Frequency Difference Of Arrival Estimation Research Articles

Multiple Signal TDOA/FDOA Joint Estimation with Coherent Integration

Passive localization relies significantly on the estimation of the Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) to accurately determine the location of a target. The precision of TDOA and FDOA estimation is affected by signal parameters of time and frequency distribution. In case of multiple signals arising at different frequency bands and intercepted simultaneously by spatially separate sensors covering a wide frequency band, the traditional method is first to separate the signals from the mixed wideband signal through digital down conversion (DDC), which brings multiple narrowband signals, and then the estimation of TDOA and FDOA of each narrowband signal can be performed using cross ambiguity function (CAF). The paper introduces a novel approach for estimating TDOA and FDOA of multiple signals simultaneously, which employs a coherent integration method. First, the cross ambiguity function for each signal is realized with the narrowband signal as the same as the traditional method. Next, the phase relation of each CAF is analyzed, then the joint CAF can be obtained with phase compensation, from which multiple signal TDOA and FDOA estimations will be implemented simultaneously. Numerical simulations are performed to compare the two methods, and the results demonstrate the superiority of the proposed algorithm.

Fast TDOA and FDOA Estimation for Coherent Pulse Signals

Time difference of arrival (TDOA) and frequency difference of arrival (FDOA) have been widely used for localizing temporally continuous signals passively. Temporal sparsity of pulse signals makes their TDOA and FDOA estimation processes much different, and computational complexity is a major concern in this area. This paper addresses the problem of fast TDOA and FDOA estimation of pulse signals and focuses mainly on narrowband coherent pulses. By decoupling the effects of TDOA and FDOA in the cost function of localization approximately, we propose a fast coarse TDOA and FDOA estimation method. The estimates are then refined with the cross-ambiguity function (CAF) algorithm within a small TDOA and FDOA neighborhood. In the simulations, the proposed method is demonstrated to have satisfying TDOA and FDOA estimation precisions, and it exceeds existing counterparts largely in computational efficiency.

A Multi-Pulse Cross Ambiguity Function for the Wideband TDOA and FDOA to Locate an Emitter Passively

The time difference of arrival (TDOA) and frequency difference of arrival (FDOA) between two receivers are widely used to locate an emitter. Algorithms based on cross ambiguity functions can simultaneously estimate the TDOA and FDOA accurately. However, the algorithms, including the joint processing of received data, require transferring a large volume of data to a central computing unit. It can be a heavy load for the data link, especially for a wideband signal obtained at a high sampling rate. Thus, we proposed a multi-pulse cross ambiguity function (MPCAF) to compress the data before transmitting and then estimate the TDOA and FDOA with the compressed data. The MPCAF consists of two components. First, the raw data are compressed with a proposed two-dimensional compression function. Two methods to construct a reference pulse used in the two-dimensional compression function are considered: a raw data-based method constructs the pulse directly from the received signal, and a signal parameter-based method constructs it through the parameters of the received signal. Second, a wideband cross-correlation function is studied to refine the TDOA and FDOA estimates with the compressed data. The simulation and Cramer–Rao lower bound (CRLB) analyses show that the proposed method dramatically reduces the data transmission load but estimate the TDOA and FDOA well. The hardware-in-the-loop simulation confirms the method’s effectiveness.

Performance Analysis of TDOA and FDOA Estimation for Pulse Signals

Time difference of arrival (TDOA) and frequency difference of arrival (FDOA) are effective measurements for localizing emitters’ radiating pulse signals, such as radar. Temporal sparsity of pulse signals makes their TDOA and FDOA estimation precisions much different from that of continuous communication and acoustic signals. The way how the precisions are affected by various parameters, e.g., temporal duration of signals, may also deviate significantly in scenarios of pulse signals from that of continuous ones. In this paper, theoretical analyses are carried out to reveal the Cramer–Rao lower bounds (CRLBs) of TDOA and FDOA estimation precisions of pulse signals and also to obtain insights on how the CRLBs are affected by various parameters, including pulse number, signal-to-noise ratio (SNR), pulse width, and pulse repetition interval (PRI). Simulation results verify the correctness of the derived CRLBs and their variations with different parameters.

LPI Property of FDA Transmitted Signal

Frequency diverse array (FDA) produces an angle range dependent and time-varying transmit beampattern due to the small frequency increment across its array elements, which provides potential applications for secure communications and radio frequency stealth. In this article, we study the low probability of intercept (LPI) properties of FDA transmitted signals under typical passive reconnaissance techniques. First, the passive reconnaissance property of direction-of-arrival estimation for FDA transmitted signals under phase interferometry measurement is evaluated, together with the corresponding Cramér–Rao bound analysis. Second, the passive reconnaissance property of time difference of arrival and frequency difference of arrival estimation for FDA transmitted signals are also evaluated for moving platforms. Both theoretical analysis and numerical results demonstrate that FDA transmitted signal indeed achieves significantly better LPI performance than phased-array transmitted signals, which is particularly useful for military applications.

Joint TDOA and FDOA Estimation for Interleaved Pulse Trains From Multiple Pulse Radiation Sources

In this article, we address the problem of estimating with high precision the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) for interleaved pulse trains radiated from multiple sources. The pulse signal parameters of multiple sources are indistinguishable and as a result conventional de-interleaving techniques fail to separate the pulses emitted from each source. By noting that cross-correlating pulses from the same source at their true TDOA and FDOA produces consistent phases, a high-precision joint TDOA-FDOA estimator is proposed. Within the developed technique, a histogram-based clustering procedure is introduced to obtain initial TDOA and FDOA estimates. Then, an expectation maximization (EM)-based method is utilized to refine their estimates, where the unknown source labels of pulse signals are hidden variables and they are estimated together with TDOA and FDOA iteratively. Simulation results reveal the superior performance of the proposed algorithm compared to existing techniques, at the cost of moderate computational complexity increment.

TDOA/FDOA estimation algorithm of frequency‐hopping signals based on CAF coherent integration

The estimation accuracy of time difference of arrival (TDOA) and frequency difference of arrival (FDOA)is determined by the frequency and time distribution, signal energy and noise. TDOA estimation is mainly decided by frequency distribution, while FDOA estimation generally relies on time distribution. Frequency-hopping (FH) signals have broad distribution in frequency and time domains, the problem of low estimation accuracy for TDOA and FDOA of single-hop signal can be overcome through multi-hop coherent integration to improve the use of efficient bandwidth and duration. Focus on the TDOA/FDOA estimation problem of FH signals; this study proposes a high accuracy TDOA/FDOA estimation algorithm, which will conduce high precision of localisation. The cross-ambiguity function (CAF) of single-hop baseband signal is first analysed, then the CAF of each hop signal is deduced, and the phase relationship of each CAF is revealed through TDOA and FDOA dimensions. Coherent integration is realised by FDOA normalised compensation and phase compensation. The theory performances of TDOA/FDOA estimation for FH signals are derived, and the influence of the signal parameters on TDOA/FDOA estimate accuracy is indicated. Monte Carlo simulations validate that the performance of proposed coherent integration TDOA/FDOA estimation algorithm for FH signals gets greater improvements than that of single-hop signal, and the performance improvements accord with the theory analysis well.

Computationally efficient TDOA, FDOA and differential Doppler rate estimation algorithm for passive emitter localization

This paper addresses the joint time difference of arrival (TDOA), frequency difference of arrival (FDOA) and differential Doppler rate estimation problem in passive emitter localization, considering the range and Doppler frequency migrations during the observation time. A computationally efficient estimation algorithm via second-order keystone transform and Lv's distribution is proposed. This method can effectively remove two types of migrations and accomplish the parameter estimation. Cross-terms suppression ability of the proposed method is also analyzed and its characteristic indicates the applicability in the scenario of multi-targets. The whole estimation step can be fast implemented by complex multiplications, fast Fourier transform (FFT) and inverse FFT operations without any searching procedure. Extensive numerical experiments validate that with a much lower computational cost, the proposed method could achieve comparable estimation performance with the maximum likelihood estimator and outperforms the other representative algorithms.

Computationally efficient TDOA and FDOA estimation algorithm in passive emitter localisation

This study addresses the joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimation problem in passive emitter localisation, involving range migration during the observation time. A computational efficient estimation algorithm based on scaled Fourier transformation is proposed. This method can effectively remove the RM and accomplish the parameter estimation. Cross-terms suppression ability of the proposed method is also analysed and its characteristic indicates the applicability in the scenario of multi-targets. The whole estimation step can be fast implemented by complex multiplications, fast Fourier transformation (FFT) and inverse FFT without any searching process. Compared with the ideal maximum likelihood estimator via extensive numerical experiments, the proposed method can achieve comparable estimation performance and have gained more than ten thousand times reduction in the computational cost, which helps practical application.

A joint TDOA and FDOA estimation algorithm based on second-order cone programming

ABSTRACTConsidering the low estimation accuracy of the traditional interpolation method, this paper, on the basis of second-order cone programming (SOCP), proposes a novel joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimation interpolation method, which can attain the sub-sample precision. The proposed method uses several discrete samples produced by cross ambiguity function (CAF) to structure the convex optimization models with regard to the interpolation surface. Then, the SOCP is utilized to obtain the interpolation surface which matches the discrete surface of CAF well. Finally, the method achieves the precision superior to the traditional TDOA and FDOA estimation directly through the search for the maximum of the continuous approximate surface. This method decreases the computational load without loss of precision and can efficiently reduce the limitation of finite sampling interval and sampling time in estimation precision. Numerical simulations show that the method in this paper is efficient and outperforms existing interpolation algorithms about estimation precision.

Joint TDOA and FDOA Estimation: A Conditional Bound and Its Use for Optimally Weighted Localization

Modern passive emitter-location systems are often based on joint estimation of the time-difference of arrival (TDOA) and frequency-difference of arrival (FDOA) of an unknown signal at two (or more) sensors. Classical derivation of the associated Cramér-Rao bound (CRB) relies on a stochastic, stationary Gaussian signal-model, leading to a diagonal Fisher information matrix with respect to the TDOA and FDOA. This diagonality implies that (under asymptotic conditions) the respective estimation errors are uncorrelated. However, for some specific (nonstationary, non-Gaussian) signals, especially chirp-like signals, these errors can be strongly correlated. In this work we derive a “conditional” (or a “signal-specific”) CRB, modeling the signal as a deterministic unknown. Given any particular signal, our CRB reflects the possible signal-induced correlation between the TDOA and FDOA estimates. In addition to its theoretical value, we show that the resulting CRB can be used for optimal weighting of TDOA-FDOA pairs estimated over different signal-intervals, when combined for estimating the target location. Substantial improvement in the resulting localization accuracy is shown to be attainable by such weighting in a simulated operational scenario with some chirp-like target signals.

Mobile Emitter Geolocation and Tracking Using TDOA and FDOA Measurements

This paper considers recursive tracking of one mobile emitter using a sequence of time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurement pairs obtained by one pair of sensors. We consider only a single emitter without data association issues (no missed detections or false measurements). Each TDOA measurement defines a region of possible emitter locations around a unique hyperbola. This likelihood function is approximated by a Gaussian mixture, which leads to a dynamic bank of Kalman filters tracking algorithm. The FDOA measurements update relative probabilities and estimates of individual Kalman filters. This approach results in a better track state probability density function approximation by a Gaussian mixture, and tracking results near the Cramer-Rao lower bound. Proposed algorithm is also applicable in other cases of nonlinear information fusion. The performance of proposed Gaussian mixture approach is evaluated using a simulation study, and compared with a bank of EKF filters and the Cramer-Rao lower bound.