Many　sensing　modalities　used　in　robotics　collect　information　in　polar　coordinates.　For　mobile　robots　and　autonomous　vehicles　these　modalities　include　radar,　sonar,　and　laser　range　finders.　In　the　context　of　medical　robotics,　ultrasound　imaging　and　CT　both　collect　information　in　polar　coordinates.　Moreover,　every　sensing　modality　has　associated　noise.　Therefore　when　the　position　of　a　point　in　space　is　estimated　in　the　reference　frame　of　the　sensor,　that　position　is　replaced　by　a　probability　density　expressed　in　polar　coordinates.　If　the　sensor　moves　from　one　location　to　another　and　the　same　point　is　sensed,　then　the　two　associated　probabilities　can　be　＇fused＇　together　to　obtain　a　better　estimate　than　either　one　individually.　Here　we　derive　the　equations　for　this　fusion　process　in　polar　coordinates.　The　result　involves　the　computation　of　integrals　of　three　Bessel　functions.　We　derive　new　recurrence　relations　for　the　efficient　computation　of　these　Bessel-functon　integrals　to　aid　in　the　information-fusion　process.　Copyright　©　2016　by　ASME.