feature temporal ordering

We want to establish which features preceed the spike and are hence relevant for forecast

inter feature persistance

We want to check which features are phased together. At first we calculate a correlation on a rolling window of a short period of 16 seconds

correlation_rolling correlation on a rolling window

Than we iterate over all features to understand which is the most temporarly correlating, we clearly see that most of the feature don’t have a window correlation while vehicle ping does

sync_violin violin plot of correlation distribution

Apart from the trivial correlations we see that the networking features are the ones most correlating

sync_correlation window correlation of features

If we look at the cross correlation with time delay we see again that vehicle_ping has the most persistent temporal correlation with latency. We realize that the upsampling creates artificial fluctuations every neighbouring second

sync_xcor cross correlation with delay

From the cross correlation we can compute the decay time

sync_decay exponential regression on the decay

We calculate for each feature a decay time

sync_decay regression on decays

and calculate the persistance as the sum of the decay curve over the decay interval

sync_persistance persistance among features

We than iterate over all features and calculate the cross and auto persistance. Large values singalize a bad sampling (artificial similarity)

sync_persistanceM matrix of persistance among features

We can calculate the persistance for other data sets

modem_persistance persistance for modem features

We now calculate the peak at the maximum cross correlation delay, smoothing is necessary to remove artefacts

sync_peak peak at the maximum cross correlation delay

Not all phase calculations lead to reasonable results, we see that many phase lag estimations are inconclusive, either null or fluctuating a lot. We are pretty cofindent that over the hundrets of spike events in general few features can anticipate the spike

sync_previous features with a negative time delay compared to camera latency

Data are pretty noisy and we want to establish temporal sorting for at least the average of all the spike events

phase_lag phase lag between features

We can roughly say that rtp and joystick features happen before the camera spike

phasing

We want to calculate the average delay between features using the cross correlation of two features. In some cases on feature is clearly reacting to the spike

delay_ram delay between camera latency and rtp_lost

In some cases the analysis is inconclusive

delay_ram delay between camera latency and camera_jitter

Some features anticipate the spike but there is still some lower modus where they happen later

delay_ram delay between camera latency and joystick

In other cases the features are completely connected

delay_ram delay between camera latency and modem_rtt

Different methods lead to similar results

delay_compare compare delay methods

For some series (deci seconds on bytes-Cellular 3) the different methods disagree on phases

delay_compare compare delay methods

If we smooth the time series we see a clear trend

modem_smooth smoothing the time series

and althought the phase calculation should be more clear methods differ in results

modem_phase estimation of phase for smoothed features

We than calculate the phase difference using cross correlation and looking at the camera latency we conferm the euristic impression that josystick_latency and vehicle_cpu happen before the spike and room_ram, vehicle_ram, force_lon, brake_pressure after. modem_tx is slghtly before the spike.

delay_fourier delay between features using cross correlation phase difference

On the deci second scale the modem features are clearly preceeding the spike. Arrival time is really noisy and shouldn’t be considered. Bytes are clearly preceeding the spike

delay_fourier delay between features using cross correlation phase difference

We want to calculate now the phasing for each time series

series_dot each series has slightly different data points

What works for the denoised time series doesn’t work for the sum of the single series where the determination of the phase difference is pretty chaotic

spike_offset phase difference between camera latency and other features

The same for the deci second dataset

spike_offset phase difference between camera latency and other features

Time lag between modem features and camera_latency

modem_lag time lag for modem features

We clearly see in average when which features preceed the latency and which follow, basically the round trip time is slower than the latency calculation while the signal is more advanced

modem_lagM time lag for modem features