A spontaneous passive alarm system activation - horn honking -

more then likely it's a door ajar switch - not a sensor .
Anti-Theft- Perimeter Alarm System
The perimeter anti-theft system provides for vehicle security through an audible and visual notification if the vehicle's exterior is invaded without the system being shut off. The system self-arms when the doors, liftgate and hood are closed and the key is OFF. Any open door, hood or liftgate will prevent the system from arming. The hood ajar switch, door ajar switches and liftgate ajar switch cause these circuits to register as normally closed circuits. The vehicle security module monitors the status of the hood ajar, door ajar and liftgate ajar switches. If these circuits indicate an open entry point, the switch opens the circuit to the vehicle security module, which energizes the horn and autolamp relays (causing the horn to sound and the lights to flash). The vehicle security module turns off the anti-theft system when it receives a command through the keyless entry keypad, remote keyless entry (RKE) transmitter, or anti-theft alarm inhibit switch.
https://www.youtube.com/watch?v=egIGBzO065U

Replace battery in remote.
Check wires inside of the boot in the door jam (slice hole in boot or pull out of one end. Check wires carefully for bubbles and weak spots from cracking.
Check wires inside door jam or under dash to left hand side carefully with flashlight for bare wires shorting. Feel free to move things around under there a bit to see if things are shorting or what have you.
The fuse box under the hood - inspect underneath of it for corroded wires and or contacts - may take a bit of work to remove it from car.
See if alarm is cleared by using drivers door key as there is a switch in there for the alarm. If this is faulty then this could be your problem beyond the wires in the door jam perhaps.
You have a short or broken wire or this switch in the door is bad.
These are some suggestions of where to start.
Do it in order of easiest but I suggest the door jam wires inside boot is most typical problem especially in colder climates like here in Canada East as the wires freeze and crack after a while.
May or may not be your problem but options.
Let us know with feedback about your progress or solutions plz.

Replace the door ajar switch.

(Inside the drivers door on the door latch is a switch called the door ajar micro switch, it is defective. With no signal from this switch the system triggers the alarm system. You must have this switch input checked, it can be the switch or the wiring to it that is defective.

One honk means all doors are closed. Door ajar you have 2 honks telling you a door is open. My 03 Explorer has had the door ajar light on for awhile

put key in driver door and turn to the left or right, whichever way unlocks the door
the alarm should stop sounding ad the car should start

holdboth the lock and unlosk buttons on your remote simultaneously for about five seconds until the lights flash and horn chirps.that should do it.if not i believe these models used a separate horn for security system.possibly fuse for this horn is bad or the horn itself is bad.to see if this horn works lower drivers window.stand outside vehicle and lock doors with remote.wait about a minute and reach in window and MANUALLY unlock and open door(do not use power door lock button)this should cause the system to activate...horn should beep and headlamps should flash.if horn beeps try my first suggestion.if it doesnt beep and just the head lamps flash check fuses and horn for security system.

try the passenger door again.

YOU MUST UNLOCK DOOR WITH KEY AND NOT BE SO QUICK TO PULL THE DOOR HANDLE

use the key and unlock the trunk...if that doesnt work do the passenger door...that should reset the alarm...