<PAGE>   1
                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549


[X]         QUARTERLY REPORT PURSUANT TO SECTION 13 or 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

For the Quarterly Period Ended      September 30, 1998
                                ------------------------------

                                       OR

[ ]         TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

For the transition period from                to
                               --------------    -------------

Commission file number              0-21682
                       ---------------------------------------

                                  SPARTA, Inc.
       -------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

           Delaware                                          63-0775889
  -------------------------------                         -----------------
  (State or other jurisdiction of                         (I.R.S. Employer)
  incorporation or organization)

       23041 Avenida de la Carlota, Suite 325, Laguna Hills, CA 92653-1595
       -------------------------------------------------------------------
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (949) 768-8161
       -------------------------------------------------------------------
              (Registrant's telephone number, including area code)

                                 Not Applicable
       -------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act or 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports) and (2) has been subject to such filing
requirements for the past 90 days.

Yes    x         No
     -----            -----

As of October 4, 1998, the registrant had 5,683,537 shares of common stock, $.01
par value per share, issued and outstanding.




<PAGE>   2


                                  SPARTA, Inc.

            QUARTERLY REPORT FOR THE PERIOD ENDED SEPTEMBER 30, 1998

                                      INDEX


PART I  FINANCIAL STATEMENTS

ITEM 1  Quarterly Financial Statements

        Statements of Income for the Nine Months Ended September 30, 1998
        and September 30, 1997 (Unaudited)

        Balance Sheets as of September 30, 1998 and December 31, 1997
        (Unaudited)

        Statement of Cash Flows for the Nine Months Ended September 30, 1998 and
        September 30, 1997 (Unaudited)

        Notes to Consolidated Financial Statements (Unaudited)

ITEM 2  Management's Discussion and Analysis of Financial Condition and Results
        of Operations

PART II OTHER INFORMATION

SIGNATURE

EXHIBIT 11  Computations of Earnings per Share



<PAGE>   3

                                     PART I
                              FINANCIAL STATEMENTS



CONSOLIDATED STATEMENT OF INCOME
         (UNAUDITED)

<TABLE>
<CAPTION>

                                   THREE MONTHS ENDED SEPTEMBER 30    NINE MONTHS ENDED SEPTEMBER 30
                                   --------------------------------  --------------------------------
                                        1998             1997             1998             1997
                                   ---------------  ---------------  ---------------  ---------------
<S>                                <C>              <C>              <C>              <C>
SALES                                 $24,169,000      $23,408,000      $70,763,000      $63,519,000
                                   ---------------  ---------------  ---------------  ---------------
COSTS AND EXPENSES:

  Labor costs and related
     benefits                          14,100,000       12,316,000       38,637,000       33,342,000

  Subcontractor & other costs           5,824,000        7,121,000       18,406,000       17,271,000

  Facility costs                        1,798,000        1,620,000        5,434,000        5,157,000

  Travel and other                        515,000          328,000        2,199,000        2,068,000

  Interest expense, net                    58,000           26,000          256,000          134,000
                                   ---------------  ---------------  ---------------  ---------------

                                       22,295,000       21,411,000       64,932,000       57,972,000
                                   ---------------  ---------------  ---------------  ---------------

INCOME BEFORE PROVISION FOR
  TAXES ON INCOME                       1,874,000        1,997,000        5,831,000        5,547,000

PROVISION FOR TAXES ON INCOME             787,000          839,000        2,449,000        2,330,000
                                   ---------------  ---------------  ---------------  ---------------

NET INCOME                            $ 1,087,000      $ 1,158,000      $ 3,382,000      $ 3,217,000
                                   ===============  ===============  ===============  ===============

BASIC EARNINGS PER SHARE              $      0.20      $      0.15      $      0.48      $      0.42
                                   ===============  ===============  ===============  ===============

DILUTED EARNINGS PER SHARE            $      0.16      $      0.14      $      0.45      $      0.39
                                   ===============  ===============  ===============  ===============
</TABLE>





* EARNINGS PER SHARE AMOUNTS PRESENTED FOR PRIOR YEARS HAVE BEEN RESTATED IN
  ACCORDANCE WITH STATEMENT OF FINANCIAL ACCOUNTING STANDARDS NO. 128, "EARNINGS
  PER SHARE".



    The accompanying notes are an integral part of the financial statements


<PAGE>   4

CONSOLIDATED BALANCE STATEMENT
         (UNAUDITED)

<TABLE>
<CAPTION>
                                                   SEPTEMBER 30        DECEMBER 31,
                                                       1998                1997
                                                  ----------------    ----------------
                                                    (Unaudited)          (Audited)
<S>                                              <C>                  <C>
ASSETS

CURRENT ASSETS
  Cash                                                $   178,000         $   198,000
  Accounts receivable                                  18,941,000          23,557,000
  Prepaid expenses                                        503,000             448,000
                                                  ----------------    ----------------
    TOTAL CURRENT ASSETS                               19,622,000          24,203,000

  Equipment and improvements, net                       9,049,000           7,321,000
  Other assets                                          2,000,000           1,685,000
                                                  ----------------    ----------------
    TOTAL ASSETS                                      $30,671,000         $33,209,000
                                                  ================    ================


LIABILITIES AND STOCKHOLDERS' EQUITY
CURRENT LIABILITIES
  Accrued compensation                                $ 4,726,000         $ 5,723,000
  Accounts payable and other accrued expenses           1,043,000           3,005,000
  Current portion of notes payable                        433,000             477,000
  Income tax payable                                           --             199,000
  Deferred income taxes                                 2,708,000           2,446,000
                                                  ----------------    ----------------
    TOTAL CURRENT LIABILITIES                           8,910,000          11,850,000

NOTES PAYABLE                                                  --           2,658,000
SUBORDINATED NOTES PAYABLE                                328,000             646,000
DEFERRED INCOME TAXES                                     828,000           1,677,000

Commitments and contingencies

REDEEMABLE PREFERRED STOCK
  Preferred stock, $.01 par value; 2,000,000
  shares authorized; 569,039 and 569,039 
  shares issued and outstanding                         4,604,000           3,926,000

STOCKHOLDERS' EQUITY
  Common stock, $.01 par value, 25,000,000
  shares authorized; 13,692,211 and 13,070,700 
  shares issued                                           137,000             131,000
  Additional paid-in capital                           30,909,000          26,340,000
  Retained earnings                                    27,857,000          25,152,000
  Treasury stock                                     (42,902,000)        (39,171,000)
                                                  ----------------    ----------------
    TOTAL STOCKHOLDERS' EQUITY                         16,001,000          12,452,000
                                                  ----------------    ----------------

TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY           $ 30,671,000        $ 33,209,000
                                                  ================    ================
</TABLE>





    The accompanying notes are an integral part of the financial statements


<PAGE>   5

CONSOLIDATED STATEMENT OF CASH FLOWS
           (UNAUDITED)

<TABLE>
<CAPTION>
                                                            NINE MONTHS ENDED SEPTEMBER 30
                                                         -------------------------------------
                                                               1998                1997
                                                         -----------------    ----------------
<S>                                                         <C>                 <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net Income                                                   $3,382,000          $3,217,000
  Adjustments to reconcile net income to net 
    cash provided by operating activities:
      Depreciation and amortization                               960,000           1,134,000
      Loss on sale of equipment                                    19,000             105,000
      Employee compensation paid in stock                       2,382,000           1,690,000
      Changes in assets and liabilities:
        Accounts receivable                                     4,132,000           (245,000)
        Prepaid expenses                                         (55,000)              11,000
        Other assets                                              168,000           (137,000)
        Accrued compensation                                    (998,000)           1,227,000
        Accounts payable and other accrued expense            (1,961,000)         (1,388,000)
        Income taxes payable/receivable                            63,000           (393,000)
        Deferred income taxes                                   (847,000)           (849,000)
      Tax benefit relating to stock plan                          404,000              84,000
                                                         -----------------    ----------------
          NET CASH PROVIDED BY OPERATING ACTIVITIES             7,649,000           4,456,000
                                                         -----------------    ----------------

CASH FLOWS FROM INVESTING ACTIVITIES:
    Capital expenditures                                      (2,707,000)         (2,178,000)
                                                         -----------------    ----------------
          NET CASH USED IN INVESTING ACTIVITIES               (2,707,000)         (2,178,000)
                                                         -----------------    ----------------

CASH FLOWS FROM FINANCING ACTIVITIES:
  Proceeds from issuance of stock                               1,789,000           1,622,000
  Cash purchases of treasury stock                            (3,731,000)         (3,785,000)
  Net (repayments) proceeds line-of-credit agreement          (2,658,000)             802,000
  Principal payments on debt                                    (362,000)           (886,000)
                                                         -----------------    ----------------
          NET CASH USED IN FINANCING ACTIVITIES               (4,962,000)         (2,247,000)
                                                         -----------------    ----------------

NET DECREASE IN CASH                                             (20,000)              31,000
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                  198,000             151,000
                                                         -----------------    ----------------
CASH AND CASH EQUIVALENTS AT END OF PERIOD                        178,000             182,000
                                                         =================    ================

SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION: 
  Cash paid during the period for:
    Interest                                                  $   266,000         $   134,000
                                                         =================    ================
    Income taxes                                              $ 3,235,000         $ 3,494,000
                                                         =================    ================

</TABLE>



    The accompanying notes are an integral part of the financial statements



<PAGE>   6

                                  SPARTA, INC.

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                   ------------------------------------------
                                   (Unaudited)


NOTE A - BASIS OF PRESENTATION
------------------------------

The accompanying financial information has been prepared in accordance with the
instructions to Form 10-Q and therefore does not necessarily include all
information and footnotes necessary for a fair presentation of financial
position, results of operations and cash flows in conformity with generally
accepted accounting principles.

The Company's fiscal year is the 52 or 53 week period ending on the Friday
closest to December 31. The Company's last fiscal year ended on January 2, 1998;
and, its third quarter ended October 4, 1998 and corresponding third quarter
last year on October 3, 1997. To aid the reader of the financial statements, the
year end has been presented as December 31, 1997 and the quarters and nine
months ended September 30, 1997 and September 30, 1998.

In the opinion of management, the unaudited financial information for the
nine-month periods ended September 30, 1998 and September 30, 1997 reflects all
adjustments (which include only normal, recurring adjustments) necessary for a
fair presentation thereof.

NOTE B - RECEIVABLES
--------------------

Unbilled accounts receivable include $1,778,000 of costs incurred on projects
for which the Company has been requested by the customer to begin work under a
new contract or extend work under a present contract, but for which final
contract negotiations or formal contracts or contract modifications have not
been executed at September 30, 1998.

NOTE C - INCOME TAXES
---------------------

Income taxes for interim periods are computed using the estimated annual
effective rate method.







<PAGE>   7

ITEM 2.   MANAGEMENT'S DISCUSSION AND ANALYSIS
          ------------------------------------
          OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS
          ------------------------------------------------

The Management Discussion and Analysis of Financial Condition and Results of
Operation contains forward-looking statements that involve risks and
uncertainties. The Company's actual results may differ significantly from
projections contained in forward-looking statements. For a more complete
discussion of the factors which could cause such a difference, the Company's
Form 10-K for the year ended December 31, 1997, should be consulted.

The following table sets forth, for the periods indicated, selected financial
results from the Company's continuing operations and audited Financial
Statements.

RESULTS OF OPERATIONS
<TABLE>
<CAPTION>
                                 Three months ended September 30,  Nine months ended September 30,
                                 -------------------------------- --------------------------------
                                     1998             1997             1998            1997
                                 --------------  ---------------  ---------------  --------------
<S>                                <C>            <C>               <C>              <C>
  Sales                             24,169,000       23,408,000       70,763,000      63,519,000
  Gross profit (1)                   2,231,000        1,967,000        6,543,000       5,919,000
  Gross profit as a % of costs          10.17%            9.17%           10.19%          10.28%
  Net income (2)                     1,087,000        1,158,000        3,382,000       3,217,000
  Number of staff                          699              610              699             610
</TABLE>

<TABLE>
<CAPTION>
                                                                    Balance at
                                                 ------------------------------------------------
                                                 September 30,    December 31,     September 30,
                                                      1998             1997            1998
                                                 ---------------  ---------------  --------------
<S>                                               <C>               <C>              <C>
  Funded 12 month backlog                            33,000,000       29,900,000      37,500,000
  Total 12 month contract
    backlog                                         105,200,000       93,200,000      92,200,000
  Stockholders equity                                16,001,000       12,452,000      12,032,000
  Equity per share (3)                                     2.58             1.89            1.92
  Stock repurchase notes                                761,000        1,123,000       1,255,000
  Line of credit                                             --        2,658,000       1,263,000
  Number in days sales in
    receivables                                              75               93              83
  Current ratio                                             2.4              2.1             2.0
</TABLE>



(1) The Company defines gross profits as sales less costs and expenses excluding
    interest costs and certain expenses which cannot be billed to its 
    government customers.
(2) Prior to adjustments for interest and accretion on stock - See Exhibit 11.
(3) Equity per share based on weighted shares of common stock outstanding for
    period ending, including weighted shares of preferred stock outstanding.


REVENUES

The Company's contract revenues for the third quarter were up 3.3% from the
corresponding three month period in 1997. Third quarter sales of $24,619,000
were the highest quarterly total in the Company's history. Profitability for the
three month period ended September 30, 1998 was up 13.4% when compared to the
corresponding period of 1997. Profitability as a percent of costs increased from
9.17% to 10.17% for the corresponding period in 1998. Borrowings against the
Company's line of credit were zero as of the end of the 3rd quarter compared to
a borrowing level of $1,262,000 at the end of the corresponding period in 1997.
The Company has been successful in reducing its days sales from 80 days at June
30, 1998 to 75 days at September 30, 1998. Reduced spending for capital and IR&D
projects as well as improvement in days sales outstanding in the second half of
the year has contributed to this reduction in borrowing requirements.




<PAGE>   8

NEW CONTRACTS AND ANNUALIZED BACKLOG

During the third quarter, the Company reversed roles with the small business
prime contractor on the Range Facilities and Information Support Services
(RF&ISS) contract at NASA Dryden. As the new prime contractor on this program,
the Company's Technical Services Operation (TSO) will gain a small increase in
sales this fiscal year, but a large increase in sales over the next three years
(about $9,000,000 increase per year). The International Systems Operation (INSO)
won a competitive bid with the Army's Missile Systems Intelligence Command
(MSIC) for the Laboratory Operation Support (LOS) contract. This is a
$43,000,000 contract over five years. Backlog increases were experienced on
several existing contracts by the Company's Command, Control, Communications,
Computer Intelligence Operation (C4IO), the Advanced Systems and Technology
Operation (ASTO), and the Defense Programs Operation (DPO). The Company had one
major competitive loss during the quarter by its Technical Services Operation
(TSO). It was a bid to the Air Force Research Laboratory at Edwards Air force
Base for the Rocket Propulsion Services Program. It was a $30,000,000 program
over five years.

In summary, the Company's funded backlog at the end of the third quarter was
$33,000,000 as compared to $37,500,000 for the same period last year. Annualized
contract backlog increased 12.9% in the first three quarters from the backlog
starting the year. Backlog went from $93,200,000 at the start of the year to
$105,000,000 at the end of the third quarter. The Company plans to submit many
proposals in the next two quarters as the opportunity backlog is still very
strong.

LIQUIDITY AND CAPITAL RESOURCES

The Company's primary sources of liquidity are funds provided by operations and
the bank line of credit. The Company's line of credit limit is $12,000,000.
Borrowings under the line of credit at September 30, 1998 were zero. Days sales
outstanding decreased to 75 days at September 30, 1998, from 80 days at June 30,
1998, and from 83 days at September 30, 1997. The Company continues to actively
monitor receivables with emphasis placed on collection activities. The Company's
debt-to-equity ratio, as defined by the bank, was 0.4 at September 30, 1998
versus 0.8 at December 31, 1997 and 0.7 at September 30, 1997. All capital
expenditures were financed through operating funds and the revolving line of
credit. The Company's cash flow from operations plus borrowing under its line of
credit are expected to provide sufficient funds for the Company's operations,
common stock repurchases, capital expenditures, and future long-term debt
requirements.

STOCKHOLDER EQUITY

The Company increased stockholder's equity from $12,452,000 at the end of 1997
to $16,001,000 at September 30, 1998. The Company's strong earnings and net
proceeds from the sale and repurchase of stock have accounted for this increase.
The Company is now repurchasing all the stock from terminating employees and
intends to continue to do so for the foreseeable future.

STOCK PURCHASE AGREEMENT

In November, 1994, the Company entered into a Stock Purchase Agreement (the
"Agreement") with Science Applications International Corporation ("SAIC"), under
which SAIC was obligated to buy, during the first year of the Agreement, shares
of the Company's Preferred Stock with an aggregate price of $1,200,000. Under
the Agreement, SAIC also has the option, but not the obligation, to buy
additional shares of Preferred Stock, provided that SAIC's total purchases
during any quarter may not exceed $600,000 and provided further, that the total
number of shares of Preferred Stock purchases during any quarter may not exceed
the total number of shares of Common Stock offered to the Company for repurchase
by the Company's existing stockholders. The purchase price for all shares
purchased under the Agreement by SAIC is equal to the then current Formula Price
applicable to the Company's Common Stock. The Agreement grants SAIC the option
to require the Company to repurchase all of the Preferred Stock held by SAIC at
the Formula Price at time of option exercise. In the event the option is
exercised, the Company may issue SAIC a subordinated note bearing an interest
rate equal to the lesser of prime or 10%. SAIC suspended its purchase of Company
preferred stock in the last quarter of 1996 and has not purchased any stock
since. The total purchase as of September 30, 1998 of $2,400,000 (569,039
shares) of Company Preferred Stock represents 9.10% of the Company's total
outstanding stock. Through September 30, 1998 accretion of Preferred Stock was
$2,204,000.


<PAGE>   9

EFFECTS OF FEDERAL FUNDING FOR DEFENSE PROGRAMS

The Company continues to have over 90% of its contracts with the Department of
Defense. The Company anticipates little or no effect on its anticipated sales
for 1998 as a result of the outcome of the November, 1998 federal elections for
the Senate and House of Representatives. However, sales in its government
business areas for 1999 and subsequent years could be impacted by this election
and the yet to be resolved federal budget for Government Fiscal Year 1999.




<PAGE>   10



PART II   OTHER INFORMATION

ITEM 1    LEGAL PROCEEDINGS

The Company has no investigations, claims, and lawsuits arising out of its
business, nor any known to be pending.

ITEM 2    CHANGES IN SECURITIES

Not Applicable

ITEM 3    DEFAULTS UPON SENIOR SECURITIES

Not Applicable

ITEM 4    SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

The Company's Annual Meeting will be held on May 1, 1998 at which time proxies
and shareholders present voted on and approved the 1997 Stock Plan, the Amended
and Restated Certificate of Incorporation, the Directors and the continuation of
Price Waterhouse as auditor.

ITEM 5    OTHER MATERIALLY IMPORTANT EVENTS

Not Applicable

ITEM 6    EXHIBITS AND REPORTS ON FORM 8-K

No report(s) on Form 8-K were filed by the Company during the fiscal quarter for
which this report is filed.

          (a) Exhibits

          Exhibit No.         Exhibit
          -----------         -------

             11               Statement re: Computation of Per Share Earnings

             27               Financial Data Schedule


<PAGE>   11


                                    SIGNATURE


Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



                                                   SPARTA, INC.


                                                   /s/ B. Warren Knudson
                                                   -----------------------------
Date:   AUGUST 19, 1998                            B. Warren Knudson
                                                   Vice President and Chief
                                                   Financial Officer
                                                   (Principal Finance and
                                                   Accounting Officer)



<PAGE>   12


                                  EXHIBIT INDEX

                                  SPARTA, INC.

                        QUARTER ENDED SEPTEMBER 30, 1998




Exhibit                                                              Sequential
  No.             Description of Exhibits                             Page No.
-------           -----------------------                            ----------

   11             Statement re:  Computation of Per Share Earnings

   27             Financial Data Schedule