Application of adaptive time delay estimation to ultra-short baseline location of frogman
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Ultra-Short Base Line (USBL) positioning equipment is needed to realize high precision ranging and direction finding for effective coordination and command when frogmen or underwater robots perform underwater security, salvage and search operations. Frogman positioning equipment includes miniature sound beacon and USBL positioning solution unit (frogman positioning watch or shipborne positioning terminal). The miniature sound beacon and locator watch are worn by the frogman. The USBL receiver array of the frogman locator watch can be mounted on the tip of the diving helmet in order to prevent the body from blocking the receiving signal. Before each positioning equipment is launched, a certain synchronization mechanism is used to synchronize signals at a close distance. After synchronization, each acoustic beacon periodically transmits positioning signals of different frequencies or codes. The positioning solving unit receives the sound beacon signal within the corresponding synchronization period, and calculates the distance between different frogmen or between frogmen and shipborne positioning terminal continuously according to the delay difference. Meanwhile, the USBL direction finding algorithm is used to measure the azimuth Angle between frogmen or between frogmen and shipborne positioning terminal. On the frogman side, the calculated orientation information can be displayed by means of a wristwatch or eyepiece.
When measuring the distance of frogman USBL equipment, the global coarse measurement of time delay can be carried out by correlation method, and the local fine measurement can be carried out by conventional cross spectrum method. Since the measuring distance is usually tens to hundreds of meters, and the sampling frequency is generally 3-6 times of the signal carrier frequency (about 20kHz), this traditional delay measurement method can be used in typical signal-to-noise ratio under the premise of ensuring the accuracy of time synchronization. The delay estimation accuracy of 0.1Ts (Ts is the sampling interval) provided by the system can achieve high ranging accuracy. At present, the problem of high precision positioning of frogman USBL is the lack of direction finding accuracy and robustness, and the direction finding problem of narrow band and wide band signals can be classified as high precision time delay estimation [1-2].
Since frogmen mainly work in complex shallow water environment, adaptive delay estimation method has the characteristics of strong adaptability to the environment. This paper attempts to apply the hybrid modulation Lagrange direct delay estimation method to the high precision direction finding of the frogman USBL. It can modulate the fractional delay filter to the center frequency of the beacon signal when the center frequency is known, so as to provide higher delay estimation accuracy at a lower order. Considering the possible medium and low SNR environment in practical use, this paper will discuss the specific application mode of the hybrid modulation Lagrange direct delay estimation method and verify the simulation according to the characteristics of the frogman USBL formation and signal itself.
1. Location and direction finding of frogman USBL based on adaptive delay estimation
1.1 USBL positioning model of frogman
The reception of the transmitted signals of the frogman positioning beacon can be completed by using the simple structure of the ternary plane receiving array, as shown in Figure 1. Array elements 0, 1 and 2 are arranged in an equilateral triangle, and array element 0 is located at the origin of coordinates as the reference array element. The distance between array element 1 and element 2 and reference element 0 is d, and the sound velocity in water is c. To avoid phase ambiguity, d is less than half the wavelength of the signal.
Figure 1. Schematic diagram of positioning direction finding for frogman triadic array
The signals received by the receiving array 0 and 1 can be expressed as
Where: k is the time of sampling point, τis the delay of indirect received signal of array element 0 and 1; s k() is a narrowband signal with known center frequency emitted by frogman locator beacon. Noise 0 () w k and 1 () w k are Gaussian white noise with mean 0, variance σ0 2 and σ1 2, respectively, and are not correlated.
As shown in Figure 1, the size of the system array is small compared with the slant distance R, so it can be considered as the case of far-field reception, that is, the sound lines sent by the same acoustic beacon and received by the three array elements of the array are parallel. The typical incident Angle solving model of far-field signals is shown in Figure 2.
Figure 2. A typical model for calculating the incidence Angle of far-field signals
The relation between the time difference of array 0 and array 1 receiving the signals transmitted by the same acoustic beacon and the incidence Angle of signal θ01 is
The incidence Angle θ01 can be obtained after the time difference τ 01 is measured by the delay estimation method.
Then we need to determine the incidence direction of the incident signal. As shown in Figure 1, element 0 and element 1 are located on the Ox axis, and element 2 is located in the fourth quadrant. The incident signal can be judged from the left side or the right side according to the positive and negative sign of τ01. Different from the formation of isosceles right triangle, to judge whether the incident signal comes from the upper half or the lower half, we need to judge the numerical range of τ 02, or to virtualize an element 3 between element 0 and element 1. The output of the signal is 3 () x k = 0 1 [() ()]/2 x k x k +, and then according to the positive and negative sign of the delay τ 23, we can judge whether the incident signal comes from the upper half plane or the lower half plane, and then judge which quadrant the signal comes from. The direction finding Angle is calibrated in the range of 360°.
1.2 Adaptive delay estimation algorithm
The adaptive time delay estimation algorithm has the advantages of strong environment adaptability and less statistical prior knowledge. The Least Mean Square error (LMS) delay estimation algorithm is a kind of adaptive delay estimation algorithm based on LMS algorithm for iteration. When the algorithm converges, the filter weight coefficient converges to the form of sinc function, and the peak position corresponds to the estimated value of the delay. The structure of LMS Time Delay Estimation (LMSTDE) is shown in Figure 3.
Based on the traditional LMSTDE algorithm, a constrained delay estimation method is developed. Such as Explicit Time Delay Estimation (ETDE)[3], Explicit Time Delay and Gain Estimation (ETDGE)[4], etc. ETDE will time delay estimation is modeled as a fractional delay type a sinc Finite length unit impulse Response (Finite Im pulse Response, FIR) filter weight coefficient estimates, by directly in the adaptive algorithm for time delay to update for the integers
FIG. 3 Block diagram of LMS adaptive delay estimation algorithm
It reduces the interpolation of filter weight coefficient in LMSTDE, and has the advantages of small computation and high precision. But it is proved to be a biased estimation under the condition of finite length filter or low signal-to-noise ratio. By adding a gain control to ETDGE, unbiased estimation under finite length filter can be obtained. However, due to the large passband ripple of sinc type decimal-delay FIR filter, the estimation accuracy of ETDGE for single-frequency signal is not ideal [5-7].
The method of Mixed Modulation Lagrange Explicit Time Delay Estimation (MMLETDE) [8-9] combines sinc interpolation with Lagrange interpolation. For band-limited signals, The delay estimation accuracy is higher than sinc type fractional delay filter. If the center frequency of the band-limited signal is known, the fractional delay filter can be modulated to the center frequency of the signal to provide higher delay estimation accuracy at a lower order.
The structure of the hybrid modulation Lagrange direct delay estimation method is the same as that in FIG. 3, but the updating way of the filter coefficient is different. The updating equation is as follows: [9]
Is Lagrange fractional time delay filter, and the expression is
The two signals of the USBL receiving array are taken as the reference signal and the delay signal input, and the appropriate convergence factor is selected to converge gradually to the true value of the two signal delay. To ensure system convergence, μ should satisfy:
Where, σx 2 is the variance of the input signal; Omega is the center angular frequency of the input signal.
In order to eliminate the effects of formation installation error, sound velocity error, sound line bending, circuit additional phase and circuit noise, the following simulated signals are used to evaluate the accuracy of positioning direction finding of frogman USBL under the corresponding adaptive time delay estimation algorithm.
The signal center frequency is 22 kHz, the sampling frequency is 100kHz, the array spacing d is slightly less than half wavelength, and the signal window length is 80 sampling points. When the Signal to Noise Ratio (SNR) was 20 dB (adding typical additive Gaussian white noise), the simulation was carried out using MMLETDE algorithm, the number of iterations was 45, and the convergence factor μ-0.08.
Using the above simulation conditions, when the signal is perpendicular to the connection of 0 and 1 and incident at 90°, the simulation results are shown in Figure 4. As can be seen from Figure 4, the estimated time delay measured is 0.005 3 Ts (taking the mean value of stationary segment), and the corresponding direction finding result is 89.87°. In other words, when the signal-to-noise ratio is high (greater than 20 dB), the hybrid modulation Lagrange direct delay estimation method can provide a delay estimation accuracy of 0.001Ts, and corresponding direction finding accuracy is better than 1°. When the signal-to-noise ratio decreases (less than 15 dB), the performance of the hybrid modulation Lagrangian direct delay estimation method deteriorates and the direction finding results deteriorate.
FIG. 4 Delay estimation curve when SNR=20 dB and the signal is vertically incident
The actual transmitting sound source level of frogman USBL beacon can reach more than 172dB, the absorption coefficient of seawater corresponding to the system operating frequency is about 4.5dB km-1, and the propagation loss is about 56.3dB at 500m. The working environment is 2 ~ 10 m underwater, and the ambient noise in the working frequency band is about 72dB in the third-class sea state. According to this, it can be estimated that the theoretical signal-to-noise ratio of the received signals of the frogman USBL array can reach 20 ~ 30dB in typical working environment. However, if the frogman receiving array is flexibly worn in the form of a watch, it will produce a certain block to the received signal; At the same time, in order to reduce the requirement on the sound source level of transmitting beacon, this paper adopts two approaches to realize the MMLETDE high-precision time delay estimation and USBL direction finding under the medium and low signal-to-noise ratio (10-20 dB).
2 Application of adaptive delay method at low signal-to-noise ratio
2.2 Modify the adaptive delay estimation algorithm
Another way of thinking is to modify the original MMLETDE adaptive delay estimation algorithm when there is uncorrelated noise.
Figure 5 Direction finding error of adaptive delay estimation method when SNR=20 dB
Figure 6 Direction finding error of adaptive delay estimation method when SNR=15 dB
FIG. 7 Direction finding error of adaptive delay estimation method when SNR=10 dB
By substituting Formula (1) into the output error function of the original MMLETDE, we can get:
The mean square error function can be written as
Using the unbiased impact response estimation method, the adjusted mean square error function is obtained
Its instantaneous error is
The instantaneous error is used to update the estimated delay difference, as follows:
For the frogman USBL positioning receiving system, the typical working scene is the far-field situation, where 0 () x k and 1 () x k are obtained by receiving the Gaussian noise of parallel incident s k() superimposed on its similar area, and the difference between them is only 0~2 sampling time. When the number of sampling points of the two signals is large, the updated equation of time delay estimation stored in noise is finally obtained
Simulation parameters are the same as those in Section 2.1. In order to reduce the order of the filter as much as possible, bandpass filtering is performed before signal processing (generally completed by hardware front-end acquisition part in actual equipment). In addition, in order to better meet the conditions of the gamma ≅ 1, signal window size can be increased slightly, the 100 sampling points here, Simulation was performed on the modified MMLETDE at low and medium signal-to-noise ratio, and the simulation results were shown in Figure 8-10.
As can be seen from Figure 8-10, the performance of the modified MMLETDE is slightly higher than that of the first method, and it can provide 1° ~ 3° direction finding accuracy at low and medium signal-to-noise ratio, which can meet the typical positioning direction finding accuracy requirements of frogman USBL.
FIG. 8 Modified direction finding error of adaptive delay estimation method when SNR=20 dB
FIG. 9 Corrected direction finding error of adaptive delay estimation method when SNR=15 dB
FIG. 10 Modified direction finding error of adaptive delay estimation method when SNR=10 dB
3 Conclusion
In this paper, the mixed modulated Lagrange direct time delay estimation method is applied to the high precision direction finding of the frogman USBL. Based on the characteristics of the USBL formation and signal itself, the specific application method of the mixed modulated Lagrange direct time delay estimation in the direction finding of the frogman USBL with low signal-to-noise ratio is discussed. The results show that the proposed adaptive delay estimation method can achieve the direction finding accuracy of 1° ~ 3° at low signal to noise ratio.
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