A method of spatial correction for acoustic positioning biotelemetry
© Charles et al. 2016
Received: 19 September 2015
Accepted: 20 January 2016
Published: 3 February 2016
It has been stated that there is a certain amount of intrinsic error inherent in all remote sensing methods, including acoustic telemetry, which has gained popularity in both freshwater and marine environments to record fine-scale movements over small spatial scales. We performed stationary tag trials on three freshwater lakes where we placed transmitters at known locations around the lakes and used radio-acoustic positioning and telemetry (RAPT) system-derived location data to assess the measurement and systematic biases of the system. We used a geostatistical technique called ordinary kriging to deal with the systematic errors and a state-space model to represent the measurement error of the data. Furthermore, we applied the kriging correction and a continuous-time correlated random walk model in a state-space framework to predict locations of a lake trout.
The stationary tagging trials produced a complex pattern of spatial error within each lake that could not properly be accounted for by a simple filtering process. Using fivefold cross-validation, positioning error was reduced from 93 to 99 % in three small lakes. We also identified tag depth as a potential source of measurement error. The application of a state-space model resulted in the contraction of home ranges of lake trout by 10–32 % and a 3–32 % reduction in total distance travelled.
Our results indicate that the systematic biases were a greater source of error than the measurement errors using a RAPT system. Consequently, the addition of a state-space model had relatively little effect on the quality of the spatial correction compared with the kriging method. The kriging method was able to compensate for the systematic biases produced by the RAPT systems and in turn increased the quality of data returned.
KeywordsRemote sensing Kriging Telemetry State-space model Error correction Radio-acoustic positioning and telemetry (RAPT)
Animal biotelemetry has rapidly evolved in the few decades since its inception. Where once manually locating an individual animal with a telemetry transmitter was a significant milestone, now satellite transmitters and large-scale coastal tracking networks allow for the long-range monitoring of many individuals over large geographic ranges and time spans. In addition, automated positioning systems, often used in aquatic environments, allow for the near-continuous monitoring of multiple animals simultaneously and can provide fine-scale movement data over multiple years . Despite the rapid technological advances in biotelemetry, and its widespread application by researchers, several inherent issues remain unresolved. Irrespective of the type of telemetry system in use, all locations of telemetry-tagged animals are associated with some degree of positional error (or inaccuracy). Further, because it is not possible to continuously monitor individuals, there are periods of time for which no positional information is available. Both of these issues require the development of analytical tools to make better use of telemetry data.
The use of automated telemetry positioning systems in aquatic environments has allowed for detailed examination of fine-scale spatial patterns in fish and other aquatic biota. Typically these telemetry systems incorporate three or more stationary hydrophone receivers that are positioned in a triangular array. The hydrophone receivers continually listen for acoustic transmissions from transmitters at set frequencies, and positions are calculated based on the arrival times of transmitter signals . To test for positional accuracy, stationary acoustic transmitters are placed in varying proximities to the triangular arrays. Despite the rigorous testing of positional error [3–6], little attention has been paid to the systematic errors (bias) introduced by positioning telemetry systems. A limitation of positioning animals with acoustic telemetry systems is that accuracy deteriorates as distance from the monitoring system increases , possibly due to signal degradation or echo effects in acoustically complex environments. Unfortunately, this can result in areas that are often biologically important, such as nearshore regions, with positional data of low precision and accuracy. As a result, these data are often excluded from analyses, even after filtering to ensure the highest quality data [7, 8].
The concept of positioning animals by time difference of arrival (TDOA) is employed by a wide variety of systems (Vemco radio-acoustic positioning (VRAP) system, Vemco positioning system (VPS), Lotek, etc.). The basic principle of these types of systems relies on a set of three or more receivers detecting a signal from a transmitter, and based on the difference in arrival time of this signal, a position can be calculated. The complexity of lake basins may affect signal pathways or create echoes such that measurement and systematic errors are not uniformly distributed across the detection range of the hydrophones, and thus, additional analyses may be needed to properly interpret the data. One such method is a geostatistical technique called kriging . Kriging is a well-established method of linear interpolation that can be used to estimate values for random spatial processes, which incorporates any spatial autocorrelation within the model. Kriging is a powerful tool for dealing with sparse spatial data since complete spatial coverage is often unfeasible in real-world situations. In the context of our study, we used kriging to map the error of the radio-acoustic positioning and telemetry (RAPT) system across the lake surface using limited sample sites to estimate RAPT system error at unsampled locations.
We use two technical terms throughout this paper to describe the error structure observed from the RAPT system: systematic error and measurement error. Systematic error describes the expected distance of a calculated location from its true location, while measurement error is defined as the variability of detections around the central detection point, regardless of the transmitter’s true location. We can think of spatial detections generated by a remote sensing system as a best guess by the software and hardware used to detect it. As systems continue to detect transmitters and assign spatial coordinates, it is the responsibility of the researcher to understand that these positions are not the absolute true position, but rather a best estimate. The purpose of performing stationary tag trials is twofold: (1) quantify the distance from the actual location of the tag to the position calculated by the software (systematic error) and (2) quantify the error in two dimensions of the RAPT system (measurement error). By placing tags at known coordinates (marked by a hand-held GPS unit) and analysing the resulting detection patterns, we are able to estimate the variability of the system across a spatial gradient.
In order to separate artificial noise (measurement errors) from relevant biological information, it is possible to quantify data quality classes and model them via a state-space model (SSM) . A principle application of SSMs is to analyse time-series data to estimate the state of an unobserved process from observed data. Another advantage of using a state-space model is that the filtering process does not remove “noisy” data points, but instead accounts for noise in the data . In the case of animal tracking data, coordinates (observed state) at an observed time t can be used to estimate an animal’s true location (unobserved state) at a future time. Using estimates for the measurement error of a system, we can use the power of a SSM to increase the value of our data by not only retaining more data, but also correcting the error that is inherent in all remote sensing methods. We modelled individual fish movement as a correlated random walk (CRW) using R  and the “CRAWL” package , which allows the flexibility to model continuous movement with data collected at irregular intervals.
The main objective of this study was to introduce and apply multiple methods for correcting spatial error of a RAPT system. Using telemetry data from a spatial array of stationary tags, we employ kriging  to quantify and correct the systematic error of telemetry systems located in three lakes. A secondary objective of this study was to apply a SSM to both the raw and “corrected” telemetry data. SSMs do not directly address spatially biased errors, but they can be used to address random measurement errors introduced by the telemetry system from both a raw and “corrected” data set. We quantify the performance of both kriging and SSM on telemetry data of free-ranging lake trout (Salvelinus namaycush) by using movement and habitat usage metrics to assess improvement.
Stationary tag trials
Stationary tag trials were performed to test the accuracy and precision of the RAPT systems (Fig. 1). Each stationary location consisted of an anchor, a line to the surface, and a float. For deployment, a tag was placed in a plastic bottle with holes in it to allow water to flow through, and the bottle was attached to the anchor line at a known depth. Tags were deployed at each location for ~24–72 h except for rare circumstances where tags were left at stations for more than 1 week. The location of each stationary tag trial was recorded using a hand-held GPS unit (GPSMap76 or GPSMap60CSX; measurement error reported by the GPS units for all locations was 2–4 m). Beginning in the fall of 2005, stationary trials were conducted in Lake 375. Three tags were used at 19 stations around the lake, most of which fell outside the RAPT triads. Only one stationary trial was deployed within the north triad in Lake 375, and this tag was placed near an experimental aquaculture cage. Unfortunately, during the early stages of this experiment the focus was to (1) determine whether the RAPT system could detect tags near the shoreline and (2) identify sources of error outside the triads with less attention paid to the error structure within the triad so we have limited information about the error structure within the triads on Lake 375. The spatial trials were improved upon for Lakes 373 and 626 by expanding the number of stations and placing more emphasis within the triads, but nearshore areas were still considered important. The stationary tag trials carried out in Lake 373 (summer 2009 and fall 2013), employed 12 tags and 46 stations. Some stations in Lake 373 were sampled at multiple depths to test whether depth affected positioning. The stationary tag trials performed in Lake 626 in 2010 and 2013 used 15 tags in 45 locations. We retested three locations in the spring of 2015 in Lake 373 to examine potential temporal changes in data quality.
There is no inter-tag variation in detection quality
Depth does not affect telemetry positioning
Water temperature (seasonal effect) or thermocline does not affect acoustic signals travelling through the water
The errors will display temporal consistency, and thus, a single stationary tag trial is sufficient for correcting multiple years of data
The error structure of the detections follows a bivariate Gaussian distribution
Correcting the data
Validation of the kriging method
We used a fivefold cross-validation to test the predictability of the kriging method. In fivefold cross-validation, the data set gets partitioned randomly into five equally sized subdata sets, and one subsample is taken as the testing set and the remaining subsamples are used as the model training set. The training set is used as input into the kriging method, and the testing set is used to test the predictability of the model. The process is repeated five times to independently use each subsample as the testing set. Further validation was performed in Lake 373 by a “leave-one-out” procedure “Appendix”). This procedure involved sequentially removing one station from the data set, performing the kriging method, and calculating the spatial error on the raw and corrected data.
State-space models are used to estimate the state of unobserved processes from observations while accounting for measurement errors and stochasticity in the process . In the present case of this study, the true location is the unobserved process. As is common with many remote sensing methods for geolocation data, there are latitudinal and longitudinal variances (measurement errors) associated with the observed location. We can use a SSM to account for the variances of the observed locations while simultaneously using maximum likelihood to estimate an animal’s true position. In the context of this study, we have assumed that the measurement errors follow a bivariate normal distribution around the mean spatial coordinates from each stationary tag trial. To model telemetry positions in continuous time, we followed methods described by Johnson et al.  to put a continuous-time correlated random walk model into a SSM framework. The telemetry data collected for this study differ from Argos data in that the quality class for each detection is not recorded, and thus, we assume measurement errors display a Gaussian structure for all detections within the SSM framework where the mean and standard deviation are fixed. Although we understand that telemetry systems can be subject to dilution of precision, in the context of our study we decided to treat all detections with equal weight since only the highest quality data were retained during processing. In order to estimate the SSM parameters, we used the crawl package .
Performance of correction techniques
To assess the quality of data, we spatially quantified systematic errors using kriging and used the SSM to correct measurement errors. We tested the performance of each method independently and simultaneously and quantified the improvements. Using observed telemetry data from a tagged lake trout in each of the three study lakes, we present four scenarios: (1) raw data, (2) data corrected for measurement error (only SSM), (3) data corrected for systematic error (only kriging), and (4) data corrected for both measurement and systematic errors. In order to compare the performance of each scenario, we used three indicators to measure activity and space use: total distance travelled, 100 % home range size calculated using the minimum convex polygon (MCP) , and 50 % kernel density estimator (KDE) . We used the adehabitatHR library  to calculate the MCP and KDE using the R statistical language. We chose to use the MCP method to describe the absolute home range and a KDE for detecting biologically important areas . Total distance travelled was used to show how biases in the telemetry data can influence calculations in animal behaviour and bioenergetics. For the purpose of this study, we have assumed that there is no spatial variation in detection quality among stationary tag locations. Thus, we model bias as varying in space and treat measurement error as equal among all locations.
Stationary tag trials
Summary of stationary tag trial data for RAPT systems in Lakes 373, 375, and 626 at the Experimental Lakes Area
Maximum depth (m)
# stations used in kriging
# detections removed
# duplicate detections
In Lake 375, the mean northing error was 33.35 m and the mean easting error was 32.93 m from the true tag locations. Overall, the mean systematic error (Euclidean distance) in Lake 375 was 50.15 m. The RAPT positions of stationary tags display a high degree of precision (the data points are clustered), but there was considerable systematic error (the clusters of points do not match the known tag locations) (Fig. 3a). Closer inspection of three stations within Lake 375 (Fig. 3b–d) illustrates the spatial distribution of the positioning errors. In each case, the RAPT systems show low accuracy but good precision. Similar results were obtained in Lakes 373 and 626 in relation to the precision of the systems, but the systematic errors were much different. Of the three lakes studied, the system on Lake 373 produced the most systematic bias, which was most likely due to a combination of bathymetry and distance of stationary tags from the centre of the triad.
Correcting spatial error
Summary of fivefold cross-validation of the kriging model
Raw positions (m)
Kriged positions (m)
Comparison of 95 % kernel home range overlap for tags set at different depths using the volume of intersection statistic (VI) for four stations in Lake 373
Depth 1 (m)
Depth 2 (m)
95 % kernel home range for each depth trial at each station in Lake 373
Tag depth (m)
Comparing correction techniques
Performance of error correction techniques applied to raw RAPT data of an acoustically tagged lake trout (Salvelinus namaycush) in three different lakes at the Experimental Lakes Area
Distance travelled (m)
100 % MCP area (ha)
Core area (ha)
Kriged and SSM
Kriged and SSM
Kriged and SSM
Acoustic telemetry is a widely used method of gathering spatial distribution data for organisms in aquatic environments. It is generally accepted that RAPT systems have a certain amount of intrinsic error associated with them likely resulting from deployment in complex acoustic environments. When assessing important ecological questions like an animal’s home range, it is important to use accurate spatial positioning information. As such, we have identified a need to quantify and correct systematic biases produced by acoustic telemetry systems. Through the use of stationary tag trials and kriging, we have successfully modelled errors inherent in acoustic telemetry methods using systems from three lakes in the Canadian boreal shield, removing systematic biases and improving the accuracy of the spatial data. We chose kriging because it is well documented in the literature, straightforward to use, and worked well for our purpose. Other spatial interpolation methods such as a general additive model  could be explored by other researchers depending on their data structure and experimental design. Furthermore, we have shown that kriging can be combined with SSMs to correct measurement errors as well. The general conclusion of this study is that the systematic errors produced by the RAPT systems have a greater effect on the quality of the data compared to the measurement errors and so we believe that more effort should be applied to performing stationary tag trials to identify problem areas in study systems. We feel that the measurement error displayed by the RAPT systems in our study lakes is of lesser concern and that the quality of the data is most affected by systematic biases.
The depth of a stationary tag clearly affected the detection quality during the tag trials, but this effect had greater implications for precision than accuracy. The low degree of overlap calculated by the VI should not be a cause for concern because the VI uses three-dimensional space use in its calculation. Even at centre buoy where the shallow tag did not have high overlap with the deeper tags, the absolute difference between the mean software-derived locations for each depth was within ~5 m of each other. On an ecosystem level, an error of 5 m would not have a dramatic impact on space use and home range size. Signals that are transmitted from tags near the surface are likely subject to reflections from the surface waters. Signals in an aquatic environment are analogous to signals travelling down a canyon, where the canyon walls can reflect signals, but in the case of a freshwater or marine system one of the “walls” (the surface of the water) is a dynamic interface affected by wind and other environmental factors . Similar results were obtained by Baktoft et al. , where the authors tested an acoustic telemetry system on two lakes. The depth trials suggest that space use of tagged animals that inhabit the upper water column may be considerably overestimated compared to those living deeper in the water column. Furthermore, detections from the depth trials (Fig. 5, Table 4) show that the presence of a thermocline did not have a negative effect on the acoustic signal; therefore, we did not violate assumptions 2 or 3. In our case, the acoustic signals were unaffected by a thermal barrier, but perhaps the signals may be more sensitive in systems with a chemical barrier or other physical barrier; if so, a separate stationary tag trial may need to be conducted above and below the disturbance to determine whether separate corrections would be required.
For our purposes, we have defined our errors using an absolute measure of error in metres in two dimensions (northing and easting). An additional way to report errors currently in use by VPS is termed horizontal positioning error (HPE). In the framework of HPE, the arrival time of a signal from a transmitter to two receivers defines a branch of a hyperbola; this branch is commonly termed a hyperbolic line of position (LOP). A transmitter can be located along any point of this LOP with the actual transmitter location unknown. In order to calculate a transmitter location, a second hyperbola is calculated from a third receiver. The intersection point of these two LOPs is the location of the transmitter. See Smith  for further details about the hyperbolic positioning sensitivity, especially Figs. 4, 5 and 6. One of the main drawbacks of using HPE is that it should only be interpreted as a unitless estimate of error sensitivity while HPEm (measured horizontal position error estimate in metres) should only be used for informal purposes . The performance of the VPS system was tested in marine, estuary, and riverine environments with median HPEm of 3.3 m and less although system performance was not tested outside of the arrays . In the context of our study, we were able to specifically quantify the positioning error in two dimensions, which allowed us to use the kriging method to create the error maps in Fig. 4. We did not, however, have access to estimates for error sensitivity for our analysis. Although HPE cannot be used for error correction purposes, it does provide researchers information regarding the quality of the detections and can be used to identify areas where more receivers could be placed. Many aquatic species use nearshore areas for breeding and foraging. These areas often have important biological implications, but depending on receiver or RAPT buoy placement, these areas may receive relatively poor coverage, and thus, the error sensitivity (HPE) may be high. The kriging method returns much more informative error information than HPEm because although HPEm returns information relative to the accuracy of a detection it does not provide anything about the directionality of the error. The kriging method can quantify the precision error in two dimensions, which in turn can be used to identify complex habitat or problem areas.
In multi-species systems, researchers may want to monitor more than one species at a time using acoustic telemetry. Different species may have different physiological constraints, and in turn they may need to inhabit different niches within the water column. The depth trials we performed showed that tags detected closer to the surface were subject to “backscattering” issues, which caused higher detection variation. Consider a hypothetical system that contains two distinct species where one is a warm-water-adapted species (species A) and a second cold-water-adapted fish (species B). During periods of stratification when species B is driven deeper into the lake due to metabolic requirements and species A is unaffected, based on our results, data quality from species A would be considerably less, with respect to transmitter precision, than that of species B, and it is likely that energetic estimates would also be overestimated for species A. This type of scenario deserves some consideration when designing a study monitoring species with different habitat and metabolic requirements.
Espeland et al.  suggest that home ranges extending far beyond RAPT triads may be overestimated. While in partial agreement with this statement, we also urge researchers to use caution with this assertion as our results suggest that home ranges can also be underestimated. In our study, the RAPT systems did not have a consistent bias throughout the lake. RAPT systems either incorrectly positioned tags closer to or further from the centre of the triad, but not in a consistent fashion. In addition, RAPT systems are used in both freshwater  and marine systems [27, 28], but it is presently unknown whether RAPT systems deployed in marine systems produce the same patterns of bias that are present in freshwater systems. The method we developed in this paper aims to reduce the effects associated with telemetry errors by increasing the accuracy of the estimated positions and to simultaneously quantify and correct any biases produced by the system. In small lakes like the ones commonly present in the boreal and arctic regions, this underestimation could have a large impact on the ratio of surface area to core space use.
The utilization of a SSM is meant to account for the measurement errors of the detections. In some cases, it became apparent that the measurement errors became more variable along one axis, and in these cases the northing errors were different from the easting errors (e.g. Fig. 3b vs. c). This phenomenon was shown by Espinoza et al.  regarding tag placement inside and outside an array. The pattern detected by their VPS system is very similar to patterns detected by the RAPT systems in our study when transmitters were located far from the centre of the triads. In our study, a normal distribution was used to describe the error structure of the detections in the SSM, but  used a hidden Markov model (HMM) and a t-distribution to model measurement errors (the authors refer to them as observation errors). Although this technique did not address any systematic biases that may have been present, this approach did improve the data (with some residual scattering around the true positions). Perhaps in the future a combination of kriging to address the systematic bias and a t-distribution in a SSM to address the measurement errors may further improve telemetry data by accounting for spatial differences in measurement errors. Although we feel the need to account for measurement errors in RAPT data is relatively low due to the high precision as seen in the stationary tag trials, the fact that this type of data is collected irregularly through time presents yet another statistical challenge for analysis.
The principle of RAPT systems relies on arrival times of acoustic signals from tags to hydrophones. In our system in order for a tag to be positioned, the signal from a tag is detected by three omnidirectional hydrophones, and the arrival times of the acoustic signals are processed and run through “signal-arrival-time” difference equations, which are used to calculate the tag position [28, 29]. Some of the factors that must be taken into consideration in the origin of measurement errors are the speed of sound through water and arrival-time differences . Environmental variables may also contribute to measurement errors. Wind action causes waves, which can distort sound signals and cause anchored buoys to shift from their recorded. In our study, any unrecorded small-scale movement of the hydrophones could potentially add more noise during the signal arrival time, but the method by which the buoys were anchored limited their movement. All telemetry systems are subject to these disturbances; we controlled these variables as much as possible by mooring the buoys solidly. Receiver locations should be chosen to maximize lake coverage while minimizing potential interactions of acoustic signals (e.g. cliffs or large boulders) while continuing to maximize detection probability of the study species.
The kriging methodology proposed in this paper is a simple, yet powerful way to correct systematic errors in acoustic telemetry systems. Though some time and effort must be expended to perform a stationary tag trial in an experimental system, in our opinion the benefits outweigh the costs in order to achieve the most accurate telemetry data for aquatic species that are otherwise difficult to study on a continuous timescale. The results from the kriging analyses are likely to be robust and could be used to correct systematic errors over multiple years. The application of this method affects research areas such as bioenergetics, habitat utilization, and resource use. The ability and flexibility of this method to be used in lakes with one or more RAPT systems should allow other researchers to reduce the influence of problem telemetry data and thus increase the accuracy of inferred fish positions and movement. Regarding our three scenarios of spatial correction, we found that the kriging method had the best performance with regard to spatial correction. On its own, the SSM was not able to identify or compensate for the bias present in our study systems. At this point, it is unknown whether there is any advantage to combining the kriging and SSM solely on the reality that detection quality was not returned with the system presented in this paper. Temporal stability should be further tested by leaving tags at stationary locations for longer periods of time, possibly for the length of the study or just a single year. This would allow researchers to adjust for seasonal effects that were not apparent during the deployment of our tags. Alternately, researchers could conduct multiple short-term trials throughout the year (e.g. 1 week per month); this would yield stationary tag data that are temporally spaced, but would reduce the load on the telemetry system and the effort required on the part of the researcher to process the data.
In closing, we found that the systematic errors were more likely to influence the recorded position of the stationary tags rather than measurement errors. Although SSMs can be used to correct measurement errors, in the context of our study the SSM on its own was not able to compensate for biases introduced by the interaction between the physical environment and the telemetry system. Therefore, we recommend that any future telemetry studies should perform at least a rudimentary stationary tag trial in order to assess the performance of their system. Any such trials should attempt to cover as much of the study area as possible, with multiple stations located within each triad of receivers and many nearshore locations. It is especially important to conduct trials near areas of expected biological importance in order to draw accurate biological conclusions.
CC was involved in data collection, statistical analysis, interpretation of data, and drafting the manuscript. DMG was involved in the conception of the methods developed in this manuscript, revising the manuscript, and interpretation of data. LEH contributed to the design of the experiment, revising the manuscript, and acquisition of data. PJB was involved in study design, conception of the methods, acquisition of data, and revising the manuscript. All authors read and approved the final manuscript.
We appreciate the field support of L. Tate, L. Cruz-Font, F. Bjornson, J. Cederwall, A. Chapelsky, D. Callaghan, M. Guzzo as well as other ELA staff and students. Funding for this study was provided by Fisheries and Oceans Canada, the Experimental Lakes Graduate Fellowship, and IISD Experimental Lakes Area, Inc.
The authors declare that they have no competing interests.
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