# Ultrashort Baseline Positioning System: Implementation and Tests at Sea（1）

**Abstract**

This work presents the design, implementation, and validation at sea of an USBL acoustic positioning system.A carefully selected acoustic signal emitted from a moving platform is received on an array of hydrophones and is detected, based on a matched filter. Then it is possible to determine the time of arrival (TOA) and to estimate the position of the emitter. The system performance relies on the accurate detection of the expected signal, which may be corrupted by additive noise and multi- path phenomena, and accurate TOA estimation. The classical acoustic pure tone pulse is compared with wide band coded spread spectrum signals (SS), resulting on improved TOA resolution and stronger multi-path and noise rejection.

The use of SS signals to be received by an USBL array of close-spaced hydrophones requires advanced signal processing techniques only available using a Digital Signal Processor. Therefore, system implementation must rely on real time digital signal processing techniques that allows for improved performance and versatility. Digital matched filter implementation is tackled based on the Discrete Fourier Transform (DFT) and its properties.

The overall performance of the proposed system is validated based on the results from a series of tests at sea.

**1.Introduction**

Acoustic positioning systems are designed with the purpose of tracking the evolution of an underwater vehicle or platform. These systems rely on the measurement of the times of arrival of an acoustic signal emitted by the moving target to a set of receivers with known positions. From TOA measurements bearing and/or range can be derived, and thus the position of the target.

Underwater Acoustic Positioning Systems are commonly used in a wide variety of underwater applications, including oil and gas exploration, ocean sciences, salvage operations, marine archaeology, law enforcement and military activities.

Acoustic positioning systems can achieve an accuracy of a few centimeters to tens of meters and can be used over operating distance from tens of meters to tens of kilometers. Performance depends strongly on the type and model of the positioning system, its configuration for a particular application, and the characteristics of the underwater acoustic environment at the work site

**1.1 Positioning systems architectures**

Classical approches to underwater acoustic positioning systems are described in this section as presented in [17]. The distance between acoustic baselines (that is, the distance between the active sensing elements) is generally used to define an acoustic positioning system. In this way there are three primary types: Short Baseline (SBL), Ultra Short Baseline (USBL) and Long Baseline (LBL).

**1.1.1 Short Baseline**

In a SBL system a minimum of three receivers, about 20 to 50m apart, are installed in the hull of a surface vessel. From the detection of the acoustic signal and relative TOA measurements of different receivers a bearing is computed. If a time of flight interrogation technique is used (transducer transponder) a range to the emitter will also be available from the SBL system and thus a position can be derived.

Any range and bearing available from the SBL system is with respect to the receivers mounted on the vessel and, in this way, a SBL system needs additional tools such as vertical reference unit (VRU), gyroscope and surface nav- igation system (GPS) in order to provide a position on an Earth Reference System.

**1.1.2 Ultra Short Baseline**

Similar to SBL but here receivers are closely spaced (less than 50cm apart).The close spacing of USBL receivers requires additional accuracy on TOA estimation. In this way, USBL systems rely on a phase difference or phase comparison of the acoustic signal between receivers, instead of the relative arrival time measurement.

Like in SBL systems a time of flight interrogation technique can be used to achieve a range to the emitter. Also the position derived from USBL systems is with respect to the receivers mounted on the vessel and therefore VRU,gyroscope and GPS are needed to provide an Earth referenced position.

The main advantages of Short Baseline (SBL) and Ultra Sort Baseline (USBL) positioning systems are:

- Ship based systems (no need to deploy transponders on the seabed).
- Low system complexity makes SBL and USBL relatively easy tools to use.

Good range accuracy with time of flight systems. And the main disadvantages of these systems are:

- Detailed calibration of system is required.
- Absolute positioning accuracy depends on additional sensors (VRU and gyroscope).
- In the case of SBL system, large baselines (>40m) are needed for accuracy in deep water.

**1.1.3Long Baseline**

A network of seabed transponders, with a baseline of- ten several kilometers long, are deployed. The location of the baseline transponders either relative to each other or in global coordinates must then be measured precisely. A minimum of three transponders is needed but more may be used in order to introduce redundancy. Travel times are measured between the transponders and the vehicle to be tracked and position is calculated using triangulation techniques. Each transponder replies on a different frequency, thus allowing their signals to be distinguished from each other. The position derived from an LBL system is with respect to relative or absolute seabed coordinates and, unlike SBL and USBL, there is no need of additional components.

The main advantages of Long Baseline systems are:

- Very good position accuracy independent of water deep.
- High relative accuracy over large areas. And the main disadvantages of this systems are:
- High system complexity
- Requires comprehensive calibration at each deployment.
- Operational time consumed for deployment/recovery.

**2、Signal Processing and Positionig**

In this section a comparison is made between two possible acoustic signals to be used by the underwater position system: the traditional sinusoidal tone burst; and a spread spectrum signal. The signal detection and time of arrival (TOA) estimation problems are studied and a solution is presented based on a matched filter. A closed- form method of estimating the transponder position in a reference coordinate frame is provided. The transponder distance and direction are obtained resorting to the planar approximation of the acoustic waves.

**2.1Signal detection and TOA estimation**

The positioning system reciver has two principal functions. First it must detect if the expected signal is present in the water; if so it must then estimate the TOA of the signal. The direction and distance of the emitter are computated using the TOA measurments to different hydrophones and so the system requires accurate detection and TOA estimation of a known signal which may be corrupted by additive noise.

The optimal solution to a detection problem, from the point of view of signal to noise ratio (SNR), can be obtained resorting to the design of a matched filter, consisting of a linear system whose impulse response is a time reversed replica of the expected signal. The filter response is the correlation between the acquired and the expected signal. The arrival time correponds to the peak of the matched filter output.

For the TOA problem we can quantify the uncertainty of the estimation. The standard deviation for the TOA estimate is given

by [2]:

where BW is a measure of the signal bandwidth and

is the SNR at the matched fifilter output where n0 is the input noise level and E is the signal energy. From eq. 1 we see that there are two ways to reduce the TOA estimate variance and therefore improve the repeatability of the system: increasing the SNR; or increasing the bandwidth of the signal.

The classical signal used for underwater positioning is a narrowband tone burst, primarily because of the simplicity of the circuitry required to transmit and receive the signal. Let’s see how can we reduce the TOA estimate variance for this particular signal. In order to increase the SNR we must increase the energy of the received pulse E. For the sinusoidal signal the energy is proportional to amplitude and length. Signal amplitude is limited to transmitter power and therefore better SNR is achieved by sending a longer ping.

For the same type of signal the bandwidth is given by

Equation (4) expresses a contradiction. When it is not possible to increase the transmitter power any further the signal must be lengthen in order to increase the SNR. This provides greater energy for detection but will also increase the TOA estimation variance which is not desirable. On the other hand, in order to achieve the highest possible timing resolution with a tone burst the optimal signal is as short as possible. However this causes that optimal signal to have too little energy to allow for reliable detection at long ranges. Figure 2 shows the matched fifilter output for two sine pulses with different lengths. Both signals are corrupted by the same additive noise sequence. With the shorter pulse shown in Fig. 2a a sharp peak is obtained in the fifilter output but with poor noise rejection. Figure 2b shows that when we lengthen the pulse, the noise rejection improves but the sharpness of the peak degrades. The above discussion represents the ideal case where there is only one acoustic signal in the presence of additive white noise. In underwater acoustic however there are usually many multipaths, that are repllicas of the signal arriving later in time and at varying amplitudes caused by reflflection. This kind of scenario often arises in shallow

Figure 2: Matched fifilter output

water channels where the signal is reflflected from the sea surface (or seabed). Figure 3 shows the matched fifilter response to a sine pulse in the presence of a 2 ms delay and 75% amplitude multipath.

Figure 3: Matched fifilter output with multipath

Using a sine pulse, which has not a narrow autocorrelation peak, the response to the delayed signal is not well separated from the direct path.

We presented here the two main disadvantages of using a sine pulse.

• It is not possible to simultaneously increase range (SNR) and precision (decrease TOA estimation variance).

• Weak multipath rejection.

We can overcome these disadvantages by using a coded spread spectrum signal. SS signals are wideband signals whose autocorrelation function approaches an impulse. In addition with SS signals it is possible to maintain the bandwidth as pulse length is increased [2]. In this way, as we can see from (1), it becomes possible to increase signal energy by lengthening the SS pulse, increasing SNR and system range, and simultaneously reduce TOA estimation variance, improving system precision. Figure 4 illustrates the behaviour of the SS pulse under ideal conditions and corrupted by noise and multipath.

Figure 4: Matched fifilter output

Figure 4 demonstrates that is possible, using a SS signal, to obtain a matched fifilter response whose noise rejection characteristics are similar to the long sine pulse, but whose sharpness is similar to the short one. Also in the presence of multipath the response to reflflection and to the direct path is well separated allowing the detector to reliably fifind the fifirst peak.

Although SS signal are relatively complex, the availability of low cost, high speed, Digital Signal Processors (DSP) now make it practical to consider using these waveforms in real world applications. From here on, and during the system development and testing, we will be using a SS acoustic signal.

2.2 Positioning

The direction and distance of the emitter are computed based on planar approximation of the acoustic wave. The problem is illustrated in fifig. 5 with two receivers (i and k) projected on XY plan, a propagating plan wave, time of arrival to the receivers (ti and tk) and the unit direction vector of the emitter d = [ dx dy dz ] T with opposite sense and the same direction as the propagation vector. The distance the planar wave travels between receivers i and k is given by

where vp is the speed of sound in the water and r_{i} = [ x_{i} y_{i} z_{i} ] ^{T} , rk = [ xk yk zk] ^{T} the receivers positions on Body frame. Without the use of vectorial notation eq. 5 becomes v_{p}(t_{i}−t_{k}) = −(d_{x}(x_{i}−x_{k})+d_{y}(y_{i}−y_{k})+d_{z}(z_{i}−z_{k})). (6)

Figure 5: Planar wave approximation

If there are N receivers there will be M equations like eq. 6 with {i = 1, . . . N ; k = 1, . . . N ;i 6 = k}, being M = N 2 C all possible combinations of the N receivers. The TDOA between the receivers,∆ = [∆_{1} ∆_{2} . . . ∆_{M} ] ^{T} ,

with ∆_{1} = t_{1} − t_{2}, ∆_{2} = t_{2} − t_{3}, . . . ∆_{M} = t_{N−1} − t_{N} , can be generated by ∆ = Ct_{m},where C ∈ RM×N is a combination matrix and tm = [t1 . . . tN ] ^{T} is the vector of time measurements from all receivers. In the same way, if we defifine for the receivers positions combinations x = [x_{1} − x_{2} x_{2} − x_{3} . . . x_{N}−1 − x_{N} ] T , y = [y_{1} − y_{2} y_{2} − y_{3} . . . y_{N}−1 − y_{N} ] ^{T} , z = [z_{1} − z_{2} z_{2} − z_{3} . . . z_{N}−1 − z_{N} ] ^{T} ,the generalization of the problem for N receivers can be writen as vp∆ = −(dxx + dyy + dzz). (7) The least squares solution for the emitter’s direction as presented in [3] is given by d = −vpS #Ctm, (8)

where S = [x y z] e S # = (S T S) −1S T . Also resorting to the planar have approximation, the range of the emitter to the receiver i is given by ρ_{ei }= v_{p}t_{i} , with i = 1, . . . N,and the range to the origin of Body frame by ρ_{i} = ρ_{ei }+ d^{T} r_{i} , (9) where d is the previously computed emitter’s direction vector.

By averaging the range estimates given by 10 for all the N receivers yields

3 System development

In this section we present the implementation done with focus on data acquisition and signal processing.

The USBL acoustic positioning system developed can be diveded into two parts: emission and reception. Building the emission box was not a purpose of this work and we used an existing box with the ability to generate a DSSS acoustic signal pre-recorded in memory. On the other hand, developing and programming the reception box was the main task to be done. The heart of the reception box is the DSP that allows improved performance and versatility for the USBL acoustic positioning system. A TMS320C6713 flfloatingpoint DSP from Texas Instruments that operates at 225MHz was used. Before any DSP algorithm can be performed the signal must be in a digital form. This task is performed by a a 16 bit, 250 KSPS, 4 channel A/D converter. The system is controlled (start/stop, operation mode, data transfer, . . . ) by a host PC and the communication is ensured by a SMSC LAN91C111 Ethernet board. The reception box electronics are mounted inside a rectangular splash-proof case with four hydrophone input connectors, a GPS antenna for PPS signal access, an external power supply and an Ethernet port. Emission box is shown on fifig. 6.

Figure 6: Reception box

3.1 Acquisition

This process starts with the array of 4 hydrophones, based on piezoelectric transducers that convert an acoustic wave into an electrical signal. The electric signals arethen amplifified by 4 variable gain amplififiers. These amplifified analogue signals must be converted into a digital form. This process is performed by the ADC converter and involves the following steps: the signal is fifirst sampled, converting the analogue signal into a discrete-time continuous amplitude signal; the amplitude of each signal sample is quantized into one of 2 16 leves; the discrete amplitude levels are encoded into distinct 16 bit length binary words. This binary words, representing a digital form of the acoustic waves ‘listened’ by the hydrophones, must be temporarily stored in the DSP internal memory so that processing can be done to detect the presence of the expected signal and compute emitter’s direction.

To tackle the digital data storage problem, a FIFO (fifirst in fifirst out) data buffer was implemented. The buffer is divided into blocks and while the ADC is acquiring new data the data present in the buffer is being processed. When the acquisition is completed the oldest block is replaced by the newest data and a new cycle begins. The number and length of the blocks is now the major concern. This is a delicate problem because during the time of one block acquisition, given by L/fs where L is the block length and fs the sampling frequency, the DSP must be able to process the data present in all blocks of the buffer. In this way the blocks must be large enough to give time for the data buffer processing but not too large because of memory constrains. This trade-off led us to use blocks of the same length L as the expected signal.

A sketch of the buffer hardware implementation is shown on Fig. 7 as well as the progress of an expected signal through the buffer. As the system has four hydrophones there will be four FIFO buffers for data storage, like the one in fifig. 7.

Figure 7: FIFO data buffer of length 3L

When the system indicates the presence of the expected signal, it may be completely or just partially inside the buffer. Thus, in order to obtain accurate results, before estimate signal TOA to the different hydrophones and compute emitter position, we must be sure the expected signal is completely inside the buffer. The option of using three blocks of length L is because we want this to happen at least two times, and three is the minimum number of blocks that ensures that. Like this, the fifirst detection is always ignored and just the second consecutive detection is accepted when is guaranteed that the signal is completely inside the buffer. At this time the acquisition is temporarily stoped to allow for TOA estimation and emitter’s position computation.

It is important to remark that if just two L length blocks were used that would never be guaranteed.

3.2 Processing

In section 2.1 it was said that the use of a matched fifilter was the optimal solution for signal detection. Therefore a digital matched fifilter will be implemented in the DSP. The digital fifilter output to a set of data x[n] present in the buffer is given by the digital convolution (convolution sum) between x[n] and the fifilter’s impulse response h[n]

Because the matched fifilter purpose is to perform the correlation of the expected signal with the acquired data, it’s impulse response h[n] will be a replica of the expected signal sampled at the ADC working frequency fs. However convolution is a computational heavy operation. The standard convolution algorithm has quadratic computational complexity and, even with the use of fast digital signal processors its real-time computer implementation it is impossible in most applications. In this context it becomes important to introduce the concept of Discrete Fourier Transform (DFT) as correlation computation may be speeded up using DFT properties. Let {x[n]} = {x[0], x[1], . . . , x[N − 1]} be a sampled sequence, where N is the number of samples. Its Discrete Fourier Transform is the sequence of complex values {X[k]} = {X[0], X[1], . . . , X[N − 1]} in the frequency domain, with the same length N, given by

where Ω = 2π/NT and T is the sampling period. The inverse Discrete Fourier Transform (IDFT) restores the sequence {x[n]} given its DFT {X[k]} and it’s defifined by