Catherine, Princess of Wales, appeared in public on Saturday for the first time since her cancer diagnosis, smiling while riding in a carriage with her three children, as she took part in a ceremonial parade to celebrate the birthday of her father-in-law, King Charles III.

Crowds gathered in central London to watch as the princess and her family participated in an event full of military tradition, music and pageantry, dampened only slightly by a light rain. Her appearance is being welcomed as a sign of improvement in her medical condition and a significant moment for the British royal family, which suffered another blow this year when King Charles announced that he, too, had cancer.

However, when announcing late on Friday that she was well enough to attend events on Saturday, the princess made it clear that her recovery still had some way to go.

“I am making good progress, but as anyone going through chemotherapy will know, there are good days and bad days,” Catherine, 42, said in a statement released to the media. “On those bad days you feel weak, tired and you have to give in to your body resting,” she added. “But on the good days, when you feel stronger, you want to make the most of feeling well.”

Catherine traveled with her three children — Prince George, Princess Charlotte and Prince Louis — in a state carriage to watch the military parade. The princess waved occasionally on the short carriage ride before moving to watch the ceremony from an indoor vantage point. She is also slated to appear on the balcony of Buckingham Palace with the rest of the royal family to watch a Royal Air Force flyby.

Her husband, William, the Prince of Wales, who is colonel of the Welsh Guards, wore their ceremonial uniform and was on horseback. The princess, who is colonel of the Irish Guards, wore a white dress with black trim by Jenny Packham, a hat by Philip Treacy and the Irish Guards Regimental Brooch.