane localization to 3D localization, significantly reducing the complexity of sensor arrangement and lowering the cost of structural health monitoring systems by utilizing a small number of sensors.

An enhanced beamsteering algorithm based on MVDR for a multi-channel parametric array loudspeaker array

A multi-channel parametric array loudspeaker (PAL) array can steer an audio beam using a digital signal processing technique. However, it faces the challenge posed by grating lobes in the ultrasonic radiation pattern, which leads to unwanted sidelobes in the steering audio beam when the Nyquist criterion is not satisfied due to short ultrasonic wavelengths. As a result, the audio beam not only fails to steer in the desired direction but also loses its inherent advantage of high directivity when using a beamsteer with a delay-and-sum (DAS) structure. This work proposes an enhanced beamsteering algorithm to suppress the sidelobes by optimizing the channel weight coefficients. The nonlinear optimization problem is transformed into a linear expression, making the minimum-variance-distortionless-response (MVDR) algorithm applicable. Both simulations and experiments validate the effective suppression of sidelobes and the mitigation of sound fuzziness within the range from the sidelobe to the mainlobe. The audio beam successfully steers in the desired direction and maintains a high directivity. However, the performance of the algorithm deteriorates at high audio frequencies due to the inherent physical limitations of wave interference in sound field control strategies.

Robust adaptive beamforming for cylindrical uniform conformal arrays based on low-rank covariance matrix reconstruction

Recently, conformal arrays have attracted considerable interest because such arrays can provide reduced radar cross-section and increased angle coverage. In this article, we devise a robust adaptive beamforming (RAB) approach using cylindrical uniform conformal array (CUCA). Firstly, we derive the minimum variance distortionless response (MVDR) beamformer for the CUCA by utilizing the noise subspace of interference covariance matrix (ICM) and steering vector (SV) of the signal-of-interest (SOI). Subsequently, the ICM is reconstructed by estimating the noise-free covariance matrix of the CUCA outputs and the interference projection matrix. Specifically, the noise-free covariance matrix can be regarded as multiple low-rank covariance matrices, and each low-rank matrix is reconstructed by formulating a nuclear norm minimization (NNM) problem. With the reconstructed covariance matrix, the 2-D DOAs of sources are determined by employing 2-D MUSIC spectrum to form the interference projection matrix. In addition, the SOI SV is estimated by solving a quadratically constrained quadratic programming (QCQP) problem. Numerical results demonstrate that the proposed approach is obviously superior to the existing RAB techniques.

Enhancing efficiency in spaceborne phased array systems: MVDR algorithm and FPGA integration

Digital Beamforming (DBF) has garnered significant attention within the space community, driven by the heightened flexibility offered by satellites equipped with active antennas for diverse applications like spaceborne synthetic aperture radar (SAR) systems and communication services. This paper presents a comprehensive exploration encompassing analysis, design, and implementation of a Minimum Variance Distortionless Response (MVDR) algorithm tailored for application in a Digital Beamforming Receiver system. The described system leverages the capabilities of the high-speed Analog to Digital Converter (ADC) device EV12AQ600, space-qualified, and the high-performance FPGA XCKU085. These components are seamlessly integrated into the EV12AQ60X-ADX-EVM evaluation board, thoughtfully provided by Teledyne e2v Semiconductors. The design methodology outlined herein is driven by the overarching objective to minimize FPGA resource utilization and power consumption for spaceborne phased array systems. This objective is chiefly met through the implementation of a systolic array structure adept at processing both real and complex input samples. This innovative approach results in a substantial reduction in allocated resources compared to conventional architectures. Furthermore, the design incorporates the use of the CORDIC algorithm to compute the inverse of the correlation matrix, obviating the need for square root and division operations. This strategic utilization of algorithms enhances the system's efficiency in terms of resource utilization, computational load, and processing time. To validate the anticipated behavior of the adaptive beamforming system, various radio frequency (RF) input signals are applied to the system, which is physically instantiated on the EV12AQ60X-ADX-EVM evaluation board. The experimental results affirm the efficacy of the proposed design, underscoring its suitability for spaceborne applications.

MVDR Algorithm Based on Loading Factor and Sample Selection Strategy

The MVDR (Minimum Variance Distortionless Response) algorithm is a classic Wiener filtering method used for beamforming in array signal processing. In a one-dimensional linear array high-frequency ground wave radar system, it can be employed to suppress various types of ionospheric clutter. A key step in suppression is the use of maximum likelihood estimation (MLE) to estimate the ionospheric clutter covariance matrix. However, MLE typically assumes that samples are independently and identically distributed (i.i.d.). Traditional MVDR algorithms estimate the clutter covariance matrix using all samples, which may not satisfy the i.i.d. condition. Therefore, this paper proposes a new sample selection strategy that utilizes the Mahalanobis distance method to select samples. Meanwhile, due to the very small numerical values of the ionospheric clutter covariance matrix, even if the matrix is full-rank, numerical instability may occur during inversion. To address this issue, the paper introduces 4 different forms of regularization factors. Empirical data demonstrate that the proposed new method offers better suppression of ionospheric clutter compared to the traditional MVDR algorithm.

Iteratively Refined Multi-Channel Speech Separation

The combination of neural networks and beamforming has proven very effective in multi-channel speech separation, but its performance faces a challenge in complex environments. In this paper, an iteratively refined multi-channel speech separation method is proposed to meet this challenge. The proposed method is composed of initial separation and iterative separation. In the initial separation, a time–frequency domain dual-path recurrent neural network (TFDPRNN), minimum variance distortionless response (MVDR) beamformer, and post-separation are cascaded to obtain the first additional input in the iterative separation process. In iterative separation, the MVDR beamformer and post-separation are iteratively used, where the output of the MVDR beamformer is used as an additional input to the post-separation network and the final output comes from the post-separation module. This iteration of the beamformer and post-separation is fully employed for promoting their optimization, which ultimately improves the overall performance. Experiments on the spatialized version of the WSJ0-2mix corpus showed that our proposed method achieved a signal-to-distortion ratio (SDR) improvement of 24.17 dB, which was significantly better than the current popular methods. In addition, the method also achieved an SDR of 20.2 dB on joint separation and dereverberation tasks. These results indicate our method’s effectiveness and significance in the multi-channel speech separation field.

Improved method for drone sound event detection system aiming at the impact of background noise and angle deviation

Drones pose a hidden threat to public safety, and effective and accurate detection technology for the drone that exist in the environment is imminent, in which how to weaken the influence of target sound source localization deviation and strong background interference noise on the detection task is the key to improve the accuracy of drone sound event detection. In this paper, a method has been proposed to improve the accuracy of drone acoustic event detection, named as the linear shrinkage-subspace projection-power spectral density filter method (LSP). This method mainly including covariance matrix reconstruction, steering vector recalibration, and filter coefficient redesign method. Firstly, based on Minimum Variance Distortionless Response, the linear shrinkage method is used to suppress the interference and noise components in the signal plus interference covariance matrix, and the sample covariance matrix is reconstructed to eliminate background interference noise. Then, the correlation between the steering vector and the eigenvector is used to eliminate the angle correlation term, and the subspace projection method is combined to recalibrate the steering vector, so as to improve the ability of the beamforming method to resist the angle deviation and realize the correction of the target source positioning deviation. Next, a redesign method for wiener filter coefficients based on the estimated power spectral density is used to further weaken background interference noise. In order to verify the accuracy of the proposed method, a complete drone sound event detection system is constructed by combining the deep learning drone sound event detection classifier, and the evaluation is carried out according to different angular deviations and interference sound distances. In addition, a new evaluation criterion is proposed, named as the Machine-Human Extreme Hearing Distance Rate (MHDR), which analogizes the system's detection ability with the ear's auditory detection ability. The research results of this article indicate that the detection accuracy of the detection system shows satisfactory accuracy when the proposed method is applied to circular microphone array, that improved by 15.12 % compared to existing methods. The proposed method improves the detection accuracy of the drone acoustic event detection task under the influence of sound source position deviation and strong background speech interference, and provides a reference for the development of anti-drone technology.

Speech emotion recognition in real static and dynamic human-robot interaction scenarios

The use of speech-based solutions is an appealing alternative to communicate in human-robot interaction (HRI). An important challenge in this area is processing distant speech which is often noisy, and affected by reverberation and time-varying acoustic channels. It is important to investigate effective speech solutions, especially in dynamic environments where the robots and the users move, changing the distance and orientation between a speaker and the microphone. This paper addresses this problem in the context of speech emotion recognition (SER), which is an important task to understand the intention of the message and the underlying mental state of the user. We propose a novel setup with a PR2 robot that moves as target speech and ambient noise are simultaneously recorded. Our study not only analyzes the detrimental effect of distance speech in this dynamic robot-user setting for speech emotion recognition but also provides solutions to attenuate its effect. We evaluate the use of two beamforming schemes to spatially filter the speech signal using either delay-and-sum (D&S) or minimum variance distortionless response (MVDR). We consider the original training speech recorded in controlled situations, and simulated conditions where the training utterances are processed to simulate the target acoustic environment. We consider the case where the robot is moving (dynamic case) and not moving (static case). For speech emotion recognition, we explore two state-of-the-art classifiers using hand-crafted features implemented with the ladder network strategy and learned features implemented with the wav2vec 2.0 feature representation. MVDR led to a signal-to-noise ratio higher than the basic D&S method. However, both approaches provided very similar average concordance correlation coefficient (CCC) improvements equal to 116 % with the HRI subsets using the ladder network trained with the original MSP-Podcast training utterances. For the wav2vec 2.0-based model, only D&S led to improvements. Surprisingly, the static and dynamic HRI testing subsets resulted in a similar average concordance correlation coefficient. Finally, simulating the acoustic environment in the training dataset provided the highest average concordance correlation coefficient scores with the HRI subsets that are just 29 % and 22 % lower than those obtained with the original training/testing utterances, with ladder network and wav2vec 2.0, respectively.

Improving the Accuracy of Direction of Arrival Estimation with Multiple Signal Inputs Using Deep Learning.

In this paper, an innovative cyclic noise reduction method and an improved CAPON algorithm (also the called minimum variance distortionless response (MVDR) algorithm) are proposed to improve the accuracy and reliability of DOA (direction of arrival) estimation. By processing the eigenvalues obtained from the covariance matrix of the received signal, the signal-to-noise ratio (SNR) can be increased by up to 5 dB by the cyclic noise reduction method, which will improve the DOA estimation accuracy. The improved CAPON algorithm has a convolution neural network (CNN) structure, whose input is the processed covariance matrix of the received signal, and the CAPON spectral value is used as the training label to obtain the estimated spatial spectrum. It retains the advantages of the CAPON algorithm, which can achieve blind source estimation, and simulations show that the proposed algorithm exhibits a better performance than the traditional algorithm in conditions of various SNRs and snapshot numbers. The simulation results show that, based on a certain SNR, the root mean square error (RMSE) of the improved CAPON algorithm can be reduced from 0.86° to 0.8° compared to traditional algorithms, and the angle estimation error can be decreased by up to about 0.3°. With the help of the cyclic noise reduction method, the angle estimation error decreases from 0.04° to 0.02°.

High-performance deep-sea long-range underwater acoustic communication: Deconvolved conventional beamforming based approach

To address the challenges posed by large propagation loss and severe multipath delay spread, while aiming to improve communication rates in long-range underwater acoustic (UWA) communication, this paper introduces a novel approach: multi-beam (MB) Orthogonal Frequency Division Multiplexing (OFDM) based on deconvolved conventional beamforming (dCv). The proposed method establishes a signal processing framework for UWA channel receivers, wherein received signals corresponding to each angle beam are isolated and concentrated using the dCv technique. Subsequently, the separated signals from each angle undergo maximal-ratio combining (MRC) channel equalization followed by demodulation. Compared to conventional single-beam (SB) processing methods, the proposed approach capitalizes on multipath diversity gain achieved by combining MB outputs originating from various arrival angles. Moreover, employing dCv processing demonstrates superior performance compared to popularly employed beamforming techniques, especially when dealing with paths arriving from closely aligned angles. Additionally, the array beamforming utilized significantly enhances the signal-to-noise ratio (SNR) of each beam output, mitigating the elevated error rates in channel estimation associated with combining low SNR signals received from individual elements. Simulation results utilizing BELLHOP and experimental data from the South China Sea showcase notably improved bit error rate (BER) performance for the proposed method compared to SB equalization, MB-MRC equalization based on conventional beamforming (CBF), minimum variance distortionless response (MVDR), and worst-case performance optimization (WCPO), as well as standard MRC equalization techniques. The proposed receiver achieves error-free decoding results at a communication distance of 80 km with a data rate of 247 bps.

Comparison of conventional and adaptive acoustic beamforming algorithms using a tetrahedral microphone array in noisy environments

In situ acoustic measurements are often plagued by interfering sound sources that occur within the measurement environment. Both adaptive and conventional beamforming algorithms, when applied to the outputs of a microphone array arranged in a tetrahedral geometry, are able to capture sound sources in desired directions and reject sound from unwanted directions. Adaptive algorithms may be able to measure a desired sound source with greater spatial precision, but require more calculations and, therefore, computational power. A conventional frequency-domain phase-shift algorithm and a modified adaptive frequency-domain Minimum Variance Distortionless Response (MVDR) algorithm were applied to simulated and recorded signals from a tetrahedral array of omnidirectional microphones. The algorithms are described mathematically and demonstrated on both deterministic and real-world sound data, to quantitatively validate and compare their performance and to provide listening examples of their outputs in a variety of acoustically replicated environments. [Work supported by Portland State University.]

A unified beamforming and source separation model for static and dynamic human-robot interaction.

This paper presents a unified model for combining beamforming and blind source separation (BSS). The validity of the model's assumptions is confirmed by recovering target speech information in noise accurately using Oracle information. Using real static human-robot interaction (HRI) data, the proposed combination of BSS with the minimum-variance distortionless response beamformer provides a greater signal-to-noise ratio (SNR) than previous parallel and cascade systems that combine BSS and beamforming. In the difficult-to-model HRI dynamic environment, the system provides a SNR gain that was 2.8 dB greater than the results obtained with the cascade combination, where the parallel combination is infeasible.

A distortionless convolution beamformer design method based on the weighted minimum mean square error for joint dereverberation and denoising

This paper designs a weighted minimum mean square error (WMMSE) based distortionless convolution beamformer (DCBF) for joint dereverberation and denoising. By effectively using WMMSE with the constraint of distortionless, a DCBF is deduced, where the outputs of the weighted prediction error (WPE) filter and the WPE-based minimum variance distortionless response (MVDR) beamformer are combined to initialize target signal for balancing signal distortion, residual reverberation and residual noise. In addition, two optimization factors are introduced to reduce the reverberation and noise when the initialized target signal is used for the solution of beamformer. As a result, the designed beamformer is presented as a linear combination of the WMMSE-based convolution beamformer (CBF) and weighted power minimization distortionless response (WPD) filter. The experimental results demonstrate the superior performance of the designed beamformer for joint dereverberation and denoising compared to the reference methods.

A Phoneme-Scale Assessment of Multichannel Speech Enhancement Algorithms.

In the intricate acoustic landscapes where speech intelligibility is challenged by noise and reverberation, multichannel speech enhancement emerges as a promising solution for individuals with hearing loss. Such algorithms are commonly evaluated at the utterance scale. However, this approach overlooks the granular acoustic nuances revealed by phoneme-specific analysis, potentially obscuring key insights into their performance. This paper presents an in-depth phoneme-scale evaluation of three state-of-the-art multichannel speech enhancement algorithms. These algorithms-filter-and-sum network, minimum variance distortionless response, and Tango-are here extensively evaluated across different noise conditions and spatial setups, employing realistic acoustic simulations with measured room impulse responses, and leveraging diversity offered by multiple microphones in a binaural hearing setup. The study emphasizes the fine-grained phoneme-scale analysis, revealing that while some phonemes like plosives are heavily impacted by environmental acoustics and challenging to deal with by the algorithms, others like nasals and sibilants see substantial improvements after enhancement. These investigations demonstrate important improvements in phoneme clarity in noisy conditions, with insights that could drive the development of more personalized and phoneme-aware hearing aid technologies. Additionally, while this study provides extensive data on the physical metrics of processed speech, these physical metrics do not necessarily imitate human perceptions of speech, and the impact of the findings presented would have to be investigated through listening tests.

Supervised AutoEncoder-Based Beamforming Approach for Satellite mmWave Communication

Beamforming is a technique commonly used in wireless communication systems to enhance the signal quality of a receiver. In this study, we compare the performance of an encoder-based beamformer with convolutional neural network (CNN) and minimum variance distortionless response (MVDR) approaches in terms of signal-to-interference-plus-noise ratio (SINR). Our results show that the encoder-based approach achieved an average SINR of 25.82 dB, while the CNN approach achieved an average SINR of 22.40 dB and the MVDR approach achieved an average SINR of 17.64 dB. The performance of the encoder-based approach was found to be superior to that of the CNN approach but much superior to that of the MVDR approach. The encoder-based approach outperformed the CNN approach by 3.42 dB and MVDR approach by 8.18 dB on average. In addition, the unique contribution of our encoder-based approach is presenting a new perspective on beamforming in mmWave communication. We further discuss its potential impact on addressing challenges related to LEO satellite systems.

Adaptive beamforming for maximum SINR in the presence of correlated interferences

The conventional steering vector (SV) based beamformers such as the minimum variance distortionless response (MVDR) can suffer from severe performance degradation due to the signal cancellation in the presence of correlated interferences. A partially correlated interference can be decomposed into two components, the coherent component and the other uncorrelated with the desired signal. The SVs of the desired signal and the coherent interference components compose the composite steering vector (CSV). In this paper, a beamforming method is presented that can achieve the maximum signal-to-interference-plus-noise ratio (SINR) via the use of the CSV and the interference covariance matrix (ICM) formed by the uncorrelated interference components only. The estimates of the CSV and the ICM are extracted from the sample matrix through oblique projections. In the estimation process, neither the interference powers nor the desired signal power is estimated, though the direction estimation is carried out using the multiple signal classification (MUSIC). We make theoretical performance analysis, which shows that the CSV based method is more effective as the correlation between the desired signal and the interferences increases and as the desired signal power becomes small. Simulation results demonstrate that it not only converges very quickly to the maximum SINR but also is robust to pointing errors.

Distortion‐less carrier phase tracking space‐time adaptive processor based on power inversion criterion for GNSS anti‐jamming receiver

AbstractSpace‐time adaptive processor (STAP) has been widely used for global navigation satellite system (GNSS) anti‐jamming receiver due to its good anti‐jamming performance. When direction of satellite is unknown, STAP can be implemented based on power inversion (PI) criterion. However, existing space‐time PI algorithm will introduce tens to hundreds of degrees biases into carrier phase, and sometimes will even cause cycle slips, which will reduce the success rate of ambiguity resolution, ultimately deteriorating positioning accuracy. A distortion‐less carrier phase tracking space‐time PI algorithm is proposed. The main novelty is that the proposed algorithm keeps the coefficients of the temporal taps as real values by imposing constraints on the weights of the antenna array. Several experiments are implemented to verify the effectiveness of the proposed algorithm. For comparison, the results of PI algorithm and minimum variance distortion‐less response (MVDR) algorithm are shown. Results show that when the number, style, and direction of interferences and the direction of GNSS signal vary, different degrees of biases are introduced into carrier phases for the PI and the MVDR algorithm. However, no bias is introduced into the proposed algorithm. As a result, the effectiveness of the proposed algorithm is verified.