DVL error modeling

In our experiment, we mainly used the linear velocity measurement value. In [1] authors gave the error model of DVL. We plan to model the DVL error with the method similar with IMU error model.

Experiment condition

The DVL is hang vertically and sunk in water by a rope. When it is in the static state, the data are sampled by a laptop on the land. The test time is more than 4 hours to model for the error. The sample rate is 2Hz. Underwater temperature is 9.8 degree. The altitude of 4 beams are 8.220, 2.280, 8.220, 8.150(m) [pay attention, there is some error on the second beam] respectively. Sound velocity is 1446.0m/s. RPY(Roll, Pitch, Yaw) are 0.37, 1.04,124.84 degree respectively.

Experiment principle

A general sensor error model can be described as following form:

where s_m is the output of sensor, s_t is the true value of sensor, s_f is the scale factor error, b(t) is the bias term. b₀ is the constant null-shift which can be obtained by online estimator. b₁(t) is time variant component of the bias term. It’s the most complex part in modeling for the sensor’s error and can be finished as following two steps.

1. Measuring its Allan variance to judge what is the form of time variant term.

2. Calculating the time constant and white noise character/ just white noise character.

b_w(t) can be modeled as the band limit white noise. It is thought of as the standard deviation when the sensor is subject to a zero input and sampled at a rate much higher than the maximum frequency content of b₁(t).

Fig1.DVL test at pool in SIA

Experiment Data

Fig 2. the long time experiment data curve

According to the data in the experiment, the standard deviation of error is

Unit: m/s

Tab1 Standard deviation of b_w

So the b_w can be seen as the Gaussian distribution with the zero-mean and standard deviation shown in table1.

Fig 3. Allan variance

In the experimental curve, when the time is less than 10s, the slope is –1/2. If we integrated the velocity to provide the position, the position error will be random walk position. When the timer is longer than 10s the better error model is 1^st Gaussian Markov process. That is

b₁(t)=(-1/ )* b₁(t) + w_b(t)

Fig4 Autocorrelation curve

From the curve the time constant .

,

Recaculate the data sampled at 2Hz frequency and obtain the data with frequency is 1/60Hz, the standard deviation of new data serve as the variance of additive white noise.

Unit: m/s

Tab2. additive noise

Original data and pdf version of this report can be found in attachments