DeadReckoning: Calculates Dead Reckoning
In TrackReconstruction: Reconstruct Animal Tracks from Magnetometer, Accelerometer, Depth and Optional Speed Data

Description Usage Arguments Details Value Author(s) References Examples

This function takes triaxial magnetometer, accelerometer and optional speed data to estimate the path traveled (pseudotrack) by a tagged animal based on Wilson et al. (2007).

1 2	DeadReckoning(rawdata, betas, decinc, Hz = 16, RmL = 2, DepthHz = 1, SpdCalc=1, MaxSpd=NULL)

`rawdata`	matrix or data frame of magnetometer and accelerometer with column headings specified in Details.
`betas`	matrix or data frame of coefficients (slope and intercept) that standardizes magnetometer and accelerometer data between -1 and +1. This can come from the `Standardize` function.
`decinc`	vector of c(Declination, Inclination) values in decimal degrees format in that order.
`Hz`	frequency of data collection in Hz of magnetometers. The assumption here is that the accelerometer Hz is at least as high as the magnetometers and that all the magnetometer channels have the same Hz. See Details.
`RmL`	Running mean length in seconds, required to separate "dynamic" and "static" acceleration.
`DepthHz`	Frequency of data collection in Hz of Depth channel.
`SpdCalc`	Integer of value 1,2,3 or 4 (5 and 6 are unsupported) depending on type of speed data supplied, see details.
`MaxSpd`	If `SpdCalc`=3, the max speed of your animal in m/s. If `SpdCalc`=4, the constant speed of your animal in m/s.

Rawdata must have columns DateTime or separated as Date and Time, plus Depth, MagSurge, MagHeave, MagSway, AccSurge, AccHeave, AccSway and optional Speed in a data frame with those exact column names (Mag=Magnetometer and Acc= Accelerometer). It must have an extra number of rows =Hz*RmL*0.5 at beginning and end that will be trimmed on final output. Because some users may program tags to collect acceleration data at a higher Hz than magnetometer data (for example when looking for a Jerk signal), the DeadReckoning function automatically subsets the data set to those samples (rows) that do NOT have "NA" in the MagSurge column.

Betas is a [2,6] data frame with intercept in the first row and slope in the second row and can be directly taken from Standardize function output or user input. If you do not use the output of the Standardize function, the row names must be c("B0 Intercept","B1 Slope") and the column names must be c("MagSurge","MagHeave","MagSway","AccSurge","AccHeave","AccSway") though the order is not important. See the help on the Standardize function for more information.

Declination and inclination data can be found at various internet sites such as the World Magnetic Model 2010 Calculator from the British Geological Survey (see references).

RmL-please read Shepard et al.(2008) and perhaps Wilson et al.(2007) for information on an appropriate Running Mean Length for your data and study animal.

SpdCalc
=1 if Speed is supplied in rawdata at the same Hz as Acc and Mag Hz in m/s.
=2 if Speed is supplied in m/s but at Hz lower than Acc and Mag.
=3 if no speed is supplied and should be estimated from integrating (a running sum) the dynamic portion of the surge channel of acceleration and normalized using a linear model to meters/second from 0 to your max speed (MaxSpd) input.
=4 a constant speed is assumed which is entered as the MaxSpd.
=5 if no speed is supplied and should be estimated from accent and decent rates. ***Not yet implemented.***
=6 if speed is to be calculated from sound data. ***Not yet implemented***

data.frame with columns DateTime, Xdim, Ydim, Depth and Speed. DateTime is the data and time columns pasted together using as.character. Xdim and Ydim are cartesian coordinates from the origin in meters. Depth has been linearly interpolated from initial Depth Hz to Magnetometer Hz and Speed is either that supplied by the user or calculated via one of the methods outlined above.

Brian Battaile

One possible source for declination and inclination data http://www.geomag.bgs.ac.uk/data_service/models_compass/wmm_calc.html

Wilson R.P., Liebsch,N., Davies,I.M., Quintana,F., Weimerskirch,H., Storch,S., Lucke,K., Siebert,U., Zankl,S., Muller,G., Zimmer,I., Scolaro,A., Campagna,C., Plotz,J., Bornemann,H., Teilmann,J. and Mcmahon,C.R. (2007) All at sea with animal tracks; methodological and analytical solutions for the resolution of movement. Deep-Sea Research II 54:193-210

Shepard E.L.C., Wilson, R.P., Halsey, L.G., Quintana, F., Laich, A.G., Gleiss, A.C., Liebsch, N., Myers, A.E., Norman, B. (2008) Derivation of body motion via appropriate smoothing of acceleration data. Aquatic Biology 4:235-241

#A simple square example
betas<-Standardize(1,1,1,1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1)
data(square)
decinc<-c(0,65)
DRoutput<-DeadReckoning(square,betas,decinc,Hz=1,RmL=2,DepthHz=1,SpdCalc=1)
plot(DRoutput$Ydim,DRoutput$Xdim)

#Standardize tag output
betas<-Standardize(1,1,-1,1,1,1,-57.8,68.76,-61.8,64.2,-70.16,58.08,
-10.1,9.55,-9.75,9.72,-9.91,9.43)
#Declination and inclination data for study area
decinc<-c(10.228,65.918)
#data set with 7 associated GPS fixes in the "gpsdata02" data set
data(rawdata)
DRoutput<-DeadReckoning(rawdata,betas,decinc,Hz=16,RmL=2,DepthHz=1,SpdCalc=3,MaxSpd=3.5)
plot(DRoutput$Ydim,DRoutput$Xdim)

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