In this paper, the application of the emerging compressed sensing (CS) theory and the geometric characteristics of the targets in radar images are investigated. Currently, the signal detection algorithms based on the CS theory require knowing the prior knowledge of the sparsity of target signals. However, in practice, it is often impossible to know the sparsity in advance. To solve this problem, a novel sparsity adaptive matching pursuit (SAMP) detection algorithm is proposed. This algorithm executes the detection task by updating the support set and gradually increasing the sparsity to approximate the original signal. To verify the effectiveness of the proposed algorithm, the data collected in 2010 at Pingtan, which located on the coast of the East China Sea, were applied. Experiment results illustrate that the proposed method adaptively completes the detection task without knowing the signal sparsity, and the similar detection performance is close to the matching pursuit (MP) and orthogonal matching pursuit (OMP) detection algorithms.

To solve the problem of attitude determination using magnetometers independently and uniquely, which is important for underwater vehicles, a type of full attitude determination method based on geomagnetic gradient tensor is proposed in this paper. In this method, a group of non-linear equations concerning geomagnetic gradient tensors is established, where a quaternion is selected to calculate three attitude angles of an underwater vehicle. The optimal quaternion is estimated using Newton Down-hill to optimise the object function. The detailed steps of the full attitude determination based on geomagnetic gradient tensor are given, and the effects of the initial angle error and the sensor noise on the attitude determination are investigated. Simulations show that the algorithm can identify precisely and quickly the attitudes even in the presence of larger initial angle error and sensor noise, which proves the attitude determination algorithm.

A tri-axial magnetometer (TAM) needs to calibrate its instrument parameters, including non-orthogonality, scale factor among three-axis, and bias, to improve measurement precision. In general, most scalar calibrations require a scalar magnetometer to measure magnetic field intensity as a reference field for calibration, which will increase the cost of the calibration facilities. In this paper, a scalar calibration method of total instrument errors of TAM, independent of magnetic field intensity, is proposed based on the constrained optimization using the sequential quadratic programming (SQP) algorithm. The relationship between the residual error of calibration and the attitude amount for different standard deviations (STDs) of noise is numerically demonstrated, and the effect of noise on calibration accuracy is also theoretically and numerically analyzed. A tri-axial fluxgate magnetometer is used to experimentally test the scalar calibration algorithm independent of magnetic field intensity. The result shows that the measurement error of geomagnetic field intensity is reduced to 15.52nT and 14.99nT by applying the scalar calibration using SQP and the differential evolution (DE) algorithms, respectively.

Tilt vibrations inevitably have negative effects on some precise engineering even after applying horizontal and vertical vibration isolations. It is difficult to adopt a traditional passive vibration isolation (PVI) scheme to realize tilt vibration isolation. In this paper, we present and develop a tilt active vibration isolation (AVI) device using a vertical pendulum (VP) tiltmeter and a piezoelectric transducer (PZT). The potential resolution of the VP is dependent on the mechanical thermal noise in the frequency bandwidth of about $0.0265 \mathrm{nrad}$, which need not be considered because it is far below the ground tilt of the laboratory. The tilt sensitivity of the device in an open-loop mode, investigated experimentally using a voltage controller, is found to be $\left(1.63\pm 0.11\right)\times {10}^5 \mathrm{V}/\mathrm{rad}$. To compensate for the hysteresis nonlinearity of the PZT, we experimentally established the multi-loop mathematical model of hysteresis, and designed a parallel controller consisting of both a hysteresis inverse model predictor and a digital proportional–integral–differential (PID) adjuster. Finally, the response of the device working in close-loop mode to the tilt vibration was tested experimentally, and the tilt AVI device showed a good vibration isolation performance, which can remarkably reduce the tilt vibration, for example, from 6.0131 μrad to below 0.0103 μrad.

The accuracy of a magnetic gradient tensor (MGT) measured by tri-axial magnetometer cross arrays (TAMCAs) is compromised by inherent errors in individual tri-axial magnetometers (TAMs) and inter-sensor misalignment angles (MAs), both of which degrade the resultant MGT data quality. This paper proposes a novel lossless scalar calibration algorithm that eliminates mathematical approximations while tracking the fluctuation of the reference magnetic intensity (MI). The calibration algorithm is developed to improve TAMCAs’ measurement precision; however it is difficult to provide a completely accurate MGT by experiments. Therefore, we have designed a kind of validation experiment based on a constrained Euler localization to demonstrate the effectiveness of the calibration algorithm. The fundamental principles of the proposed lossless scalar calibration methodology are systematically presented, accompanied by a numerical analysis of relative errors calibrating TAMCA parameters. Key influencing factors are carefully investigated, including the TAM noise level quantified by standard deviation (STD), calibration dataset size, and STD of reference MI fluctuations. In the experiments, to validate the effectiveness of calibrating TAMCAs composed of four fluxgate TAMs (FTAMs), we measured the true geo-MI using a proton magnetometer and regarded an energized circular coil as the alternating current (AC) magnetic source of the constrained Euler localization, respectively. The results indicated that the lossless scalar calibration algorithm significantly improves the measurement accuracy of the geo-MI of the calibration site and MGT of the energized coil.

The passive magnetic detection and localization technology of the magnetic field has the advantages of good concealment, continuous detection, high efficiency, reliable use, and rapid response. It has important application in the detection and localization of submarines and mines. The conventional location algorithm needs magnetic gradient tensor system moving to other points, we propose a kind of linear location algorithm with a unique solution based on a single measurement of the cuboid tri-axial magnetometer array. The magnetic gradient tensor of the magnetic target is first calculated at the center points of the six rectangles of the cuboid array, and then the distance between the magnetic target and the rectangle center of the cuboid array is calculated. Finally, according to the square difference of the distances of the three pairs of parallel rectangles, a linear equation set about the position coordinates of the magnetic dipole is formed and then these position coordinates are calculated fast. We derive an analytical formula of the location error for the linear location algorithm. The simulation shows that the position of the target can be calculated accurately and the relative error of the position is <1%, and the location errors are positively correlated with the noise standard deviation of the three-axis magnetometer, and more they are proportional to the non-orthogonality between every two axes, sensitivity deviation and bias of the three-axis magnetometer. The location errors of the linear location algorithm through numerical simulations are consistent with the location errors calculated by the analytical formula.