Illumina is pursuing mitochondrial DNA (mtDNA) sequencing. An advantage here is that cells contain many copies of mtDNA sequences (as opposed to just one copy of each gDNA haplotype), and mtDNA contains hyper-variable regions which confer strong individual specificity. This is potentially advantageous in crime scene samples, where the DNA could be damaged through degradation processes like sun exposure. http://www.illumina.com/areas-of-interest/forensic-genomics/...
Ion Torrent/ThermoFisher are going after the same STR targets, but using their Torrent and Proton NGS platforms (rather than PCR). Unlike regular PCR methods, this can provide things like allele frequency estimates, and can call more than one base into variable regions (which provides more information, and can potentially be used to infer things like height, ethnicity, hair or eye color). https://www.thermofisher.com/us/en/home/industrial/human-ide...
Carlos Bustamante (a Stanford Professor, and world expert in ancient genomics / diverse population genomics: https://med.stanford.edu/profiles/carlos-bustamante) has founded IdentifyGenomics, which is a startup focused on new methods for forensic DNA sequencing (disclosure: I know Carlos, but I'm not involved in his startup).
Definitely an important problem, and will be interesting to who succeeds in converting forensic investigators to use NGS at scale.