Range walk and array rotation in space-time adaptive processing:effects and compensations

This paper proposes a unified clutter model incorporating the effects of range walk and array rotation for space-time adaptive processing（STAP） in airborne multi-channel early-warning radar.Based on this clutter model,STAP performance is then analyzed from the perspective of covariance matrix tapering（CMT）.For STAP performance degradation due to array rotation,a determinate compensation method is proposed based on the CMT method.Numerical examples are provided to verify the analysis and the proposed compensation method.

Direct data domain approach to space-time adaptive processing

In non-homogeneous environment, traditional space-time adaptive processing doesn＇t effectively suppress interference and detect target, because the secondary data don＇ t exactly reflect the statistical characteristic of the range cell under test. A ravel methodology utilizing the direct data domain approach to space-time adaptive processing （ STAP ） in airbome radar non-homogeneous environments is presented. The deterministic least squares adaptive signal processing technique operates on a ＂snapshot-by-snapshot＂ basis to dethrone the adaptive adaptive weights for nulling interferences and estimating signal of interest （SOI）. Furthermore, this approach eliminates the requirement for estimating the covariance through the data of neighboring range cell, which eliminates calculating the inverse of covariance, and can be implemented to operate in real-time. Simulation results illustrate the efficiency of interference suppression in non-homogeneous environment.

STATISTICAL SPACE-TIME ADAPTIVE PROCESSING ALGORITHM

For the slowly changed environment-range-dependent non-homogeneity, a new statistical space-time adaptive processing algorithm is proposed, which uses the statistical methods, such as Bayes or likelihood criterion to estimate the approximative covariance matrix in the non-homogeneous condition. According to the statistical characteristics of the space-time snapshot data, via defining the aggregate snapshot data and corresponding events, the conditional probability of the space-time snapshot data which is the effective training data is given, then the weighting coefficients are obtained for the weighting method. The theory analysis indicates that the statistical methods of the Bayes and likelihood criterion for covariance matrix estimation are more reasonable than other methods that estimate the covariance matrix with the use of training data except the detected outliers. The last simulations attest that the proposed algorithms can estimate the covariance in the non-homogeneous condition exactly and have favorable characteristics.

Diagonally loaded SMI algorithm based on inverse matrix recursion

The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.

Improved STAP algorithm based on APES

Space-time adaptive processing（STAP） has been proven to be one of the best techniques capable of detecting weak moving targets in strong clutter environment and has been widely applied in airborne ground moving target indication（GMTI） radar.This paper applies an amplitude and phase estimation（APES） approach to two aspects of the STAP algorithm.Firstly,APES is applied to accurately describe the clutter characteristic in angle-Doppler domain.Then,APES is incorporated into the standard STAP algorithm to improve its performance without increasing transmitting/receiving channel and pulse number.The experimental examples show that the detection performance can be improved by using the APES technique,as well as the high computational complexity can be avoided.

Target location with signal fitting and sub-aperture tracking for airborne multi-channel radar

The location of a moving target based on signal fitting and sub-aperture tracking from an airborne multi-channel radar is dealt with.The proposed approach is applied in two steps：first,the ambiguous slant-range velocity is derived with a modified single-snapshot multiple direction of arrival estimation method,and second,the unambiguous slant-range velocity is found using a track-based criterion.The prominent advantage of the proposed approach is that the unambiguous slant-range velocity can be very large.Besides,the first stage is carried out at the determinate range-Doppler test cell by azimuth searching for fitting best to the moving target signal,therefore,the location performance would not be sacrificed in order to suppress clutter and/or interference.The effectiveness and efficiency of the proposed method are validated with a set of airborne experimental data.

STAP method based on atomic norm minimization with array amplitude-phase error calibration

In this paper,a space-time adaptive processing(STAP)method is proposed for the airborne radar with the array amplitude-phase error considered,which is based on atomic norm minimization(ANM).In the conventional ANM-based STAP method,the influence of the array amplitude-phase error is not considered and restrained,which inevitably causes performance deterioration.To solve this problem,the array amplitude-phase error is firstly estimated.Then,by pre-estimating the array amplitude-phase error information,a modified ANM model is built,in which the array amplitude-phase error factor is separated from the clutter response and the clutter covariance matrix(CCM)to improve the estimation accuracy of the CCM.To prove that the atomic norm theory is applicable in the presence of the array amplitude-phase error,the clutter sparsity is analyzed in this paper.Meanwhile,simulation results demonstrate that the proposed method is superior to the state-of-the-art STAP method.Moreover,the measured data is used to verify the effectiveness of the proposed method.

W ideband interference suppression based on space-time filter

Based upon the diagonal loading technique and the structure of the space-time adaptive processors, a novel anti-jamming method of satellite navigation is proposed. According to matrix in- verse theorem, the range of the diagonal loading values for space-time adaptive wideband signal pro- cessing structure is deduced, and the optimum equation of diagonal loading beam forming algorithm of space-time structure is obtained. Then, by the analysis of two-dimensional oriented vector in di- rection of the perturbation interference, the wideband interference covariance matrix obtained in the weights training period is modified. Finally, the optimum weight of multi-linear constrained space- time adaptive beam-forming alogrithm is derived for anti-interference filter processing. The new method effectively widens the null steering beams tion results prove the robustness of the proposed when discrepancy happens. The computer simula- method.

IMPROVED DOPPLER WARPING METHOD FOR AIRBORNE RADAR WITH NON-SIDELOOKING ARRAY

Traditional range-dependency compensation space time adaptive processing(STAP)methods usually involve aligning the clutter spectrums in a certain point to reduce the clutter non-homogeneity.A novel compensation STAP method is proposed as an improved Doppler warping(DW)method for airborne radar with non-sidelooking radar.This method facilitates DW method to bring clutter spectrum of different range gates together in the mainlobe and subsequently compensation to accomplish space angle of different range gates alignment at multiple Doppler bins.Simulation results show that the proposed method can further reduce the clutter non-homogeneity of non-sidelooking array and significantly outperform traditional algorithms with only a little increase of the computation load.

NEW METHOD FOR REDUCED RANK STAP—NON CLUTTER CHANNEL METHOD

For reduced-rank space-time adaptive processing(STAP) in airborne radar, this paper presents a new method — non clutter channel(NCC） method which is easy to implement in real radar systems. The NCC method uses those “channels” located in the non-clutter domain to construct the reduce-rank transformation matrix. This method avoids eigen-decomposition and the computational cost is very low. The performance is compared with that of several other methods; the simulation demonstrates that the NCC method can well approach the optimum performance and even outperform some more complex methods in low rank.

Improved Multistage Wiener Filters in Nonhomogeneous Clutter Environments

A new method combining space-time preprocessing with multistage Wiener filters（STPMWF）is proposed to improve the performance of space-time adaptive processing（STAP）in nonhomogeneous clutter scenario.The new scheme only requires the data from the primary range bin,thus it can suppress discrete interferers efficiently,without calculating the inverse of covariance matrix.Comparing to the original MWF approach,the proposed scheme can be regarded as practical solutions for robust and effective STAP of nonhomogeneous radar data.The theoretical analysis shows that our STPMWF is simple in implementation and fast in convergence.The numeric results by using simulated data exhibit a good agreement with the proposed theory.

Robust two-stage reduced-dimension STAP algorithm andits performance analysis

A new two-stage reduced-dimension space-time adaptiveprocessing （STAP） approach, which combines the subcoherentprocessing interval （sub-CPI） STAP and the principalcomponent analysis （PCA）, is proposed to achieve a more enhancedconvergence measure of effectiveness （MOE）. Furthermore,in the case of the subspace leakage phenomenon, theproposed STAP method is modified to hold the fast convergenceMOE by using the covariance matrix taper （CMT） technique. Bothsimulation and real airborne radar data processing are providedto analyze the convergence MOE performance of the proposedSTAP methods. The results show the proposed method is moresuitable for the practical radar applications when compared withthe conventional sub-CPI STAP method.

Adaptive beamforming and phase bias compensation for GNSS receiver

Adaptive antenna arrays have been used to mitigate the interference on global navigation satellite system（GNSS） receivers. The performance of interference mitigation depends on the beamforming algorithms adopted by the antenna array. However,the adaptive beamforming will change the array pattern in realtime, which has the potential to introduce phase center biases into the antenna array. For precise applications, these phase biases must be mitigated or compensated because they will bring errors in code phase and carrier phase measurements. A novel adaptive beamforming algorithm is proposed firstly, then the phase bias induced by the proposed algorithm is estimated, and finally a compensation strategy is addressed. Simulations demonstrate that the proposed beamforming algorithm suppresses effectively the strong interference and improves significantly the capturing performance of GNSS signals. Simultaneously, the bias compensation method avoids the loss of the carrier phase lock and reduces the phase measurement errors for GNSS receivers.

Analysis of Moving Target Detection in Space-Surface BiSAR

Based on the geometric structure of multi-channel space-surface bistatic aperture radar（SS-BiSAR）,the time-frequency and spatial-frequency relationships of clutter and moving target are detailedly analyzed.It is found that the prepositive stationary receiver can improve the spatial separation between moving target and correspondingly competitive clutter,furthermore the processing scheme of space-time adaptive processing（STAP） in SS-BiSAR echo domain is given.Meanwhile,compared to the STAP in monostatic synthetic aperture radar（SAR）,it is firstly proved that the minimum detectable velocity in SS-BiSAR system can improve R0/R1（transmitter-to-target distance over receiver-to-target） times.Finally,the computer simulation verifies the effectiveness of the STAP processing scheme.

A NEW METHOD TO COMPENSATE CLUTTER RANGE DEPENDENCE FOR FORWARD LOOKING AIRBORNE RADARS

The clutter direction-Doppler curves are not aligned on the near range bins for forward looking airborne radar. As a result, the performance of clutter suppression by Space-Time Adaptive Processing (STAP) degrades greatly because of the clutter range dependence. To deal with this problem, a new compensated method is proposed in this paper. The method rebuilds the clutter covariance matrix based on spatial high resolution Minimum Variance Distortionless Response (MVDR) spectrum, and then finds a matrix to transform the covariance matrix of short-range gate to the referred far-range gate. The method can compensate the clutter range dependence well. The simulation results show validity of the method.

AN APPROACH TO SUPPRESS SHORT-RANGE CLUTTER FOR NON-SIDE LOOKING AIRBORNE RADAR

When the Airborne Early Warning(AEW) radar transmits medial or high Pulse Repetitive Frequency(PRF) signal,the range ambiguity occurs.The clutter of short-range clutter has serious range dependence problem for non-Side Looking Airborne Radar(non-SLAR).As a result,the clutter plus noise covariance matrix can not be estimated correctly,and the performance of clutter suppression obtained by Space-Time Adaptive Processing(STAP) degrades greatly.The uniform linear array has not elevation degrees;therefore,the short-range clutter can not be suppressed directly.A short-range clutter suppression method is proposed.The method first estimate the elevation angles of the ambiguous short-range gate,then eliminates short-range clutter by space time interpolation and adds moving target protection in the procedure.This method can suppress the short-range clutter well.Simulation results show the validity of the method.

Two-Dimensional Direction Finding via Sequential Sparse Representations

The problem of two-dimensional direction finding is approached by using a multi-layer Lshaped array. The proposed method is based on two sequential sparse representations,fulfilling respectively the estimation of elevation angles,and azimuth angles. For the estimation of elevation angles,the weighted sub-array smoothing technique for perfect data decorrelation is used to produce a covariance vector suitable for exact sparse representation,related only to the elevation angles. The estimates of elevation angles are then obtained by sparse restoration associated with this elevation angle dependent covariance vector. The estimates of elevation angles are further incorporated with weighted sub-array smoothing to yield a second covariance vector for precise sparse representation related to both elevation angles,and azimuth angles. The estimates of azimuth angles,automatically paired with the estimates of elevation angles,are finally obtained by sparse restoration associated with this latter elevation-azimuth angle related covariance vector. Simulation results are included to illustrate the performance of the proposed method.

Micro Evolutionary Processes and Adaptation

It would be well to note that in the absence of clear data about the formation of adaptation systems,or mechanisms of their occurrence,all that is recognized is the realization of the micro evolutionary processes.There is no well-defined connection between information exchange and formation

Fuzzy Stochastic Differential Equations Driven by a Fuzzy Brownian Motion

In our previous work, we study fuzzy Itôintegrals driven by a fuzzy Brownian motion. In this article, we continue this study. The purpose of this paper is to study the weak uniqueness of fuzzy stochastic differential equations taking into account fuzzy Brownian motion. For instance, we construct the fuzzy stochastic differential equation driven by a fuzzy Brownian motion. To define and prove our results, we use the fuzzification, the alpha cut method and the Hausdorff distance between two fuzzy quantities. Some results are to our credit in this article like the instance, we construct the fuzzy stochastic differrential equation driven by fuzzy Brownian motion. Furthermore, we develop fuzzy Itôcalculus driven by a fuzzy Brownian motion. Our result complement existing ones in that the fuzzy version of Brownian motion is taken into account.

Enhanced performance of triboelectric mechanical motion sensor via continuous charge supplement and adaptive signal processing

The development of automation industry is inseparable from the progress of sensing technology.As a promising self-powered sensing technology,the durability and stability of triboelectric sensor(TES)have always been inevitable challenges.Herein,a continuous charge supplement(CCS)strategy and an adaptive signal processing(ASP)method are proposed to improve the lifetime and robustness of TES.The CCS uses low friction brushes to increase the surface charge density of the dielectric,ensuring the reliability of sensing.A triboelectric mechanical motion sensor(TMMS)with CCS is designed,and its electrical signal is hardly attenuated after 1.5 million cycles after reasonable parameter optimization,which is unprecedented in linear TESs.After that,the dynamic characteristics of the CCS-TMMS are analyzed with error rates of less than 1%and 2%for displacement and velocity,respectively,and a signal-to-noise ratio of more than 35 dB.Also,the ASP used a signal conditioning circuit for impedance matching and analog-to-digital conversion to achieve a stable output of digital signals,while the integrated design and manufacture of each hardware module is achieved.Finally,an intelligent logistics transmission system(ILTS)capable of wirelessly monitoring multiple motion parameters is developed.This work is expected to contribute to automation industries such as smart factories and unmanned warehousing.