Multiple checkbox results with Ajax instead of button submit

This works on the first checkbox only.

        <input type="checkbox" id="check-filter" name="filter[]" value="<?php echo $filter['filter_id']; ?>" checked="checked" />
        <?php echo $filter['name']; ?>
        <?php } else { ?>
        <input type="checkbox" id="check-filter" name="filter[]" value="<?php echo $filter['filter_id']; ?>" />
        <?php echo $filter['name']; ?>

$('#check-filter').on('click', function() { filter = [];

$('input[name^=\'filter\']:checked').each(function(element) {
    filter.push(this.value);
});

location = '<?php echo $action; ?>&filter=' + filter.join(',');

});