I dealt with this in my MPhil dissertation (1986, University of Hyderabad) . It was written in Telugu. 

I was applying the Paninian approach to case /kaaraka as delineated in  Sādhanasamuddeśa of  Vakyapadiya of  Bhartrhari. 

Usually , Sambandha , the genitive / possessive case is presented as denoted by the 6th case marker. But this is not listed among the conventionally listed six kaarakas. 

But interestingly , Bhartrhari treats this as a kaaraka. 

sāmānyaṃ kārakaṃ tasya saptādyā bhedayonayaḥ /
ṣaṭ karmākhyādibhedena śeṣabhedas tu saptamī // BVaky_3,7.44 //

( copied from the GRETIL website) 

Sādhanasamuddeśa of  Vakyapadiya of  Bhartrhari , after this verse has sections each called  adhikāra dedicated to different kaarakas. 

śeṣa , 'the remainder' is dealt in  śeṣādhikāraḥ

[atha śeṣādhikāraḥ]
saṃbandhaḥ kārakebhyo 'nyaḥ kriyākārakapūrvakaḥ /
śrutāyām aśrutāyāṃ vā kriyāyāṃ so 'bhidhīyate // BVaky_3,7.156 //
dviṣṭho 'py asau parārthatvād guṇeṣu vyatiricyate /
tatrābhidhīyamānaḥ san pradhāne 'py upayujyate // BVaky_3,7.157 //
nimittaniyamaḥ śabdāt saṃbandhasya na gṛhyate /
karmapravacanīyais tu sa viśeṣo 'varudhyate // BVaky_3,7.158 //
sādhanair vyapadiṣṭe ca śrūyamāṇakriye punaḥ /
proktā pratipadaṃ ṣaṣṭhī samāsasya nivṛttaye // BVaky_3,7.159 //
niṣṭhāyāṃ karmaviṣayā ṣaṣthī ca pratiṣidhyate /
śeṣalakṣaṇayā ṣaṣṭhyā samāsastatra neṣyate // BVaky_3,7.160 //
anyena vyapadiṣṭasya yasyānyatropajāyate /
vyatirekaḥ sa dharmau dvau labhate viṣayāntare // BVaky_3,7.161 //
prādhānyaṃ svaguṇe labdhvā pradhāne yāti śeṣatām /
sahayoge svayoge 'taḥ pradhānatvaṃ na hīyate // BVaky_3,7.162 //
[iti śeṣādhikāraḥ]

( copied from the GRETIL website) 

Here, he, very clearly, categorizes sambandha as a kaaraka 

in 

saṃbandhaḥ kārakebhyo 'nyaḥ kriyākārakapūrvakaḥ /
śrutāyām aśrutāyāṃ vā kriyāyāṃ so 'bhidhīyate // BVaky_3,7.156 //

 Deriving from  śrutāyām aśrutāyāṃ vā kriyāyāṃ , I identified  śrutakriyā and aśrutakriyā as terms and concepts and under the influence of Chomskyan ideas , I translated them as ground structure verb and deep structure verb respectively. 

I compared Fillmore's analysis of Genitive in The Case for Case https://linguistics.berkeley.edu/~syntax-circle/syntax-group/spr08/fillmore.pdf 

to this approach.