Depersonalizing location traces

Positional information is provided while minimizing the possibility that personally identifiable information can be derived therefrom. Positional information is received in the form of trails that can be aggregated. Individual cells of a grid reflect a quantity of aggregated trails through those cells, an average intensity and direction of movement through those cells, or a more detailed distribution thereof. Alternatively, individual trails are aggregated to an aggregated trail in the form of a line. Further obfuscation of personally identifiable information occurs by resampling aggregated positional information, by introducing false positional information, or by falsely modifying existing positional information, in a manner that does not impact the overall aggregations, and by pruning, or deleting, positional information, especially around sensitive locations, such as a user's home, place of business, or other location that users typically would seek to keep private. Provision of positional information is delayed until a sufficient amount is received.