16 Correlating Telemetry Traces

We can use a cross-correlation function to try to identify the extent to which traces are similar across drivers. The approxfun() estimator does a very simple interpoloation between consecutive values in the original dataset, which means that actual telemetry data values are pinned in the prediction model and used for local estimation.

ts_estimator = function(df, x, y, points){
  estimator_ = approxfun(df[[x]], df[[y]])
  estimator_(points)
}

We can use this function to estimate different properties from the time series telemetry data.

ogier_speed_est = ts_estimator(trj_ogier, "cum_dist", "speed", segments)

## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## collapsing to unique 'x' values

evans_speed_est = ts_estimator(trj_evans, "cum_dist", "speed", segments)

## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## collapsing to unique 'x' values

speed_correlation_ogier_evans =  ccf(ogier_speed_est, evans_speed_est)

speed_correlation_ogier_evans

## 
## Autocorrelations of series 'X', by lag
## 
##    -19    -18    -17    -16    -15    -14    -13    -12    -11    -10     -9 
##  0.111  0.140  0.072  0.065 -0.027 -0.026  0.007 -0.020  0.006 -0.087 -0.051 
##     -8     -7     -6     -5     -4     -3     -2     -1      0      1      2 
## -0.013 -0.027 -0.079 -0.010  0.015  0.080  0.273  0.487  0.929  0.509  0.328 
##      3      4      5      6      7      8      9     10     11     12     13 
##  0.080  0.030  0.036 -0.008 -0.001  0.031 -0.028 -0.167 -0.055 -0.073 -0.015 
##     14     15     16     17     18     19 
## -0.052 -0.009  0.088  0.073  0.125  0.087

We can report on the correlation at different lags by using the lag value as an index value:

lag = 0

speed_correlation_ogier_evans[lag]

## 
## Autocorrelations of series 'X', by lag
## 
##     0 
## 0.929

Brake cross-correlation:

ogier_brk_est = ts_estimator(trj_ogier, "cum_dist", "brk", segments)

## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## collapsing to unique 'x' values

evans_brk_est = ts_estimator(trj_evans, "cum_dist", "brk", segments)

## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## collapsing to unique 'x' values

ccf(ogier_brk_est, evans_brk_est)

It occurs to me that if we use a high resolution sample, for example at the level of 1m, we might be able to detect consistent areas where one driver brakes sooner than another. This may be hard to spot in rally telemetry, but it may be something observable in circuit races over many laps of the same circuit.