The optimization process and recommendations:

1. Avoid Subqueries (query line: 4): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

ALTER TABLE `positionview` ADD INDEX `positionview_idx_outboun_referen_respons_equipme` (`outbound`,`referenceIdentifier`,`responseType`,`equipmentTimestamp`);

The optimized query:

SELECT
        * 
    FROM
        (SELECT
            DISTINCT 
                ON (iNumber) positionview.equipmentTimestamp,
                positionview.name,
                positionview.iNumber,
                positionview.datauserprovidername,
                positionview.latitude,
                positionview.longitude 
        FROM
            positionview 
        WHERE
            positionview.outbound = false 
            AND positionview.referenceIdentifier IS NULL 
            AND positionview.responseType = 'XYZ' 
            AND positionview.equipmentTimestamp >= '2013-02-09 10:04:14.476' 
            AND positionview.equipmentTimestamp <= '2016-02-12 10:04:14.476' 
        ORDER BY
            positionview.iNumber DESC) AS derivedInnerQuery 
    ORDER BY
        derivedInnerQuery.equipmentTimestamp DESC