Development of mobile communication and sensing technologies forms location based big data, bringing revolution to human's living, business pattern and scientific research. Diversity of usage patterns and redundancy among various sources of location based big data make it impossible for classical location preservation methods to protect privacy systemically. Privacy preservation for location based big data measures user's location privacy in all possible aspects and therefore protects user's privacy in information theory semantic. Starting with an introduction to the concept of location based big data, its associated privacy threats and a universal measurement-based attack model, this paper surveys the state of the art of privacy preservation techniques for location based big data. Based on different privacy protecting strength, various big privacy preservation techniques can be categorized into heuristic privacy measurement, probability deduction and private information retrieval based technologies. The principles, mechanisms and characteristics of various techniques are described in detail, with special emphasis on a proceeding research topic: Private information retrieval based technology. Following a comprehensive analysis and comparison of existing techniques, privacy protecting for location based big data under situations like combination of location information and non location information and attacker's arbitrary background knowledge is highlighted as future research directions.