A small group of alien biologists and scientists land on earth. They want to study us earthlings and our culture, society, etc. But they do not want to interfere with us, so they have to come up with a way to be able to study us up close without being noticed by us. But these aliens do not have cloaking devices small enough to be used on anything other than ships. What technology could they use to go unnoticed by the human population?
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Without even advanced tech, there are billions of cameras recording the public, billions of phone conversations going on, and no telling how many stored videos easily available for every kind of human interaction (including every form of sex, fighting, talking, humor, etc).
Internal cameras surveil inside of buildings, workplaces, prisons, etc. Tapes are stored for years.
No matter what the aliens look like, they can watch anything from a dog's birthday party (filmed on the corner of my residential block) to sex to somebody literally being beaten to death. Or a board meeting, if you want that. Or Congress, or sports, or an actual autopsy in medical school.
It depends on the aliens; if the are visually similar to humans(or their technology allows them to do so), they could hide in plain sight using disguises; if not, they could set up potentially set up remote surveillance which they could monitor from a safe place.
If they don't need to be directly there, they could hack into our networked devices (Smartphones, webcams, Google Home/Amazon Echo equivalents etc.) or simply connect to the internet, many people put a surprising amount about their life online for anyone to see.
As an extraterrestrial visitor and xenoanthropologist, I have had some success in this matter.
My people look like miniature haystacks, about 10 cm wide and 4 cm high, in various colors of red, brown, tan, and white. I personally am a sort of pale yellow. We usually eat only at long intervals, but between meals we can wave our tendrils around and draw some nourishment from the air. We are spread quite thin over the populated worlds and there are fewer than a dozen of us on Earth.
When I first arrived I mostly watched people at a distance, from static blinds, usually on a window ledge or in a tree. For the first three years I didn't dare move except on Hallowe'en. During the fourth year a pair of bluejays made a nest in me. My advisor came 850 light-years to see if I was still alive.
Then I accidentally discovered that sometimes when I touch a human, I can influence his decisions and behavior. I'm not sure, but I suspect it eventually destroys the human's attention span. I don't know what my ethics committee would make of that because I haven't told them yet.
For the last twenty years I've been riding around on this guy's head and observing you all up close. I've made him take me everywhere, business negotiations, board meetings, we've been on TV, Jimmy Fallon, Charlie Rose -- I have so much data I'll be writing books for years.
You'd think somebody would notice a haystack alien riding on the head of a public figure, but so far I'm getting away with it. You Earth peoples is so dumb.
Not to be too simplistic, but humans are a noisy bunch...
We've been throwing electromagnetic energy into space for quite a few decades now. Radio, TV, Internet, Satellite, Microwave, X-ray, you name it, it's still propagating out there in the great void.
They would only need to setup a few receiving dishes in various locations covering different frequencies, and they could tap into pretty much most of the history of the human race, especially if they managed to link into the internet and/or have an FTL drive.
Sending a stealthy drone in to add a transmissions link onto one or more satellites would give them said internet access.
To be honest, overcoming the language barrier again, and again, and again would probably be more challenging than tapping into our signals, at least until they figured out the dictionary apps we've already made.
Step 1 The aliens take a look at the encryption protecting our banking systems. Once they stop laughing, they make themselves squillionaires.
Step 2 They use their new wealth to get into real estate. Working through proxies (law firms and real estate agents) they buy apartment buildings, offices, shopping malls, hotels, schools, creches.
Step 3 They use their UltraExtremeNoLimit credit card to buy millions of smoke detectors etc. & use their ship-board 3d printer to add their alien science snooper sensors. This is a lot of work, but hey, grad students!
Step 4 They re-package the modded products and have their real estate corps maintenance crews install them everywhere.
Step 5 Their paper to the Intergalatic Social Sciences journal has a squillion byte appendix detailing every moment of the lives of 300M earthlinks is rejected by all referees as being unsupported by sufficient data.
Even if a cloaking device is so large that it needs to be housed in a structure as large as a ship, they could still build that large device on the ground (bringing in parts via transporter, cloaked shuttle craft, or building it in the middle of nowhere and then tunneling to where they need to be to observe).
This is was what the Federation did in the Star Trek episode Who Watches The Watchers -- they built an observation post hidden by a holographic wall (and then the holographic generator failed, exposing the observation team, so make sure you have a backup cloaking device).
Biological Robot Bugs and Other Creepy Crawlies
Bugs of some sort already exist in nearly every habitat Earthlings are found. They are small, many equipped with antennae already, and lots can fly, providing great 360 measuring opportunity. They are light enough that when the Earthlings are sleeping, they can even touch and travel around on them without detection; some are designed to live on or inside them even. That is about as up close as could be desired.
Unique modifications can even work to get added niche "interaction" without being perceived as interaction: lightning bugs encourage juvenile Earthlings to capture them and provide entry into homes in a jar for good vantage point (no need to hide to escape destruction), ants in an "ant farm" will also have a good in the home view, honey bee hives nurtured by bee farmers are a great cover for field work on gardeners and farmers, and leeches can join the medical science community by offering wound healing opportunities as a nifty way to study living blood cells and other body defenses.
And have you ever noticed how the dragonflies actually try to get our attention with their teasingly close in/dart away tactics? Very effective.