Assessment of the acoustic telemetry positioning system
The performance of the acoustic telemetry system was assessed by determining positions
of three beacon tags. The beacon tags were associated with two acoustic receivers located
above intakes 1 and 5, and another one about 275 m from the powerhouse (Figure 1b in
the main article). The position estimates for the beacon tags were computed with the
software ALPS (Lotek Wireless Inc., Newmarket, Canada), using detections recorded in
15 randomly selected days when the receivers also detected tagged bull trout.
The number of positions obtained for each beacon tag per hour was divided by the
number of positions expected (i.e., 120) based on their burst rate of 30 seconds. The
resulting proportions were multiplied by 100 and the values were used as a measure of
positioning efficiency.
Overall, median positioning efficiency was highest in the spring and lowest in the
fall (Figures 1a, 1c, 1e). There was substantial variation in positioning efficiency among
beacon tags, with those located on the powerhouse wall having the lowest values in each
season (Figures 1a, 1c, 1e). Positioning efficiency for the beacon tags located on the
powerhouse wall decreased with increases in operational discharge (Figures 1b and 1d).
For the beacon tag located about 275 m from the powerhouse, positioning efficiency
decreased with operational discharge changing from low to intermediate values and then
increased with higher discharge (Figure 1f). The reasons for this unlikely relationship
with discharge are unclear and indicate that other factors (e.g. wind, precipitation) not
evaluated here might also have been responsible for variation in positioning efficiency of
that beacon tag.
1
The easting and northing components of the position estimates were subtracted
from the corresponding components of the fixed known locations of the beacon tags to
compute positioning errors. Positioning errors were classified according to the quality
class of each position as determined by their reliability number. Reliability number is a
variable computed by ALPS that represents the effective number of receivers
participating in the computation of a position estimate, with smaller errors occurring with
increasing reliability number [1]. In our study, reliability number ranged from 0 to 7 and
accordingly we categorized each positioning error into one of seven possible classes.
Approximately 90% of the positions had absolute errors under 50 m on both the
easting and northing components. Positions with absolute errors under 10 m on the
easting and northing components comprised, respectively, 63% and 43% of the data
(Figures 2a–b). As expected, error in the position estimates decreased in magnitude and
variability with increasing reliability number (Figures 2c–d).
We estimated the parameters of a t-distribution (using the “fitdistr” function in the
R package “MASS”; [2]) fitted to the errors in the easting and northing components of
positions in each reliability number class (Table 1). We used the estimates to fix the
parameters of the t-distribution describing the positioning error in the observation
equation (Eq. 2 in Additional file 2) of the DCRWS state-space model.
References
1. Niezgoda G, Benfield M, Sisak M, Anson P: Tracking acoustic transmitters by code
division multiple access (CDMA)-based telemetry. Hydrobiologia 2002, 483:275–
286.
2
2. Venables WN, Ripley BD: Modern Applied Statistics with S. 4th edition. New York:
Springer; 2002.
3
Table 1 Maximum likelihood estimates of t-distribution parameters fitted to
positional error data on the easting and northing components
Parameter
m
t
n
1
177.52
748.94
99.68
2
15.69
24.10
0.80
3
3.71
13.67
1.38
4
2.05
6.01
1.74
5
−1.62
4.25
1.79
6
−3.94
4.62
4.50
7
−1.83
0.90
2.22
1
—
—
—
2
23.78
24.64
0.69
3
−10.59
19.21
1.64
4
−11.57
15.63
4.39
5
−6.78
9.92
7.31
6
−3.20
0.92
0.88
7
−3.77
0.38
1.41
RN class
Easting
Northing
The location and scale parameters are denoted, respectively, by m and t , and n denotes
degrees of freedom. RN stands for reliability number and is a measure of position quality.
It was not possible to estimate the parameters for RN class 1 in the northing component.
4
Therefore, in the DCRWS state-space model, parameter values for RN class 1 in the
northing component were fixed to the values estimated for RN class 1 in the easting
component. The units for the location and scale parameters are meters.
5
Figure 1 Efficiency of the acoustic telemetry system in positioning beacon tags by
season (a, c, e) and hourly mean total operational discharge (b, d, f). (a, b) Beacon
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tag on receiver above intake 1. (c, d) Beacon tag on receiver above intake 5; (e, f) Beacon
tag on a receiver located about 275 m from the powerhouse. See Figure 1b in the main
article for the location of the receivers and beacon tags. The lines in (b, d, f) denote a
LOESS smoother identifying the trend in the data.
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Figure 2 Error in the position estimates of three beacon tags (data were pooled).
Cumulative empirical distribution function of the absolute error in the (a) easting and (b)
northing components of the beacon tags position estimates. Relationship between
reliability number (RN) and positioning error in the (c) easting and (d) northing
components.
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