For　the　networked　linear　switching　system,　a　minimal　conservative　Kalman　filter　design　method　is　proposed　in　the　network　transmission　environment　with　multiple　packet　losses　of　both　measurement　and　switching　signal　packets.　Both　the　measurement　signal　and　the　switching　signal　transmitted　in　the　same　packet　may　be　lost　through　the　network.　The　random　multiple　packet　dropout　phenomenon　is　assumed　to　be　subject　to　the　Bernoulli　random　binary　distribution.　A　novel　Kalman　filter　is　designed　to　estimate　the　state　values　by　minimizing　the　filtering　error　covariance.　Then,　the　desired　Kalman　gain　matrices　are　derived,　which　is　a　novel　switched　Kalman　gain　matrix　containing　a　random　change　of　switching　rate.　In　addition,　the　stability　of　the　Kalman　filter　is　analyzed　in　this　paper.　Finally,　simulation　results　show　the　effectiveness　of　the　proposed　filter.　©　2023　IEEE.