Scanlogd should be what you are looking for. However, this is TCP oriented.
scanlogd detects port scans and writes one line per scan via the
syslog(3) mechanism. If a source address sends multiple packets to
different ports in a short time, the event will be logged.
For most NMap scans Snort and p0f are both capable IDS. How to Detect NMAP Scan Using Snort is a guide about configuring Snort to detect: nmap -sP -p 22 192.168.1.105
among other scans.
Ping Scan [-sP] This scan type lists the hosts within the specified
range that responded to a ping. It allows you to detect which
computers are online, rather than which ports are open. Four methods
exist within Nmap for ping sweeping.
The first method sends an ICMP ECHO REQUEST (ping request) packet to
the destination system. If an ICMP ECHO REPLY is received, the system
is up, and ICMP packets are not blocked. If there is no response to
the ICMP ping, Nmap will try a "TCP Ping", to determine whether ICMP
is blocked, or if the host is really not online.
A TCP Ping sends either a SYN or an ACK packet to any port (80 is the
default) on the remote system. If RST, or a SYN/ACK, is returned, then
the remote system is online. If the remote system does not respond,
either it is offline, or the chosen port is filtered, and thus not
responding to anything.
When you run an Nmap ping scan as root, the default is to use the ICMP
and ACK methods. Non-root users will use the connect() method, which
attempts to connect to a machine, waiting for a response, and tearing
down the connection as soon as it has been established (similar to the
SYN/ACK method for root users, but this one establishes a full TCP
connection!)
The ICMP scan type can be disabled by setting -P0 (that is, zero, not
uppercase o).
Source
What's the most effective way to detect nmap scans speaks about this further.