The Internet of Things (IoT) requires proximity intelligence for many of its applications, especially for identification and locating. Passive radio frequency identification (RFID) locating beyond centimeter accuracy is highly desirable to enable advanced motion tracking, accurate robotic feedback, and gesture recognition. In the conventional RFID system, since the reader-to-tag (downlink) and tag-to-reader (uplink) signals overlap on the same carrier frequency, the self-jamming problem caused by strong leakage signals from the transmitter to the receiver is notorious and poses many constraints on the received signal quality, operation bandwidth, modulation flexibility and system complexity. We show that harmonic backscatter locating is more effective than the conventional backscatter by exploiting nonlinear elements in passive devices to generate second or higher-order harmonics as the uplink response. Separation of downlink and uplink on different carriers allows immediate self-jamming cancellation and direct un-modulated carrier phase decoding, which bring better received signal quality and broad bandwidth of operation, both of which are critical for the locating system. We take advantage of a hardware and software co-design approach and resolve ambiguous phase cycles with heuristically optimized sparse carrier frequencies in the proposed heuristic multifrequency continuous wave (HMFCW) ranging algorithm. We designed a 3D real-time locating system for passive devices based on the harmonic backscatter concept which achieved a measured median error less than 3.5cm with repetitious evaluations in different indoor environments. We further embrace three different diversities: spatial diversity, frequency diversity and time diversity. By exploiting time diversity, we show that the error tolerance can be greatly enhanced to tolerate strong body motion interference, which is critical for many indoor scenarios. With the help of frequency diversity, we show that the antenna size can be greatly reduced and millimeter accuracy indoor ranging can be reliably achieved even with miniaturized low-directivity antennas. By jointly embracing spatial diversity provided by the low-cost passive RFID tags and frequency diversity provided by the broadband harmonic backscatter, we demonstrate ubiquitous tagless objects locating with centimeter accuracy even for small objects which cannot be easily detected by conventional RF systems.