class StateVector {
protected:
    float* _v;

public:

    StateVector():_v(new float[size()]) {}
    virtual ~StateVector() { delete [] _v; }

    virtual size_t size() = 0;

    // ...

};

class PositionState : public StateVector {
public:
    size_t size() { return 3; }
    float* x()    { return _v; }
};

class MovingState : public PositionState {
public:
    size_t size() { return PositionState::size() + 3; }
    float* v()    { return _v + PositionState::size(); }
};

template <typename State>
class StateTransition {

    Matrix<float> _m;

    // constructor for Matrix takes #rows, #cols
    StateTransition():_m(State().size(), State().size()) {}

    // ...

};

class StateVector {
    float* _v;
    StateVector:_v(new float[size()]) {}

    virtual static size_t size() = 0;
};

class PositionState {
    static size_t size() { return 3; }
    // ...
};

// etc.

template <typename State>
class StateTransition {

    Matrix<float> _m;

    StateTransition():_m(State::size(), State::size()) {}
};