Monopulse Resolution of Interferometric Ambiguities

Ambiguities in interferometers with high angular accuracy must be resolved to achieve a practical system design. A new technique for ambiguity resolution is described and is based on monopulse circuitry used with the interferometric elements. The overall angular accuracy of the system is achieved by the interferometer; the angular accuracy of the monopulse subsystem is used to resolve interferometric ambiguities. An expression for the probability of correct ambiguity resolution is derived as a function of element size and monopulse accuracy which indicates that high probability of ambiguity resolution results when the size of the interferometric elements are a fraction of the interferometric baseline. Finally, a comparison between conventional monopulse and interferometric system designs is made for the three principal parameters, signal sensitivity, angular accuracy, and field of view, that dictate the appropriate choice for a particular application. Interferometric systems are more appropriate than monopulse systems for those applications in which angular accuracy and field of view are more important than signal sensitivity.     

Synthetic Aperture Radar

The general theory of side-looking synthetic aperture radar systems is developed. A simple circuit-theory model is developed; the geometry of the system determines the nature of the prefilter and the receiver (or processor) is the postfilter. The complex distributed reflectivity density appears as the input, and receiver noise is first considered as the interference which limits performance. Analysis and optimization are carried out for three performance criteria (resolution, signal-to-noise ratio, and least squares estimation of the target field). The optimum synthetic aperture length is derived in terms of the noise level and average transmitted power. Range-Doppler ambiguity limitations and optical processing are discussed briefly. The synthetic aperture concept for rotating target fields is described. It is observed that, for a physical aperture, a side-looking radar, and a rotating target field, the azimuth resolution is ?/? where ? is the change in aspect angle over which the target field is viewed, The effects of phase errors on azimuth resolution are derived in terms of the power density spectrum of the derivative of the phase errors and the performance in the absence of phase errors.     

一种稀疏阵列下的二维DOA估计方法

研究了稀疏阵列下二维波达方向（DOA）的估计问题,提出一种基于不动点迭代的空间谱估计（FPC-MUSIC）算法。首先建立基于矩阵填充的DOA估计信号模型,并验证该信号模型满足零空间性质（NSP）,其次通过不动点迭代算法将稀疏阵列信号恢复为完整信号,最后利用恢复信号估计二维DOA。该算法可在稀疏阵列下大幅度降低谱估计平均副瓣,在大幅度降低阵元数的同时具有较高的估计精度。计算机仿真表明：FPC-MUSIC算法可在稀疏阵列下准确估计二维DOA,验证了该算法的有效性和优越性。     

Relative positioning of multiple moving platforms using GPS

To obtain subdecimeter level accuracy in relative kinematic positioning, the use of double differenced GPS carrier phase measurement with carrier phase ambiguities fixed to their correct integer values must be adopted. If multiple platforms are available in the configuration, the redundancy provided by the multiplicity of platforms can speed up the time to integer ambiguity fixing while at the same time improve the reliability of the solution. An approach to effectively construct ambiguity constraints through the multiplicity of platforms is presented herein. The use of these ambiguity constraints to position multiple moving platforms with respect to each other is then discussed. A series of simulations and field tests are designed and conducted to investigate the effects of different system parameters on this approach, with a configuration of up to 10 moving platforms. The test results show that the use of ambiguity constraints can improve the time to integer ambiguity fixing by up to 67%, relative to the case when no constraints are used. In addition, the use of ambiguity constraints is found to enhance the ability of the multiple platform system to detect wrong ambiguity fixes.     

Design of a practical tracking algorithm with radar measurements

The extended Kalman filter (EKF) has been widely used as a nonlinear filtering method for radar tracking problems. However, it has been found that if cross-range measurement errors of the target position are large, the performance of the conventional EKF degrades considerably due to nonnegligible nonlinear effects. A new filtering algorithm for improving the tracking performance with radar measurements is developed based on the fact that correct evaluation of the measurement error covariance is possible in the Cartesian coordinate system. The proposed algorithm may be viewed as a modification of the EKF in which the variance of the range measurement errors is evaluated in an adaptive manner. The filter structure facilitates the incorporation of the sequential measurement processing scheme, and this makes the resulting algorithm favorable to both estimation accuracy and computational efficiency. Computer simulation results show that the proposed method offers superior performance in comparison to previous methods. Moreover, our developed algorithm provides some useful insight into the radar tracking problem     

Interferometer Design for Elevation Angle Estimation

Radars that are developed for the purpose of monitoring aircraft landings in the terminal air traffic control system can be designed to exploit the relatively high signal-to-noise ratio that characterizes the power budgets calculated for such a link. An interferometer using a pair of low gain antennas can be used to obtain passive coverage over a targe azimuth and elevation sector. A large baseline can be used to obtain the desired elevation angle estimation accuracy. In this paper an optimal tradeoff between the width of the subarray aperture and the width of the interferometer baseline is performed that achieves a specified elevation angle estimation error while minimizing the overall height of the interferometer configuration. The algorithm searches through the class of antenna patterns that can be synthesized from so-called finite impulse response, linear phase digital filters. For the specific problem of designing an elevation sensor for monitoring landing aircraft on final approach, the elevation angle can be estimated with no more than 1-mrad rms error when the aircraft is within ± 60° azimuth, 2.5° to 40° elevation, using two 7-wavelength subarray antennas spaced 8 wave-lengths apart. The design of a separate sensor for resolving the interferometer ambiguities is formulated as a hypothesis testing problem and solved using statistical decision theory. A bound on the probability of an ambiguity error is derived that accounts for the effects of ground reflection multipath and receiver noise.     

短基线动态相对定位中GPS单历元解算整周模糊度方法

针对短基线动态相对定位中快速解算整周模糊度的难题，提出了一种新的方法——GPS单历元解算整周模糊度。文中对相关的观测方程、载波相位的观测精度、真假解的识别等问题进行了详细讨论。试验证明，该方法正确、可靠，解决了快速解算整周模糊度这个难题，克服了传统方法需要进行静态初始化等问题。将该方法应用在车辆、舰船等移动载体上，可以实现真正意义上的实时动态相对定位，具有重要的应用价值。     

基于自适应遗传算法的DGPS整周模糊度快速解算

 鉴于遗传算法(GA)所具有的全局搜索特性,也为了更快速准确地解算差分全球定位系统(DGPS)整周模糊度,将自适应遗传算法(AGA)引入DGPS整周模糊度的搜索中。首先根据全球定位系统(GPS)载波相位双差方程求解出双差整周模糊度的浮点解,并以基线长度作为约束条件确定整周模糊度的搜索范围;然后利用白化滤波的方法对整周模糊度进行降相关处理,降低整周模糊度各分量之间的相关性;最后将自适应遗传算法应用在整周模糊度的解算过程中,搜索整周模糊度的最优解。仿真计算结果表明,与LAMBDA算法和简单遗传算法相比,自适应遗传算法能够快速地求解整周模糊度,也具有较好的可靠性和鲁棒性。     

Dimension reduction for array processing with robust interference cancellation

We present a robust solution for data reduction in array processing. The purpose is to reduce the computation and improve the performance of applied signal processing algorithms by mapping the data into a lower dimension beamspace (BS) through a transformation. Nulls steering to interference are incorporated into a transformation using the subspace projection technique, and the BS spatial spectrum estimation accuracy is evaluated and maximized with a measure. The derived transformation tries to preserve the full-dimension Cramer-Rao bounds (CRBs) for the parameters of interest while rejecting undesired signals effectively. When compared with an optimal method and an adaptive approach, simulation results show that significant improvements are obtained in terms of BS direction-of-arrival (DOA) estimation root-mean-squared error (RMSE), bias, and resolution probability.     

Performance improvement for constellation SAR using signal processing techniques

A new concept of spaceborne synthetic aperture radar (SAR) implementation has recently been proposed - the constellation of small spaceborne SAR systems. In this implementation, several formation-flying small satellites cooperate to perform multiple space missions. We investigate the possibility to produce high-resolution wide-area SAR images and fine ground moving-target indicator (GMTI) performance with constellation of small spaceborne SAR systems. In particular, we focus on the problems introduced by this particular SAR system, such as Doppler ambiguities, high sparseness of the satellite array, and array element errors. A space-time adaptive processing (STAP) approach combined with conventional SAR imaging algorithms is proposed which can solve these problems to some extent. The main idea of the approach is to use a STAP-based method to properly overcome the aliasing effect caused by the lower pulse-repetition frequency (PRF) and thereby retrieve the unambiguous azimuth wide (full) spectrum signals from the received echoes. Following this operation, conventional SAR data processing tools can be applied to focus the SAR images fully. The proposed approach can simultaneously achieve both high-resolution SAR mapping of wide ground scenes and GMTI with high efficiency. To obtain array element errors, an array auto-calibration technique is proposed to estimate them based on the angular and Doppler ambiguity analysis of the clutter echo. The optimizing of satellite formations is also analyzed, and a platform velocity/PRF criterion for array configurations is presented. An approach is given to make it possible that almost any given sparse array configuration can satisfy the criterion by slightly adjusting the PRF. Simulated results are presented to verify the effectiveness of the proposed approaches.     

Multipath mitigation method based on Gaussian mixture model in RF relative measurement

Radio Frequency (RF) technology represents a high-precision relative navigation solution that has significant potential for application to earth-orbiting satellites. In precision applications, multipath errors dominate the total error because observables, which are used to estimate carrier-phase integer ambiguity, are not always subject to a Gaussian distribution when dual-frequency ambiguity estimation methods are used in the presence of multipath. As it has been shown that ranging observables obey a Gaussian mixture distribution, this study proposes improvements to the accuracy of estimation based on multipath mitigation founded on the Gaussian mixture model. To this end, such a model is created for integer ambiguity resolution in the presence of multipath, using which the theoretical error in dual-frequency ambiguity estimation is derived. Expectation Maximization (EM), which aids dual-frequency ambiguity estimation, is subsequently proposed to reduce the effect of multipath errors. Finally, two experimental scenarios are implemented to test the performance of the proposed method. The results show that EM-aided dual-frequency ambiguity estimation reduces the range error to approximately 20% in comparison with simple dual-frequency ambiguity estimation. Therefore the proposed technique is effective for multipath mitigation in RF relative measurement.     

多峰值信号的伪码相位估计法

 考虑到多峰值信号的出现以及传统相位估计法的不足与缺陷, 特别是针对传统方法无法提取多峰值信号主峰的不足,以及在非整数采样条件时相位误差估计的较大缺陷,提出了一种提高多峰值信号伪码相位精度的估计方法。首先通过频域提取处理去除副峰引发的模糊性,达到提取主峰的目的;然后建立了插值方程,从而提高相位估计精度。在此基础上进行了验证与评估,结果表明,此估计法可以正确提取多峰值信号的主峰,相对于传统方法而言,相位估计精度明显提高。     

Omega Lane Ambiguity Resolution Using Methods of Statistical Decision Theory

Lane ambiguity is an inherent problem of navigation systems using phase measurements. A lane ambiguity resolution technique combining methods of hyperbolic and range-range modes of navigation has been developed. The basis of this approach is that the ensemble of received phases at any location forms a unique set and therefore the lane resolution problem reduces to finding a position such that the expected set of phases (or the phase predicted for the position of the navigator) matches the received set. This method of lane resolution is not constrained by lane widths and using the phase data of 10.2, 13.6, and 11? kHz; lane resolution has been accomplished for distances of up to 120 nmi. This method of lane resolution requires phase data from at least four stations at any frequency and is very sensitive to uncompensated propagation phase shifts.     

Sensitivity analysis of the maximum likelihood direction-findingalgorithm

A first-order analysis is performed of the sensitivity of the maximum likelihood (ML) direction-finding algorithm to system errors which cause differences between the array manifold used by the algorithm and the true array manifold. The effect of such errors on the directions-of-arrival (DOA) estimates is investigated. The ability of the ML algorithm to resolve two closely spaced sources in the presence of phase and gain errors in the array elements or in the receivers, or errors in the element locations, is analyzed. A formula for computing the failure threshold of the algorithm as a function of source separation and other system parameters is derived and tested by simulation. The analysis assumes that the exact covariance matrix of array element outputs is known     

Bearing Ambiguity and Resolution in Interference Direction Finders

Radio direction finders based on the principles of interference measurement provide increased angular resolution as the number of bearing ambiguities increase. In spite of the diversity of interference direction finder design, the resolution of bearing ambiguities reduces to a simple relative phase measurement on crossed baselines less than ?/2 long. This principle is applied in a review of current interference direction finder (DF) designs from the Adcock to the multiwavelength interferometer including both analog and digital bearing computation and display. Analysis shows that simple digital logic circuits may be used to resolve bearing ambiguities in multichannel DF rather than the "sense" displays of conventional analog design. This technique has the advantage of keeping direction finding and sense finding functions simultaneous but separate so that the DF information is not degraded by the injection of the ambiguity resolving sense signal.     

非球面镜检测误差的逆向求解法

应用误差理论以及其在数据处理中的方法,根据具体的非球面加工中系统误差与随机误差的存在情况,分析影响精度的实际因素,采用误差消除的逆向求解思想,建立正确的数学模型,进行科学计算得出消除测量误差后的测量数据,正确地把握误差大小的方向,可指导非球面加工的有序进行,以得到理想的非球面面形。     

Resolution of a 2π ambiguity problem in multiple frequencyspectral estimation

An algorithm is proposed to resolve a fundamental 2π ambiguity problem occurring in multiple frequency spectral estimation. Given M frequencies f_m, and I separate frequency estimators with unambiguous bandwidths F_i, the ambiguity problem can be stated as solving for the fm, given the estimator outputs, α_mi, (1⩽m⩽M;1⩽i⩽I) where f_m=α_mi+K_miF_i and K_mi is some integer. The proposed algorithm exhaustively resolves all possible α_mi groupings into single frequency values using a noise insensitive technique that exchanges system bandwidth for noise protection. The correct multiple frequencies are then defined as the single frequencies that repeat a specified number of times. A complete analysis is included     

Ambiguity Resolution for Satellite Doppler Positioning Systems

The implementation of satellite-based Doppler positioning systems frequently requires the recovery of transmitter position from a single pass of Doppler data. The least-squares approach to the problem yieds conjugate solutions on either side of the satellite subtrack. It is important to develop a procedure for choosing the proper solution which is correct in a high percentage of cases. A test for ambiguity resolution which is the most powerful in the sense that it maximizes the probability of a correct decision is derived. When systematic error sources are properly included in the least-squares reduction process to yield an optimal solution the test reduces to choosing the solution which provides the smaller valuation of the least-squares loss function. When systematic error sources are ignored in the least-squares reduction, the most powerful test is a quadratic form compasison with the weighting matrix of the quadratic form obtained by computing the pseudoinverse of a reduced-rank square matrix. A formula for computing the power of the most powerful test is provided. Numerical examples are included in which the power of the test is computed for situations that are relevant to the design of a satellite-aided search and rescue system.     

Correlation analysis of PCB and comparison of test-analysis model reduction methods

The validity of correlation analysis between finite element model（FEM） and modal test data is strongly affected by three factors, i.e., quality of excitation and measurement points in modal test,FEM reduction methods, and correlation check techniques. A new criterion based on modified mode participation（MMP） for choosing the best excitation point is presented. Comparison between this new criterion and mode participation（MP） criterion is made by using Case 1 with a simple printed circuit board（PCB）. The result indicates that this new criterion produces better results. In Case 2, 35 measurement points are selected to perform modal test and correlation analysis while 9 selected in Case 3.System equivalent reduction expansion process（SEREP）, modal assurance criteria（MAC）, coordinate modal assurance criteria（CoMAC）, pseudo orthogonality check（POC） and coordinate orthogonality check（CORTHOG） are used to show the error introduced by modal test in Cases 2 and 3. Case 2 shows that additional errors which cannot be identified by using CoMAC can be found by using CORTHOG.In both Cases 2 and 3, Guyan reduction, improved reduced system（IRS） method, SEREP and Hybrid reduction are compared for accuracy and robustness. The results suggest that the quality of the reduction process is problem dependent. However, the IRS method is an improvement over the Guyan reduction, and the Hybrid reduction is an improvement over the SEREP reduction.     

SAR resolution in the presence of phase errors

The author analyzes the effects of phase errors on synthetic aperture radar (SAR). The theory is applied to the following question: how does the achievable resolution vary with the carrier frequency when optimum quadratic focus and/or optimum processing interval (synthetic aperture length) are used? Numerous related results are given, so that much of the material is tutorial. For phase errors corresponding to uncompensated motion, the best achievable RMS resolution with any phase error spectrum satisfies the derived equation. For motion-induced phase errors it is seen that resolution improves with increasing carrier frequency when the first term in the expression applies (e.g. for phase errors concentrated at low frequencies) and resolution is independent of carrier frequency when R δ/v/v is the smaller term (e.g. with broad band or high frequency phase errors)