<PAGE>   1

                       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        March 31, 1999
                                   ---------------------------

                                       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 April 4, 1999, the registrant had 5,808,222 shares of common stock, $.01
par value per share, issued and outstanding.


<PAGE>   2

                                  SPARTA, Inc.

              QUARTERLY REPORT FOR THE PERIOD ENDED MARCH 31, 1999

                                      INDEX


PART I      FINANCIAL STATEMENTS

ITEM 1      Quarterly Financial Statements

            Statements of Income for the Three Months Ended March 31, 1999 and
            March 31, 1998 (Unaudited)

            Balance Sheets as of March 31, 1999 and December 31, 1998
            (Unaudited)

            Statement of Cash Flows for the Three Months Ended March 31, 1999
            and March 31, 1998 (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


<PAGE>   4

                        CONSOLIDATED STATEMENT OF INCOME
                                   (UNAUDITED)

ITEM 1. FINANCIAL STATEMENTS

<TABLE>
<CAPTION>
                                                 Three Months ended March
                                               -----------------------------
                                                  1999              1998
                                               -----------       -----------
<S>                                            <C>               <C>        
Sales                                          $25,518,000       $22,944,000
                                               -----------       -----------
Costs and expenses:

  Labor costs and related benefits              15,008,000        12,441,000

  Subcontractor & other costs                    5,788,000         5,865,000

  Facility costs                                 1,827,000         1,813,000

  Travel and other                                 399,000           640,000

  Interest expense, net                             84,000            82,000
                                               -----------       -----------
                                                23,106,000        20,839,000
                                               -----------       -----------
Income before provision
  taxes on income                                2,412,000         2,103,000

Provision for taxes on                             965,000           883,000
                                               -----------       -----------
Net income                                     $ 1,447,000       $ 1,220,000
                                               ===========       ===========
Basic earnings per share                       $      0.20       $      0.14
                                               ===========       ===========
Diluted earnings per share                     $      0.19       $      0.13
                                               ===========       ===========
</TABLE>

     The accompanying notes are an integral part of the financial statements
<PAGE>   5

                         CONSOLIDATED BALANCE STATEMENT
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                       March 31,          December 31,
                                                                          1999                1998
                                                                      ------------        ------------
                                                                      (Unaudited)           (Audited)
<S>                                                                   <C>                 <C>         
ASSETS

Current Assets
  Cash                                                                $    314,000        $    174,000
  Accounts receivable                                                   23,673,000          25,108,000
  Prepaid expenses                                                         688,000             548,000
  Income Taxes receivable                                                       --             556,000
                                                                      ------------        ------------
    Total current assets                                                24,675,000          26,386,000

  Equipment and improvements, net                                        9,879,000           9,634,000
  Other assets                                                           1,919,000           1,750,000
                                                                      ------------        ------------
    Total Assets                                                      $ 36,473,000        $ 37,770,000
                                                                      ============        ============

LIABILITIES AND STOCKHOLDERS' EQUITY
Current Liabilities
  Accrued compensation                                                $  3,760,000        $  5,820,000
  Accounts payable and other accrued expenses                            2,329,000           5,525,000
  Current portion of notes payable                                         403,000             474,000
  Deferred income taxes                                                  3,109,000           2,737,000
                                                                      ------------        ------------
    Total current liabilities                                            9,601,000          14,556,000

Notes payable                                                            2,836,000           1,266,000
Subordinated notes payable                                                 486,000             359,000
Deferred income taxes                                                      261,000             544,000
Redeemable Preferred Stock
  Preferred stock, $.01 par value; 2,000,000 shares authorized;
  569,039 and 569,039 shares issued and outstanding                      5,525,000           5,207,000
Stockholders' equity
  Common stock, $.01 par value, 25,000,000 shares authorized;
  14,230,405 and 13,886,286 shares issued                                  142,000             139,000
  Additional paid-in capital                                            34,481,000          32,077,000
  Retained earnings                                                     29,705,000          28,576,000
  Treasury stock                                                       (46,564,000)        (44,954,000)
                                                                      ------------        ------------
    Total stockholders' equity                                          17,764,000          15,838,000
                                                                      ------------        ------------

Total Liabilities and Stockholders' Equity                            $ 36,473,000        $ 37,770,000
                                                                      ============        ============
</TABLE>

    The accompanying notes are an integral part of the financial statements

<PAGE>   6

                      CONSOLIDATED STATEMENT OF CASH FLOWS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                     Three Months ended March 31
                                                                    ------------------------------
                                                                        1999               1998
                                                                    -----------        -----------
<S>                                                                 <C>                <C>        
Cash flows from operating activities:
  Net Income                                                        $ 1,447,000        $ 1,220,000
  Adjustments to reconcile net income to net
    cash provided by operating activities:
      Depreciation and amortization                                     406,000            370,000
      Loss on sale of equipment                                              --              1,000
      Employee compensation paid in stock                             1,405,000          1,467,000
      Changes in assets and liabilities:
        Accounts receivable                                           1,435,000           (470,000)
        Prepaid expenses                                               (140,000)          (221,000)
        Other assets                                                   (173,000)           141,000
        Accrued compensation                                         (2,060,000)        (3,091,000)
        Accounts payable and other accrued expense                   (3,196,000)        (1,690,000)
        Income taxes payable/receivable                                 928,000            821,000
        Deferred income taxes                                          (281,000)          (283,000)
      Tax benefit relating to stock plan                                289,000            115,000
                                                                    -----------        -----------
          Net cash provided by (used in) operating activities            60,000         (1,620,000)
                                                                    -----------        -----------
Cash flows from investing activities:
    Capital expenditures                                               (650,000)          (825,000)
                                                                    -----------        -----------
          Net cash used in investing activities                        (650,000)          (825,000)
                                                                    -----------        -----------
Cash flows from financing activities:
  Proceeds from issuance of stock                                       713,000            620,000
  Cash purchases of treasury stock                                   (1,411,000)          (425,000)
  Net proceeds from line-of-credit agreement                          1,570,000          2,685,000
  Principal payments on debt                                           (142,000)          (548,000)
                                                                    -----------        -----------
          Net cash provided by financing activities                     730,000          2,332,000
                                                                    -----------        -----------
Net increase (decrease) in cash                                         140,000           (112,000)
Cash and cash equivalents at beginning of period                        174,000            198,000
                                                                    -----------        -----------
Cash and cash equivalents at end of period                          $   314,000        $    86,000
                                                                    ===========        ===========
Supplemental disclosures of cash flow information:
Cash paid during the period for:
    Interest                                                        $    93,000        $    83,000
                                                                    ===========        ===========
    Income taxes                                                    $    30,000        $ 1,251,000
                                                                    ===========        ===========
</TABLE>

    The accompanying notes are an integral part of the financial statements

<PAGE>   7

                                  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 3, 1999;
and, its first quarter ended April 4, 1999 and corresponding first quarter last
year on April 5, 1998. To aid the reader of the financial statements, the
year-end has been presented as December 31, 1998 and the quarters and three
months ended March 31, 1999 and March 31, 1998.

In the opinion of management, the unaudited financial information for the
three-month periods ended March 31, 1999 and March 31, 1998 reflects all
adjustments (which include only normal, recurring adjustments) necessary for a
fair presentation thereof.

NOTE B - RECEIVABLES

Unbilled accounts receivable include $2,256,000 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 March 31, 1999.

NOTE C - INCOME TAXES

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



<PAGE>   8

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, 1998, 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 March 31
                                   ----------------------------
                                      1999              1998
                                   ----------        ----------
<S>                                <C>               <C>       
Sales                              25,518,000        22,944,000
Gross profit (1)                    2,270,000         2,219,000
Gross profit as a % of costs             9.76%            10.71%
Net income (2)                      1,447,000         1,220,000
Number of staff                           716               647
</TABLE>

<TABLE>
<CAPTION>
                                                            Balance at
                                          -----------------------------------------------
                                           March 31         December 31         March 31
                                              1999              1998              1998
                                          -----------       ------------       ----------
<S>                                       <C>               <C>               <C>       
Funded 12 month backlog                    47,600,000        37,600,000        38,400,000
Total 12 month contract backlog           115,200,000       104,700,000        88,200,000
Stockholders equity                        17,764,000        15,838,000        14,589,000
Equity per share (3)                             2.79              2.36              2.35
Stock repurchase notes                        889,000           833,000           986,000
Line of credit                              2,836,000         1,266,000         5,343,000
Number in days sales in receivables                88                82                97
Current ratio                                     3.0               2.1               3.0
</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 first quarter were up 11.2% from the
corresponding three-month period in 1998. Gross profit for the three-month
period ended March 31, 1999 was up 2.3% when compared to the corresponding
period of 1998. Gross profit as a percent of costs decreased from 10.71% to
9.76% for the corresponding period in 1998. Despite the slight decrease in
profitability, current profit rates remain at historical levels.

NEW CONTRACTS AND ANNUALIZED BACKLOG

The Company had one major competitive win during the first quarter, a Navy
Surface Weapons Center contract won by its Advanced Systems and Technology
["AST"] Operation as a subcontractor to EG&G. The Company's share is expected to



<PAGE>   9

be as much as $7,000,000 over five years. The Company's Electro-optic Systems
Division also signed a sole source three-year $4,200,000 contract with ASM
Lithography ["ASML"] in early April for nanAlign(TM) development and future
integration into ASML's next generation stepper. The Company experienced three
major competitive losses. One was the JTAMDO SETA contract, a $30,000,000 five
year prime bid by AST Operation and two $5,000,000 seven year bids by Technical
Services Operation as subcontractor for the ITOP-2 procurement.

Annualized contract backlog increased 10.0% in the first quarter over backlog at
the beginning of the year. Backlog went from $104,700,000 to $115,200,000 at the
end of the first 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 against the Company's line of credit totaled $2,836,000 as of the end
of the 1st quarter compared to a borrowing level of $5,343,000 at the end of the
corresponding period in 1998. The reduction in borrowings is largely due to the
Company's concerted effort to control expenditures for independent research and
development as well as a planned reduction of investment in product initiatives.
Days sales outstanding increased to 88 days at March 31, 1999 from 82 days at
December 31, 1998. In comparison with the corresponding period of 1998, however,
the days sales outstanding has experienced a significant decrease dropping 9
days from the 97 days reported at March 31, 1998. 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 0.5 at March 31,
1999 versus 0.5 at December 31, 1998 and 0.7 at March 31, 1998. 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 $15,838,000 at the end of 1998
to $17,764,000 at March 31, 1999. 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 March 31, 1999 of $2,400,000 (569,039 shares) of
Company Preferred Stock represents 8.92% of the Company's total outstanding
stock. Through March 31, 1999 accretion of Preferred Stock was $3,125,000. It is
the Company's intent, with which SAIC has agreed, to begin quarterly purchases
of stock held by SAIC starting with the May 21, 1999 Stock Repurchase Date,
using funds as available within the stock repurchase limitation.

EFFECTS OF FEDERAL FUNDING FOR DEFENSE PROGRAMS

The Company continues to have approximately 90% of its contracts with the
Department of Defense. The Company's government contracts may be terminated, in
whole or in part, at the convenience of the customer (as well as in the event of
default). In the event of a termination for convenience, the customer is
generally obligated to pay the costs incurred by the


<PAGE>   10

Company under the contract plus a fee based upon work completed. There were no
contracts terminated in the first quarter of 1999. The Company does not
anticipate any termination of programs and contracts in 1999. However, no
assurances can be given that such events will not occur.

In addition to the right of the U.S. government to terminate contracts for
convenience, U.S. government contracts are conditioned upon the continuing
availability of congressional appropriations. These appropriations are subject
to unforseen changes in the allocation of the overall Department of Defense
budget. Funding in support of the current conflict in Kosovo could impact
Company contracts which have only received partial funding.

YEAR2000

The statements in the following section constitute "YEAR2000 Readiness
Disclosure" within the meaning of the YEAR2000 Information and Readiness
Disclosure Act.

YEAR2000 Plan

In 1997, the Company informally initiated a program on its internal web site to
prepare computing infrastructure for year 2000 ("YEAR2000") readiness. In 1998,
the Company initiated a more formal program to complete the preparation and to
perform testing of the Company's computing systems and microchip dependent
infrastructure. In addition to computing and microchip technology, the
evaluation of potential business disruptions relating to vendors, suppliers,
facilities, customers, and utilities is also a part of this program. The Company
has appointed a senior information systems engineer as Corporate Information
Systems Director ("CISD"). Included in the CISD's assignment is the
responsibility for corporate YEAR2000 readiness. The Company's Network Steering
Group ("NSG"), an on-going organization of the Company's top information system
personnel, will support the CISD in YEAR2000 issues. The CISD reports directly
to the Executive Committee and will periodically brief the Audit Committee of
the Board of Directors on YEAR2000 progress. The last briefing to the Executive
and Audit Committees was in May 1999.

The Company's YEAR2000 Plan has been documented in its latest Form 10K for 1998.
The CISD established a four-phase program, as shown in the accompanying chart
and in Form 10K, to ensure that the Company's IT systems will be ready for
YEAR2000.

<TABLE>
<CAPTION>
===============================================================================================
                          7/1/98 TO   10/1/98 TO  1/1/99 TO   4/1/99 TO  7/1/99 TO   10/1/99 TO
IT REMEDIATION             9/30/98    12/31/98     3/31/99     6/30/99    9/30/99    12/31/99
-------------------------- ----------- ---------- ----------- ---------- ----------- ----------
<S>                       <C>         <C>        <C>         <C>        <C>         <C>
PI - Increasing Awareness               --------------

PII - Developing and                       --------------------------
Assessing

PIII - Remediation                                      ----------------------------------

PIV - Testing                                         ------------------------------------

NON-IT REMEDIATION

Evaluation of Embedded
Chip Systems                               ----------------------

Remediation and Test of                             ----------------------
Embedded Systems

Contingency Planning                                   --------------------------------------
===============================================================================================
</TABLE>

The darkened portions of the schedule bars note changes to the original
schedule, based on effort accomplished in the first quarter. The Remediation and
Testing efforts have been extended through November and are driven by the
implementation of a new Human Resources ("HR") system. The Company's current HR
system is a commercial system whose developer has not been responsive to the
need to become Y2K compliant. Therefore, the Company has assumed that the HR
system will not be useable after Jan. 1, 2000 and is in the process of
implementing a new system. Current plans support getting the new system on line
prior to the end of the year. However, the Company is developing a contingency
plan to support an on line time in the first quarter of 2000. Other contingency
planning, in progress, will result in the identification of additional typical
and worst case scenarios in the May time period.


<PAGE>   11

The evaluation of embedded chip systems has been extended owing primarily to
late responses from some of the lessors of Company facilities. All of the
embedded chip systems within the Company have been identified and evaluated and
remediation requirements identified.

As of this date, it is management's opinion that the Company will meet its plan
to be YEAR2000 ready for all of its critical Information Technology systems and
have adequate contingency plans in place to handle possible YEAR2000
perturbations.

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 21, 1999 at which time proxies
and shareholders present will vote on the Directors and the continuation of
PricewaterhouseCoopers as the Company's independent accountant to examine the
consolidated financial statements for the year ending January 2, 2000.

ITEM 5         OTHER MATERIALLY IMPORTANT EVENTS

               Not Applicable

ITEM 6         EXHIBITS AND REPORTS ON FORM 8-K

               Exhibit 11 --  Statement re: Computation of Per Share Earnings

               Exhibit 27 --  Financial Data Schedule

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


<PAGE>   12

                                    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.


Date: May 18, 1999                           /s/ B. Warren Knudson
                                             -----------------------------------
                                             B. Warren Knudson
                                             Vice President and Chief
                                             Financial Officer
                                             (Principal Finance and
                                             Accounting Officer)



<PAGE>   13

                                  EXHIBIT INDEX

                                  SPARTA, INC.

                          QUARTER ENDED MARCH 31, 1999

<TABLE>
<CAPTION>

Exhibit                                                                   Sequential
  No.             Description of Exhibits                                  Page No.
-------           -----------------------                                 ----------
<S>               <C>                                                     <C>
   11             Statement re: Computation of Per Share Earnings

   27             Financial Data Schedule
</TABLE>